Data Sufficiency

BTGmoderatorDC wrote: ↑

Tue Dec 20, 2022 6:00 am

For the students in class A, the range of their heights is r centimeters and the greatest height is g centimeters. For the students in class B, the range of their heights is s centimeters and the greatest height is h centimeters. Is the least height of the students in class A greater than the least height of the students in class B ?

(1) r < s
(2) g > h

OA C

Source: GMAT Prep

Given: For the students in class A , the range of their heights is r cms and the greatest height is g cms.
Range = greatest height - least height.
Rearrange this to get: least height = greatest height - range.
So, for class A, the least height = g - r

Given: For the students in class B, the range of their heights is s cms and the greatest height is h cms.
So, for class B, the least height = h - s

Target question: Is the least height of the students class A greater than the least height of the students in class B?

We can rephrase this as...
REPHRASED target question: Is h - s < g - r

Since it's often easier to deal with sums than with differences, let's rephrase the target question one more time by taking h - s < g - r and adding s and r to both sides to get...
RE-REPHRASED target question: Is h + r < g + s

Perfect!! Now that we've rephrased the target question, this question is relatively easy to solve.

Aside: We have a free video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat ... cy?id=1100

Statement 1: r < s
Since we have no information about h and g, we cannot answer the RE-REPHRASED target question with certainty.
So, statement 1 is NOT SUFFICIENT

Statement 2: g > h
Since we have no information about r and s, we cannot answer the RE-REPHRASED target question with certainty.
So, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
IMPORTANT: If we have two inequalities with the inequality symbols FACING THE SAME DIRECTION, we can add them.

Statement 1: r < s
Statement 2: h < g [I rewrote the inequality so that it's facing the same direction as that in statement 1]
ADD the inequalities to get: h + r < g + s
Perfect!! Since we can answer the RE-REPHRASED target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent