j_shreyans
For the students in class A, the range of their height is r cm and the greatest heights is g cm. For the students in class B , the range of their heights is s cm and the greatest heights is h cm. Is the least height of the students in class A greater than the least height of the students in class B?
Statement 1) r < s
Statement 2) g > h
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 - sTarget 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 - rSince 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 + sPerfect!! 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-data-sufficiency?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 + sPerfect!! Since we can answer the
RE-REPHRASED target question with certainty, the combined statements are SUFFICIENT
Answer = C
Cheers,
Brent