Firstly, there has been overall a pretty remarkable downward trend in application volume. This drop in number of applications has put a dent on revenues for schools as well as in the overall quality of the application pool. It makes sense: fewer applicants generally will mean fewer top applicants (not always true, but in this case, the percentage of good, better and best applicants seems to hold pretty constant no matter how many applicants there are in total). Neither result is attractive to these top schools.

One way to combat the drop in application volume is to try and reach outside the normal circles for folks who might think of applying to b-school who perhaps would not have in the past. Accepting the GRE instead of the GMAT is one way top schools have broadened their search. Because the GRE is widely considered a more “accessible” test for the general graduate school population, it has never in the past been given serious consideration by the b-schools, who are in agreement that the GMAT is a better indicator of b-school success. Granted, the GRE does not have a large enough statistical base to test its predictability for b-school success yet, but old traditions die hard.

Enter Harvard, Stanford and Wharton, the first and last bastion of high quality business school reputations. Certainly if you are Harvard, Stanford or Wharton, your reputation will not be dampened using any test for admission (even “guess how many fingers I am holding up behind my back?”) — the point is, no matter what these super elite schools do, their rankings will likely not suffer. So, they started accepting GRE scores in lieu of GMATs. This did indeed give them a broader look at those interested in graduate school and has enticed more students to choose b-school as their graduate education path. As could probably have been predicted, so goes H/S/W, so goes the rest of the b-school world, and sure enough, over the past several years, more and more schools have been quietly accepting GRE scores.

So which test should you use as part of your application package? If your target school accepts the GRE, should you use that instead of the (some argue more difficult) GMAT? This is indeed the question. In some respects, the GRE is a tempting alternative. For starters, it’s about $100 cheaper to take the test, which for some post-college, recession-damaged applicants, is real money. Additionally, the test is not quite as rigorous on the quantitative side, making it for some, a less punishing preparation process.

There is also the argument that it could help you stand out in the crowd, since with fewer applicants submitting GRE scores, you force yourself out of the general application pool and into a category which will require the admissions committee to consider you separately from the crowd. Is this true? The Admissions Director I spoke with said it makes no difference whether someone submits the GMAT or the GRE, but I argued that simply due to the new nature of the discussion, there will naturally be more attention drawn to applicants with GREs.

This could be simply a psychological phenomenon, and of course the risk is that the lack of reliable data out there with which to compare scores could put applicants in a no-man’s land without any real evidence of aptitude. At least with the GMAT, the scores are very well established and everyone knows what a 550 means vs. a 650 or 750. As more GRE scores show up in admissions committee evaluations, we will begin to establish some better standards for exactly what a good score is as compared to the GMAT, but as for now, it’s really anybody’s guess what that score should be.

The other challenge for b-schools who are now accepting the GRE is what to do with the scores when the time comes to tally statistics for rankings. The GMAC as well as the BW and US News rankings boards have indicated that schools need only list whether or not they accept the GRE, and are presently not required to report their average scores (which in the case of some schools, could be the average of as few as one or two applicants’ scores).

Again, as more data comes online, we may start seeing a dual category, with schools listing both their GMAT average and their GRE average. I wouldn’t bet on this, however. The same b-school traditions and history which established the GMAT in the first place will be hard to sway in another direction. The computer adaptability of the GMAT test and other technological advances it has made vs. the GRE is keeping it in a position of superiority for now.

In the final analysis, I would say that if the GMAT is kicking your tail, you might at least try your hand at the GRE, just to see if perhaps the test better meets with your abilities. If your target schools accept the GRE for admission and your score on the GRE is impressive, who knows? You might just be able to “slip in through the back door” while other applicants who are relying on mediocre GMAT scores get lost in the proverbial shuffle.

Applying to business school? Call us at 1-800-925-7737 and speak with an MBA admissions expert today, or click here to take our Free MBA Admissions Profile Evaluation! As always, be sure to find us on Facebook and Google+, and follow us on Twitter.

*Bryant Michaels has over 25 years of professional post undergraduate experience in the entertainment industry as well as on Wall Street with Goldman Sachs. He served on the admissions committee at the Fuqua School of Business where he received his MBA and now works part time in retirement for a top tier business school. He has been consulting with Veritas Prep clients for the past six admissions seasons. See more of his articles here.*

Writing Factors of an Ugly Number

Today let’s discuss the concept of ‘product of the factors of a number’.

From the two posts above, we know that the factors equidistant from the centre multiply to give the number. We also know that the behaviour is a little different for perfect squares. Let’s take two examples to understand this.

Example 1: Say N = 6

Factors of 6 are 1, 2, 3, 6

1*6 = 6 (first factor * last factor)

2*3 = 6 (second factor and second last factor)

Product of the four factors of 6 is given by 1*6 * 2*3 = 6*6 = 6^2 = [Sqrt(N)]^4

Example 2: Say N = 25 (a perfect square)

Factors of 25 are 1, 5, 25

1*25 = 25 (first factor * last factor)

5*5 = 25 (middle factor multiplied by itself)

Product of the three factors of 25 is given by 1*25 * 5 = 5^3 = [Sqrt(N)]^3

If a number, N, can be expressed as: 2^a * 3^b * 5^c *…

The total number of factors f = (a+1)*(b+1)*(c+1)…

**The product of all factors of N is given by [Sqrt(N)]^f i.e. N^(f/2)**

Let’s look at a couple of questions based on this principle:

Question 1: If the product of all the factors of a positive integer, N, is

2^(18) * 3^(12), how many values can N take?

(A) None

(B) 1

(C) 2

(D) 3

(E) 4

Solution: Since the product of all factors of N has only 2 and 3 as prime factors, N must have two prime factors only: 2 and 3.

Let N = 2^a * 3^b

Given that N^(f/2) = 2^(18) * 3^(12)

(2^a * 3^b)^[(a+1)(b+1)/2] = 2^(18) * 3^(12)

a*(a+1)*(b+1)/2 = 18

b*(a+1)*(b+1)/2 = 12

Dividing the two equations, we get a/b = 3/2

Smallest values: a = 3, b = 2. It satisfies our two equations.

Can we have more values for a and b? Can a = 6 and b = 4? No. Then the product a*(a+1)*(b+1)/2 would be much larger than 18.

So N = 2^3 * 3^2

There is only one such value of N.

Answer (B)

Question 2: If the product of all the factors of a positive integer, N, is 2^9 * 3^9, how many values can N take?

(A) None

(B) 1

(C) 2

(D) 3

(E) 4

Solution: Since the product of all factors of N has only 2 and 3 as prime factors, N must have two prime factors only: 2 and 3.

Let N = 2^a * 3^b

Given that N^(f/2) = 2^(9) * 3^(9)

(2^a * 3^b)^[(a+1)(b+1)/2] = 2^(9) * 3^(9)

a*(a+1)*(b+1)/2 = 9

b*(a+1)*(b+1)/2 = 9

Dividing the two equations, we get a/b = 1/1

Smallest values: a = 1, b = 1 – Does not satisfy our equation

Next set of values: a = 2, b = 2 – Satisfies our equations

All larger values will not satisfy our equations.

Answer (B)

Note that we can easily use hit and trial in these questions without actually working through the equations.

This is how we will do it:

N^(f/2) = 2^(18) * 3^(12)

Case 1: Assume values of f/2 from common factors of 18 and 12 – say 2

[2^9 * 3^6]^2

Can f/2 = 2 i.e. can f = 4?

If N = 2^9 * 3^6, total number of factors f = (9+1)*(6+1) = 70

This doesn’t work.

Case 2: Assume f/2 is 6

[2^3 * 3^2]^6

Can f/2 = 6 i.e. can f = 12?

If N = 2^3 * 3^2, total number of factors f = (3+1)*(2+1) = 12

This works.

The reason hit and trial isn’t a bad idea is that there will be only one such set of values. If we can quickly find it, we are done.

Why should we then bother to find it at all. Shouldn’t we just answer with option ‘B’ in both cases? Think of a case in which the product of all factors is given as 2^(16) * 3^(14). Will there be any value of N in such a case?

*Getting ready to take the GMAT? We have free online GMAT seminars running all the time. And, be sure tofind us on Facebook and Google+, and follow us on Twitter!*

*Karishma, a Computer Engineer with a keen interest in alternative Mathematical approaches, has mentored students in the continents of Asia, Europe and North America. She teaches the **GMAT** for Veritas Prep and regularly participates in content development projects such as this blog!*

Small numbers on your noteboard.

Have you found yourself on a homework problem or practice test asking yourself “can I just multiply these?”? Have you forgotten a rule and wondered whether you could trust your memory? Small numbers can be hugely valuable in these situations. Consider this example:

For integers x and y, 2^x + 2^y = 2^30. What is the sum x + y?

(A) 30

(B) 40

(C) 50

(D) 58

(E) 64

Every fiber of your being might be saying “can I just add x + y and set that equal to 30?” but you’re probably at least unsure whether you can do that. How do you definitively tell whether you can do that? Test the relationship with small numbers. 2^30 is far too big a number to fathom, but 2^6 is much more convenient. That’s 64, and if you wanted to set the problem up that way:

2^x + 2^y = 2^6

You can see that using combinations of x and y that add to 6 won’t work. 2^3 + 2^3 is 8 + 8 = 16 (so not 64). 2^5 + 2^1 is 32 + 2 = 34, which doesn’t work either. 2^4 + 2^2 is 16 + 4 = 20, so that doesn’t work. And 2^0 + 2^6 is 1 + 64 = 65, which is closer but still doesn’t work. Using small numbers you can prove that that step you’re wondering about – just adding the exponents – isn’t valid math, so you can avoid doing it. **Small numbers help you test a rule that you aren’t sure about!**

That’s one of two major themes with testing small numbers. 1) Small numbers are great for testing rules. And 2) Small numbers are great for finding patterns that you can apply to bigger numbers. To demonstrate that second point about small numbers, let’s return to the problem. 2^30 again is a number that’s too big to deal with or “play with,” but 2^6 is substantially more manageable. If you want to get to:

2^x + 2^y = 2^6, think about the powers of 2 that are less than 2^6:

2^1 = 2

2^2 = 4

2^3 = 8

2^4 = 16

2^5 = 32

2^6 = 64

Here you can just choose numbers from the list. The only two that you can use to sum to 64 are 32 and 32. So the pairing that works here is 2^5 + 2^5 = 2^6. Try that again with another number (what about getting 2^x + 2^y = 2^5? Add 16 + 16 = 32, so 2^4 + 2^4), and you should start to see the pattern. To get 2^x + 2^y to equal 2^z, x and y should each be one integer less than z. So to get back to the bigger numbers in the problem, you should now see that to get 2^x + 2^y to equal 2^30, you need 2^29 + 2^29 = 2^30. So x + y = 29 + 29 = 58, answer choice D.

The lesson? When problems deal with unfathomably large numbers, it can often be quite helpful to test the relationship using small numbers. That way you can see how the pieces of the puzzle relate to each other, and then apply that knowledge to the larger numbers in the problem. The GMAT thrives on abstraction, presenting you with lots of variables and large numbers (often exponents or factorials), but you can counter that abstraction by using small numbers to make relationships and concepts concrete.

So make sure that small numbers are a part of your toolkit. When you’re unsure about a rule, test it with small numbers; if small numbers don’t spit out the result you’re looking for, then that rule isn’t true. But if multiple sets of small numbers do produce the desired result, you can proceed confidently with that rule. And when you’re presented with a relationship between massive numbers and variables, test that relationship using small numbers so that you can teach yourself more concretely what the concept looks like.

The best way to make sure that your GMAT score report contains big numbers? Use lots of small numbers in your scratchwork.

*Getting ready to take the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!*

*By Brian Galvin*

But self-inflicted misery loves company, so in no particular order, let’s take a look at some of the things that suck and more importantly, how to cope:

**Integrated Reasoning (IR) :**It was introduced a few years ago, and even though multiple surveys and studies show it does correlate well with skills needed to succeed in business and the corporate world, schools still seem to have varying opinions on its value and how best to use it in the admissions process. For now, think of IR as the appetizer or warm-up. It’s tough, but it’s 30 minutes and can serve as a solid warmup before tackling the tougher ‘main course’ of quant and verbal. You wouldn’t start sprinting out of the gates in a race; treat the GMAT the same way, and if you bank some early points, that can’t hurt either.

**AWA:**Similar to IR, it doesn’t factor into your Total score, and schools differ on how they evaluate the essay. That being said, consider it a pre-pre-warm up, and more importantly, remember that schools can download a copy of your essay when they view your scores. So it’s important to put forth your best effort (now is NOT the time to challenge authority and write what you truly think of the GMAT or B school admissions process) and treat it as another writing sample that schools can use to evaluate your brilliance and creativity under pressure. Also, if English isn’t your first language, it’s absolutely going to be leveraged as an additional writing sample.

**Data Sufficiency:**This isn’t math, at least not in the sense that you’re used to seeing. What happened to the two trains leaving from separate stations and determining where they’ll meet? While that’s more problem solving, data sufficiency is important for schools to gauge your decision making abilities when you have limited or inaccurate information In a perfect world, you could make informed decisions with an infinite amount of time and all of the necessary details. But the world isn’t ideal, and like the cliché says, time is money. So data sufficiency quantifies what schools want to see: can you discern at what point do you have enough information to make an informed decision or at what point do you not have enough information and need to walk away.

**Getting up early/Staying up late/Giving up Happy Hour aka Time Suck:**We’ve all heard of FOMO, or “fear of missing out.” You’re likely going to have to make FOMO your new BFF while you’re preparing. In order to get the score you want, it’s important to put forth the effort. Just like training for a marathon or triathlon, you can’t take shortcuts or it’ll show on race day, and only you truly know the full measure of the effort you’re putting forth. So before you even start studying, make sure you’re mapping out a 3-4 month window where you know you can truly carve out time on a daily (regular!) basis to prepare, and more importantly, dedicate quality time to preparation.

**Expenses!:**The GMAT is expensive! And so is preparation! But if you think about it compared to the investment you’re about to make in your future and your long-term earnings potential, $250 for the test, $20 in bus fare/gas/transportation, and $50 for a celebratory steak after you crush it is a drop in the bucket. In life, there are absolutely times you should clip coupons, look for a better value and skimp on the extras. This is not one of them. Consider the GMAT the first step in a much larger investment in yourself.

It’s not rocket science (if it was, that might be the MCAT, not the GMAT), but it is important to recognize and embrace the challenges of this process. If it was easy, there would be far more individuals taking the GMAT every year (though nearly 250,000 is some decently sized competition). And one day while you’re studying, you’ll realize that while you don’t necessarily love it, the “studying for the GMAT sucks” factor is not quite as strong as it once was. Take that as your reminder to keep your eye on the end game and keep plugging away. Your former self will thank you down the road.

Are you studying for the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

]]>But before we do that, we will first look at one fundamental principle of work, rate and time (which has a parallel in distance, speed and time).

Say, there is a straight long track with a red flag at one end. Mr A is standing on the track 100 feet away from the flag and Mr B is standing on the track at a distance 700 feet away from the flag. So they have a distance of 600 feet between them. They start walking towards each other. Where will they meet? Is it necessary that they will meet at 400 feet from the red flag – the mid point of the distance between them? Think about it – say Mr A walks very slowly and Mr B is super fast. Of the 600 feet between them, Mr A will cover very little distance and Mr B will cover most of the distance. So where they meet depends on their rate of walking. They will not necessarily meet at the mid point. When do they meet at the mid point? When their rate of walking is the same. When they both cover equal distance.

Now imagine that you have two pools of water. Pool A has 100 gallons of water in it and the Pool B has 700 gallons. Say, water is being pumped into pool A and water is being pumped out of pool B. When will the two pools have equal water level? Is it necessary that they both have to hit the 400 gallons mark to have equal amount of water? Again, it depends on the rate of work on the two pools. If water is being pumped into pool A very slowly but water is being pumped out of pool B very fast, at some point, they both might have 200 gallons of water in them. They will both have 400 gallons at the same time only when their rate of pumping is the same. This case is exactly like the case above.

Now let’s go on to the question from the GMAT Club tests which tests this understanding and the concept of relative rate of work:

**Question**: Tanks X and Y contain 500 and 200 gallons of water respectively. If water is being pumped out of tank X at a rate of K gallons per minute and water is being added to tank Y at a rate of M gallons per minute, how many hours will elapse before the two tanks contain equal amounts of water?

(A) 5/(M+K) hours

(B) 6/(*M*+*K*) hours

(C) 300/(M+K) hours

(D) 300/(M−K) hours

(E) 60/(M−K) hours

**Solution**: There are two tanks with different water levels. Note that the rate of pumping is given as K gallons per min and M gallons per min i.e. they are different. So we cannot say that they both will have equal amount of water when they have 350 gallons. They could very well have equal amount of water at 300 gallons or 400 gallons etc. So when one expects that water in both tanks will be at 350 gallon level, one is making a mistake. The two tanks are working for the same time to get their level equal but their rates are different. So the work done is different. Note here that equal level does not imply equal work done. The equal level could be achieved at 300 gallons when work done would be different – 200 gallons removed from tank X and 100 gallons added to tank Y. The equal level could be achieved at 400 gallons when work done would be different again – 100 gallons removed from tank X and 200 gallons added to tank Y.

To achieve the ‘equal level,’ tank Y needs to gain water and tank X needs to lose water. Total 300 gallons (500 gallons – 200 gallons) of work needs to be done. Which tank will do how much depends on their respective rates.

Work to be done together = 300 gallons

Relative rate of work = (K + M) gallons/minute

The rates get added because they are working in opposite directions – one is removing water and the other is adding water. So we get relative rate (which is same as relative speed) by adding the individual rates.

Note here that rate is given in gallons per minute. But the options have hours so we must convert the rate to gallons per hour.

Relative rate of work = (K + M) gallons/minute = (K + M) gallons/(1/60) hour = 60*(K + M) gallons/hour

Time taken to complete the work = 300/60(K+M) hours = 5/(K+M) hours

Answer (A)

*Karishma, a Computer Engineer with a keen interest in alternative Mathematical approaches, has mentored students in the continents of Asia, Europe and North America. She teaches the **GMAT** for Veritas Prep and regularly participates in content development projects such as this blog!*

But on the radio this morning – just like on your GMAT exam – there was no Eazy-E. Logistically that’s because – as the Bone Thugs & Harmony classic “Tha Crossroads” commemorated – Eazy passed away about 20 years ago. But in GMAT strategy form, Eazy’s absence speaks even louder than his vocals on his NWA and solo tracks. “No Eazy-E” should be a mantra at the top of your mind when you take the GMAT, because on Data Sufficiency questions, choice E – the statements together are not sufficient to solve the problem – will not be given to you all that easily (Data Sufficiency “E” answers, like the Boyz in the Hood, are always hard).

Think about what answer choice E really means: it means “this problem cannot be solved.” But all too often, examinees choose the “Eazy-E,” meaning they pick E when “I can’t do it.” And there’s a big chasm. “It cannot be solved” means you’ve exhausted the options and you’re maybe one piece of information (“I just can’t get rid of that variable”) or one exception to the rule (“but if x is a fraction between 0 and 1…”) that stands as an obstacle to directly answering the question. Very rarely on problems that are above average difficulty is the lack of sufficiency a wide gap, meaning that if E seems easy, you’re probably missing an application of the given information that would make one or both of the statements sufficient. The GMAT just doesn’t have an incentive to reward you for shrugging your shoulders and saying “I can’t do it;” it does, however, have an incentive to reward those people who can conclusively prove that seemingly insufficient information can actually be packaged to solve the problem (what looks like E is actually A, B, C, or D) and those people who can look at seemingly sufficient information and prove why it’s not actually quite enough to solve it (the “clever” E).

So as a general rule, you should always be skeptical of Eazy-E.

Consider this example:

A shelf contains only Eazy-E solo albums and NWA group albums, either on CD or on cassette tape. How many albums are on the shelf?

(1) 2/3 of the albums are on CD and 1/4 of the albums are Eazy-E solo albums.

(2) Fewer than 30 albums are NWA group albums and more than 10 albums are on cassette tape.

(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked

(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked

(C) Both statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient

(D) EACH statement ALONE is sufficient to answer the question asked

(E) Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed

Statistically on this problem (the live Veritas Prep practice test version uses hardcover and paperback books of fiction or nonfiction, but hey it’s Straight Outta Compton day so let’s get thematic!), almost 60% of all test-takers take the Eazy-E here, presuming that the wide ranges in statement 2 and the ratios in statement 1 won’t get the job done. But a more astute examinee is skeptical of Eazy-E and knows to put in work! Statement 1 actually tells you more than meets the eye, as it also tells you that:

- 1/3 of the albums are on cassette tape
- 3/4 of the albums are NWA albums
- The total number of albums must be a multiple of 12, because that number needs to be divisible by 3 and by 4 in order to create the fractions in statement 1

So when you then add statement 2, you know that since there are more than 10 albums total (because at least 11 are cassette alone) so the total number could be 12, 24, 36, 48, etc. And then when you apply the ratios you realize that since the number of NWA albums is less than 30 and that number is 3/4 of the total, the total must be less than 40. So only 12, 24, and 36 are possible. And since the number of cassettes has to be greater than 10, and equate to 1/3 of the total, the total must then be more than 30. So the only plausible number is 36, and the answer is, indeed, C.

Strategically, being wary of Eazy-E tells you where to invest your time. If E seems too easy, that means that you should spend the extra 30-45 seconds seeing if you can get started using the statements in a different way. So learn from hip hop’s first billionaire, Dr. Dre, who split with Eazy long ago and has since seen his business success soar. Avoid Eazy-E and as you drive home from the GMAT test center you can bask in the glow of those famous Ice Cube lyrics, “I gotta say, today was a good day.”

Getting ready to take the GMAT? We have free online GMAT seminars running all the time. And, be sure tofind us on Facebook and Google+, and follow us on Twitter!

*By Brian Galvin*

I didn’t make up that 1.3/3.2 calculation. It comes directly from an official question, and it’s quite clearly designed to elicit the panicked response it usually gets when I ask it in class. Here is the full question:

*The age of the Earth is approximately 1.3 * 10^17 seconds, and one year is approximately 3.2 * 10^7 seconds. Which of the following is closest to the age of the Earth in years?*

*5 * 10^9**1 * 10^9**9 * 10^10**5 * 10^11**1 * 10^11*

Most test-takers quickly see that in order to convert from seconds to years, we have to perform the following calculation: 1.3 * 10^17 seconds * 1 year/3.2 * 10^ 7 seconds or (1.3 * 10^17)/(3.2 * 10^ 7.)

It’s here when many test-takers freeze. So let’s estimate. We’ll round 1.3 down to 1, and we’ll round 3.2 down to 3. Now we’re calculating or (1* 10^17)/(3 * 10^ 7.) We can rewrite this expression as (1/3) * (10^17)/(10^7.) This becomes .333 * 10^10. If we borrow a 10 from 10^10, we’ll get 3.33 * 10^9. We know that this number is a little smaller than the correct answer, because we rounded the numerator down from 1.3 to 1, and this was a larger change than the adjustment we made to the denominator. If 3.33 * 10^9 is a little smaller than the correct answer, the answer must be B. (Similarly, if we were to estimate 13/3, we’d see that the number is a little bigger than 4.)

This strategy will work just as well on tough Data Sufficiency questions:

*If it took Carlos ½ hour to cycle from his house to the library yesterday, was the distance that he cycled greater than 6 miles? (1 mile = 5280 feet.)*

*The average speed at which Carlos cycled from his house to the library yesterday was greater than 16 feet per second.**The average speed at which Carlos cycled from his house to the library yesterday was less than 18 feet per second.*

The fact that we’re given the conversion from miles to feet is a dead-giveaway that we’ll need to do some unit conversions to solve this question. So we know that the time is ½ hour, or 30 minutes. We want to know if the distance is greater than 6 miles. We’ll call the rate ‘r.’ If we put this question into the form of Rate * Time = Distance, we can rephrase the question as:

*Is r * 30 minutes > 6 miles?*

We can simplify further to get: *Is r > 6 miles/30 minutes* or *Is r > 1 mile/5 minutes?*

A quick glance at the statements reveals that, ultimately, I want to convert into feet per second. I know that 1 mile is 5280 feet and that 5 minutes is 5 *60, or 300 seconds.

Now *Is r > 1 mile/5 minutes?* becomes *Is r > 5280 feet/ 300 seconds.* Divide both by 10 to get Is r > 528 feet/30 seconds. Now, let’s estimate. 528 is pretty close to 510. I know that 510/30 is the same as 51/3, or 17. Of course, I rounded down by 18 from 528 to 510, and 18/30 is about .5, so I’ll call the original question:

*Is r > 17.5 feet/second?*

If we get to this rephrase, the statements become a lot easier to test. Statement 1 tells me that Carlos cycled at a speed greater than 16 feet/second. Well, that could mean he went 16.1 feet/second, which would give me a NO to the original question, or he could have gone 30 feet/second, so I can get a YES to the original question. Not Sufficient.

Statement 2 tells me that his average speed was less than 18 feet/second. That could mean he went 17.9 feet/second, which would give me a YES. Or he could have gone 2 feet/second, which would give me a NO.

Together, I know he went faster than 16 feet/second and slower than 18 feet/second. So he could have gone 16.1 feet/second, which would give a NO, and he could have gone 17.9, which would give a YES, so even together, the statements are not sufficient, and the answer is E.

The takeaway: estimation isn’t simply a luxury on the GMAT; on certain questions, it’s a necessity. If you find yourself grinding through a host of ungainly arithmetical calculations, stop, and remind yourself that there has to be a better, more time-efficient approach.

*GMATPrep questions courtesy of the Graduate Management Admissions Council.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

*By David Goldstein, a Veritas Prep GMAT instructor based in Boston. You can find more articles by him here. *

Once you do, then the problem is quite easy.

**Question**: Technological improvements and reduced equipment costs have made converting solar energy directly into electricity far more cost-efficient in the last decade. However, the threshold of economic viability for solar power (that is, the price per barrel to which oil would have to rise in order for new solar power plants to be more economical than new oil-fired power plants) is unchanged at thirty-five dollars.

Which of the following, if true, does most to help explain why the increased cost-efficiency of solar power has not decreased its threshold of economic viability?

(A) The cost of oil has fallen dramatically.

(B) The reduction in the cost of solar-power equipment has occurred despite increased raw material costs for that equipment.

(C) Technological changes have increased the efficiency of oil-fired power plants.

(D) Most electricity is generated by coal-fired or nuclear, rather than oil-fired, power plants.

(E) When the price of oil increases, reserves of oil not previously worth exploiting become economically viable.

**Solution**: We really need to understand this $35 figure that is given. The argument calls it “the threshold of economic viability for solar plant.” It is further explained as price per barrel to which oil would have to rise in order for new solar power plants to be more economical than new oil-fired power plants.

Note the exact meaning of this “threshold of economic viability”. It is the price TO WHICH oil would have to rise to make solar power more economical i.e. the price to which oil would have to rise to make electricity generated out of oil power plants more expensive than electricity generated out of solar power plants. So this is a hypothetical price of oil. It is not the price BY WHICH oil would have to rise. So this number 35 has nothing to do with the actual price of oil right now – it could be $10 or $15. The threshold of economic viability will remain 35.

So what the argument tells us is that tech improvements have made solar power cheaper but the price to which oil should rise has stayed the same. If you are not sure where the paradox is, let’s take some numbers to understand:

Previous Situation:

– Sunlight is free. Infrastructure needed to convert it to electricity is expensive. Say for every one unit of electricity, you need to spend $50 in a solar power plant.

– Oil is expensive. Infrastructure needed to convert it to electricity, not so much. Say for every one unit of electricity, the oil needed costs $25 and cost of infrastructure to produce a unit of electricity is $15. So total you spend $40 for a unit of electricity in an oil fired plant.

Oil based electricity is cheaper. If the cost of oil rises by $10 and becomes $35 from $25 assumed above, solar power will become viable. Electricity produced from both sources will cost the same.

Again, note properly what the $35 implies.

Raw material cost in solar plant + Infrastructure cost in solar plant = Raw material cost in oil plant + Infrastructure cost in oil plant

0 + 50 = Hypothetical cost of oil + 15

Hypothetical cost of oil = 50 – 15

That is, this $35 = Infra price per unit in solar plant – Infra price per unit in oil plant

This threshold of economic viability for solar power is the hypothetical price per barrel to which oil would have to rise (mind you, this isn’t the actual price of oil) to make solar power viable.

What happens if you need to spend only $45 in a solar power plant for a unit of electricity? Now, for solar viability, ‘cost of oil + cost of infrastructure in oil power plant’ should be only $45. If ‘cost of infrastructure in oil power plant’ = 15, we need the oil to go up to $30 only. That will make solar power plants viable. So the threshold of economic viability will be expected to decrease.

Now here lies the paradox – The argument tells you that even though the cost of production in solar power plant has come down, the threshold of economic viability for solar power is still $35! It doesn’t decrease. How can this be possible? How can you resolve it?

One way of doing it is by saying that ‘Cost of infrastructure in oil power plant’ has also gone down by $5.

Raw material cost in solar plant + Infrastructure cost in solar plant = Raw material cost in oil plant + Infrastructure cost in oil plant

0 + $45 = $35 + Infrastructure cost in oil plant

Infrastructure cost in oil plant = $10

Current Situation:

– Sunlight is free. Infrastructure needed to convert it to electricity is expensive. For every one unit of electricity, you need to spend $45 in a solar power plant.

– Oil is expensive. Infrastructure needed to convert it to electricity, not so much. For every one unit of electricity, you need to spend $25 + $10 = $35 in an oil fired power plant.

You still need the oil price to go up to $35 so that cost of electricity generation in oil power plant is $45.

So you explained the paradox by saying that “Technological changes have increased the efficiency of oil-fired power plants.” i.e. price of infrastructure in oil power plant has also decreased.

Hence, option (C) is correct.

The other option which seems viable to many people is (A). But think about it, the actual price of the oil has nothing to do with ‘the threshold of economic viability for solar power’. This threshold is $35 so you need the oil to go up to $35. Whether the actual price of oil is $10 or $15 or $20, it doesn’t matter. It still needs to go up to $35 for solar viability. So option (A) is irrelevant.

We hope the paradox and its solution make sense.

*Karishma, a Computer Engineer with a keen interest in alternative Mathematical approaches, has mentored students in the continents of Asia, Europe and North America. She teaches the **GMAT** for Veritas Prep and regularly participates in content development projects such as this blog!*

Because if his interaction with a young, milk-drinking fan is any indication, Harbaugh understands one of the key secrets to success on the GMAT Quant section:

Harbaugh, who told HBO Real Sports this summer about his childhood plan to grow to over 6 feet tall – great height for a quarterback – by drinking as much milk as humanly possible – is a fan of all kinds of milk: chocolate, 2%… But as he tells the young man, the ideal situation for growing into a Michigan quarterback is drinking whole milk, just as the ideal way to attend the Ross School of Business a few blocks from Harbaugh’s State Street office is to use whole *numbers* on the GMAT.

The main reason? You can’t use a calculator on the GMAT, so while your Excel-and-calculator-trained mind wants to say calculate “75% of 64″ as 0.75 * 64, the key is to think in terms of whole numbers whenever possible. In this case, that means calling “75%” 3/4, because that allows you to do all of your calculations with the whole numbers 3 and 4, and not have to set up decimal math with 0.75. Since 64/4 is cleanly 16 – a whole number – you can calculate 75% by dividing by 4 first, then multiplying by 3: 64/4 is 16, then 16 * 3 = 48, and you have your answer without ever having to deal with messier decimal calculations.

This concept manifests itself in all kinds of problems for which your mind would typically want to think in terms of decimal math. For example:

With percentages, 25% and 75% can be seen as 1/4 and 3/4, respectively. Want to take 20%? Just divide by 5, because 0.2 = 1/5.

If you’re told that the result of a division operation is X.4, keep in mind that the decimal .4 can be expressed as 2/5, meaning that the divisor has to be a multiple of 5 and the remainder has to be even.

If at some point in a calculation it looks like you need to divide, say, 10 by 4 or 15 by 8 or any other type of operation that would result in a decimal, wait! Leaving division problems as improper fractions just means that you’re keeping two whole numbers handy, and knowing the GMAT at some point you’ll end up having to multiply or divide by a number that lets you avoid the decimal math altogether.

So learn from Jim Harbaugh and his obsession with whole milk. Whole milk may be the reasons that his football dreams came true; whole numbers could be a major reason that your business school dreams come true, too.

Getting ready to take the GMAT? We have free online GMAT seminars running all the time. And, be sure tofind us on Facebook and Google+, and follow us on Twitter!

*By Brian Galvin*

There are many ways the GMAT test makers ensure that you’re thinking logically about the solution of the question. One common example is that the question will give you a story that you have to translate into an equation. Anyone with a calculator can do 15 * 6 * 2 but it’s another skill entirely to translate that a car dealership that’s open every day but Sunday sells 3 SUVs, 5 trucks and 7 sedans per day for a sale that lasts a fortnight (sadly, the word fortnight is somewhat rare on the GMAT). Which skill is more important in business, crunching arbitrary numbers or deciphering which numbers to crunch? (Trick question: they’re both important!) The difference is a computer will calculate numbers much faster than a human ever will, but being able to determine what equation to set up is the more important skill.

This distinction is rather ironic, because the GMAT often provides questions that are simply equations to be solved. If the thought process is so important, why provide questions that are so straight forward? Precisely because you don’t have a calculator to solve them and you still need to use reasoning to get to the correct answer. An arbitrarily difficult question like 987 x 123 is trivial with a calculator and provides no educational benefit, simply an opportunity to exercise your fingers (and they want to look good for summer!) But without a calculator, you can start looking at interesting concepts like unit digits and order of magnitude in order to determine the correct answer. For business students, this is worth much more than a rote calculation or a mindless computation.

Let’s look at an example that’s just an equation but requires some analysis to solve quickly:

*(36^3 + 36) / 36 =*

*A) 216
*

This question has no hidden meaning and no interpretation issues. It is as straight forward as 2+2, but much harder because the numbers given are unwieldy. This is, of course, not an accident. A significant number of people will not answer this question correctly, and even more will get it but only after a lengthy process. Let’s see how we can strategically approach a question like this on test day.

Firstly, there’s nothing more to be done here than multiplying a couple of 2-digit numbers, then performing an addition, then performing a division. In theory, each of these operations is completely feasible, so some people will start by trying to solve 36^3 and go from there. However, this is a lengthy process, and at the end, you get an unwieldy number (46,656 to be precise). From there, you need to add 36, and then divide by 36. This will be a very difficult calculation, but if you think of the process we’re doing, you might notice that you just multiplied by 36, and now you’ll have to divide by 36. You can’t exactly shortcut this problem because of the stingy addition, but perhaps we can account for it in some manner.

Multiplying 36 by itself twice will be tedious, but since you’re dividing by 36 afterwards, perhaps you can omit the final multiplication as it will essentially cancel out with the division. The only caveat is that we have to add 36 in between multiplying and dividing, but logically we’re adding 36 and then dividing the sum by 36, which means that this is tantamount to just adding 1. As such, this problem kind of breaks down to just 36 * 36, and then you add 1. If you were willing to multiply 36^3, then 36^2 becomes a much simpler calculation. This operation will yield the correct answer (we’ll see shortly that we don’t even need to execute it), and you can get there entirely by reasoning and logic.

Moreover, you can solve this question using (our friendly neighbour) algebra. When you’re facing a problem with addition of exponents, you always want to turn that problem into multiplication if at all possible. This is because there are no good rules for addition and subtraction with exponents, but the rules for multiplication and division are clear and precise. Taking just the numerator, if you have 36^3 + 36, you can factor out the 36 from both terms. This will leave you with 36 *(36^2 + 1). Considering the denominator again, we end up with (36 *(36^2 + 1)) / 36. This means we can eliminate both the 36 in the numerator and the 36 in the denominator and end up with just (36^2 + 1), which is the same thing we found above.

Now, 36*36 is certainly solvable given a piece of paper and a minute or so, but you can tell a lot from the answer by the answer choices that are given to you. If you square a number with a units digit of 6, the result will always end with 6 as well (this rule applies to all numbers ending in 0, 1, 5 and 6). The result will therefore be some number that ends in 6, to which you must add 1. The final result must thus end with a 7. Perusing the answer choices, only answer choice C satisfies that criterion. The answer must necessarily be C, 1297, even if we don’t spend time confirming that 36^2 is indeed 1,296.

In the quantitative section of the GMAT, you have an average of 2 minutes per question to get the answer. However, this is simply an average over the entire section; you don’t have to spend 2 minutes if you can shortcut the answer in 30 seconds. Similarly, some questions might take you 3 minutes to solve, and as long as you’re making up time on other questions, there’s no problem taking a little longer. However, if you can solve a question in 30 seconds that your peers spend 2 or 3 minutes solving, you just used the secret shortcut that the exam hopes you will use.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

*Ron Awad is a GMAT instructor for Veritas Prep based in Montreal, bringing you weekly advice for success on your exam. After graduating from McGill and receiving his MBA from Concordia, Ron started teaching GMAT prep and his Veritas Prep students have given him rave reviews ever since.*