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
OAC
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j_shreyans
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Range = greatest - least.For students in class A, the range in height is r and the greatest height is g. For students in class B, the range in height is s and the greatest height is h. Is the least height in class A greater than the least height of students in class B?
1) r<s
2) g>h
Thus:
Least = greatest - range.
In class A, least = greatest - range = g-r.
In class B, least = greatest - range = h-s.
If the least height in A is greater than the least height in B, we get:
g-r > h-s
g+s > h+r.
Question rephrased: Is g+s > h+r?
Statement 1: r < s
No information about g or h.
INSUFFICIENT.
Statement 2: g > h
No information about r or s.
INSUFFICIENT.
Statements combined:
Inequalities can be ADDED TOGETHER.
When we add, the < > must face the SAME DIRECTION in each inequality.
To match g > h in statement 2, rephrase r < s in statement 1 as s > r.
Adding together g > h and s > r, we get:
g+s > h+r.
SUFFICIENT.
The correct answer is C.
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Given: For the students in class A , the range of their heights is r cms and the greatest height is g cms.j_shreyans wrote: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
OAC
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
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Brent
Brent Hanneson - Creator of GMATPrepNow.com
