# Identifying the Paradox on GMAT Critical Reasoning Questions

Let’s take a look at a very tricky GMAT Prep critical reasoning problem today. Problems such as these make CR more attractive than RC and SC to people who have a Quantitative bent of mind. It’s one of the “explain the paradox” problems, which usually tend to be easy if you know exactly how to tackle them, but the issue here is that it is hard to put your finger on the paradox.

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!