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

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.
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\(Shortest_A = g-r\)

\(Shortest_B = h-s\)

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.

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.

BANON wrote:

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

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 -A<S-G OR A>G-S
Eq 4......... G-H>0 OR G-B-S>0 (putting value of H.) OR -B>S-G OR B<G-S
FROM this two we can easily form this
B<G-S<A..................WHERE ALL OF THE ACRONYMES ARE POSITIVE NOT NEGATIVE SO B MUST BE LESS THAN A

THAT directs us to combine these two statements for the solution

hence C

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.
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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

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.

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 [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

Answer: Option C

Check solution

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
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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?

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 \(c<d\) (signs in opposite direction: \(>\) 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!
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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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