Integrated Reasoning - Multi Source Reasoning

Quarter Wit, Quarter WisdomFor the past couple of weeks, we have been talking about integrated reasoning. Today we will continue with that and take up a multi-source reasoning question. These questions often include substantial data and require you to make inferences based on it. They test your logical and reasoning aptitude so don’t get lost in the data. Review the given information and then jump on to the questions. Then come back to the relevant part of the given information and peruse it in detail.

Given Data:

Minerals possess a number of properties that are used as an aid in their identification. These are listed below with a brief description:

Color – The color of the specimen as it appears to the naked eye under normal lighting conditions. Some minerals such as gold will only appear as one color, but due to impurities and crystal light distortion, many minerals can appear in multiple colors. Therefore, observable specimen color is the least effective property in identification.

Streak – The color of a mineral in powdered form. A streak test is performed by dragging a freshly cleaved mineral surface across an unglazed porcelain (Mohs hardness 7) surface. If the mineral is less hard than the porcelain, it will leave a stripe of color (the mineral in a powdered state). This is the true color of a mineral specimen as it lessens the impurity impact and eliminates the light distortion from the crystal. Although a mineral may have multiple observable specimen colors, it will only have one streak color.

Hardness – Minerals are identified roughly by their hardness based on the Mohs scale of mineral hardness, a list of ten minerals from #1 (softest) to #10 (hardest). All minerals will fall somewhere along the scale, based on their ability to scratch any mineral with a number lower than theirs and their inability to scratch any mineral with a number higher than theirs.

Mohs Scale of Mineral Hardness

1         Talc

2         Gypsum

3         Calcite

4         Fluorite

5         Apatite

6         Orthoclase

7         Quartz

8         Topaz

9         Corundum

10     Diamond

Specific Gravity – It is the relative weight of a mineral as compared to the weight of an equal volume of water. The specific gravity is also referred to as density and is expressed normally as an average of a small range of densities.

Common Minerals and Their Specific Gravity

Halite – 2.1

Diamond – 2.26

Gypsum – 2.3

Quartz – 2.7

Talc – 2.8

Muscovite Mica – 2.8

Corundum – 4.0

Cinnabar – 8.0

Gold – 19.3

Optical Properties - Used mainly by scientists, X-rays are sent through thin slices of mineral, producing identifying patterns of light which measure their index of refraction which is distinct for each mineral.

Properties of 3 unidentified minerals:

  1. Mineral A was not able to scratch any of the top 9 minerals on Mohs scale. Its specific gravity is 2.3 (rounded to one decimal place).
  2. The streak color of Mineral B is white. Its specific gravity is 2.3 (rounded to one decimal place)
  3. Mineral C scratches Calcite and Topaz. It is pink in color and its index of refraction is 2.417.

Questions:

Question 1: For each of the following, select ‘Yes’ if the mineral can be uniquely identified based on the information provided. Otherwise, select No.

Question 2. State True/False: It is possible that mineral A and mineral B are the same mineral.
Solutions:

Solution 1. Mineral A – No

We know that the mineral lies between 9  and 10 (excluding 9 but including 10) on the Mohs scale. Also its specific gravity could be anything from 2.25 to 2.35 (excluding 2.35). There could be many minerals with these two properties. From the given data, we see that diamond is one such mineral but it may not be the only one.

Mineral B – No

Again, there can be many minerals with streak color white. Note that every mineral has a single streak color but every streak color may not belong to a single mineral. But we can say that its hardness must be less than 7 (hardness of unglazed porcelain) on Mohs scale since it has a streak color. Also its specific gravity could be anything from 2.25 to 2.35 (excluding 2.35).

Mineral C – Yes

Index of refraction is distinct for each mineral hence given the index of refraction, we can uniquely identify the mineral.

Solution 2. We need to compare mineral A with mineral B. The known properties of the two should not clash if they are to be the same mineral. Note from above that mineral A has a hardness of more than 9 on Mohs scale while mineral B has a hardness of less than 7. So it is not possible that mineral A and B are the same.

Hope the example gave you some idea about the multi source reasoning questions.

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!

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