For the students in class A, the range of their heights is r centimete

Question

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

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

Bunuel · Accepted Answer

Each statement alone is clearly insufficient. Now, when taken together the question becomes easier if you just visualize it. Given: G>H and R<S:

------------(MIN) ---- G  , red is the range of A, r;
  (MIN) ------------ H  , blue is the range of B, s.

You can literally see that the least height of the students in class A is greater than the least height of the students in class B.

Answer: C.

Hope it's clear.

MacFauz · Answer

Shortest_A = g-r Shortest_B = h-s So question is is g-r>h-s or is g>h+(r-s) 1) r-s<0, Not sufficient. We dont know whether g is greater than h or not. 2) g>h, Not sufficient. We dont know if (r-s) is positive and when added to h is less than g or positive and when added to h is greater than g or negative. 1 & 2, g>h, and r-s is negative. So, h+r-s < h So, g>h + r -s. Sufficient. Kudos Please... If my post helped.

Desperate123 · Answer

Hi Bunuel ,

According to me C will not give the answer because , When i plug in the values say

g=15 and h = 10
r= 2 and s = 3

the max value for A is 15 and the minimum value will be 1 (since the range is 2) 
The max value for B is 10 and the minimum value will be 1 (since the range is 3)

the min value for both is 1 .. (we will not be able to ans question "Is the least height of the students in class A is greater than the least height of the students in class B"

Here , A=B

In one more instance ,

g=10 and h =9 
r=4 and s=5

the min value for A will be 2 
the min value for B will be 4

Here,

A < B

One more instance

g=12 and h =10
r=7 and s=8

the min value for A is 5
the min value for B is 2

here A > B

I was getting 3 different values.
So i marked E as my option. Can you please tell me what i am missing here.

heygmat · Answer

QUESTION A>B?........Where A is the smallest hight of class A and B is the smallest hight of class B we can simply form an equation from this problem from the question stem we can draw this as per my undestanding G-A=R, H-B=S, G for greatest hight and A for smallest in class A, R for range, H for greatest in B CLASS, B for smallest hight in B class, S for range in B CLASS from stmnet 1. we can get R-S<0 AND FROM stmnt 2. we can get G-H>0 SO WE have four equations 1.G-A=R 2.H-B=S or H= B+S 3.R-S<0 4.G-H>0 NOW action Eq.3.------R-S<0 OR G-A-S<0( putting value of R.) or -AG-S Eq 4......... G-H>0 OR G-B-S>0 (putting value of H.) OR -B>S-G OR B

Bunuel · Answer

The red parts above are not correct. How did you get those values there? Anyway:

The range of a set is the difference between the largest and smallest elements in the set.

Which means that if: g=15, h = 10, r= 2 and s = 3, then:

For A: {Largest}-{Smallest}={Range} --> 15-{Smallest}=2 --> {Smallest}=13, not 1 as you've written.
For B: {Largest}-{Smallest}={Range} --> 10-{Smallest}=3 --> {Smallest}=7, not 1 as you've written.

13>7.

The same for the second example in your post.

Hope it's clear.

Marcab · Answer

Class A: 
Smallest height=g-r
Range of heights=r
Greatest height=g
Class B:
Smallest height=h-s
Range=s
Greatest height=h

Question is asking whether g-r>h-s? or whether g+s>h+r?
Statement 1: S>r Not sufficient. Since we don't know about g & h.
Statement 2: g>h Not sufficient. Since we don't know about s & r.
On adding the two inequalities, 
We get: g+s>h+r. Hence sufficient.

Please note that we can add or multiply the inequalities but we can't divide or subtract.
Hope that helps.
-s

sukanyar · Answer

Assume smallest in class A as a
=> g - a = r
=> a = g - r

Assume smallest in class B as b
=> h - a = s
=> a = h - s

Question is whether g - r > h - s

(1) just says that r < s
Since we don't know anything about g and h, this is insufficient.

(2) says that g > h
Since we don't know anything about r and s, this is insufficient.

Combining,

s > r
g > h

Reversing the inequality r < s to s > r, so that now we have both inequalities pointing in the same direction.

Once that's the case, we can simply add the two inequalities

=> s + g > r + h
=> g - r > h - s

Hence, sufficient.

So, C.

BrentGMATPrepNow · Answer

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-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    
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

GMATinsight · Answer

Answer: Option C

Check solution

ScottTargetTestPrep · Answer

We are given that for the students in class A, the tallest student is g cm and the range in heights is r cm. If we let a = the height of the shortest student in class A, we can create the following equation: g - r = a We are also given that for the students in class B, the tallest student is h cm and the range in heights is s cm. If we let b = the height of the shortest student in class B, we can create the following equation: h - s = b We need to determine whether the height of the shortest student in class A is greater than that of the shortest student in class B. That is, we need to determine whether a > b or whether g - r > h - s. Statement One Alone: r < s Since we don’t know anything about g and h, we cannot determine whether g – r > h – s. Statement Two Alone: g > h Since we don’t know anything about r and s, we can’t determine whether g – r > h – s. Statements One and Two Together: From the two statements, we know r < s and g > h. We can multiply both sides of r < s by -1 (don’t forget to reverse the inequality sign) to get -r > -s. Adding the two inequalities gives us: (g > h) + (-r > -s) g - r > h - s Since we have determined that g - r is GREATER than h - s, we have answered the question. Answer: C

shoum27 · Answer

Hi

can we Subtract the two inequalities given in the statements 
1. r<s
2. g>h

1+2 combined : Subtracting 1 from 2 : g-r>h-s ...means Min of A > Min of B ...so C

is my steps correct?

Bunuel · Answer

ADDING/SUBTRACTING INEQUALITIES 1. You can only add inequalities when their signs are in the same direction: If a>b and c>d (signs in same direction: > and > ) --> a+c>b+d . Example: 3<4 and 2<5 --> 3+2<4+5 . 2. You can only apply subtraction when their signs are in the opposite directions: If a>b and c and < ) --> a-c>b-d (take the sign of the inequality you subtract from). Example: 3<4 and 5>1 --> 3-5<4-1 . Check for more the links below: Inequalities Made Easy!

RashedVai · Answer

remember that
range = greatest - least

which can be arranged to
greatest = least + range
or
least = greatest - range

--

(1)
these data concern ranges only; there is no indication whatsoever of how the heights compare.
insufficient

(2)
the greatest height in class a is taller than its counterpart in class b, but we know nothing about the ranges; if class a has a wider spread, its least height could well be shorter than that of class b.
insufficient

(together)
greatest height in class a = g - r
greatest height in class b = h - s
the given inequalities imply that g - r > h - s
sufficient

--

alternatively, you could have formulated g - r and h - s at the beginning of the problem (i.e., before considering statements (1) and (2) alone); these formulations make it perhaps even easier to see that (1) and (2) individually are insufficient.

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For the students in class A, the range of their heights is r centimete

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