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For the students in class A, the range of their heights is r centimete
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23 Feb 2012, 08:12
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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
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Re: For the students in class A, the range of their heights is r centimete
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23 Feb 2012, 09:32
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 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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Re: For the students in class A, the range of their heights is r centimete
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02 Nov 2012, 22:46
pramodkg wrote: For students in class A, the range of heights is r and the greatest height is g. For students in class B, the range of heights is s and the greatest height is h. Is the least height in class A greater than the least height in class B? (1) r < s (2) g > h \(Shortest_A = gr\) \(Shortest_B = hs\) So question is is gr>hs or is g>h+(rs) 1) rs<0, Not sufficient. We dont know whether g is greater than h or not. 2) g>h, Not sufficient. We dont know if (rs) 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 rs is negative. So, h+rs < h So, g>h + r s. Sufficient. Kudos Please... If my post helped.
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Re: For the students in class A, the range of their heights is r centimete
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15 Jul 2012, 01:39
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.



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Re: For the students in class A, the range of their heights is r centimete
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15 Jul 2012, 02:16
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 Bwe can simply form an equation from this problem from the question stem we can draw this as per my undestanding GA=R, HB=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 RS<0 AND FROM stmnt 2. we can get GH>0 SO WE have four equations 1.GA=R 2.HB=S or H= B+S 3.RS<0 4.GH>0 NOW action Eq.3.RS<0 OR GAS<0( putting value of R.) or A<SG OR A>GSEq 4......... GH>0 OR GBS>0 (putting value of H.) OR B>SG OR B<GS FROM this two we can easily form this B<GS<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



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Re: For the students in class A, the range of their heights is r centimete
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15 Jul 2012, 05:34
Desperate123 wrote: 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. 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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Re: For the students in class A, the range of their heights is r centimete
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02 Nov 2012, 23:13
Class A: Smallest height=gr Range of heights=r Greatest height=g Class B: Smallest height=hs Range=s Greatest height=h Question is asking whether gr>hs? 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
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Re: For the students in class A, the range of their heights is r centimete
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23 May 2015, 04:58
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.



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Re: For the students in class A, the range of their heights is r centimete
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25 Feb 2016, 08:24
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
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... REREPHRASED 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: http://www.gmatprepnow.com/module/gmatdatasufficiency?id=1100 Statement 1: r < s Since we have no information about h and g, we cannot answer the REREPHRASED 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 REREPHRASED 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 REREPHRASED target question with certainty, the combined statements are SUFFICIENT Answer = C Cheers, Brent
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Re: For the students in class A, the range of their heights is r centimete
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13 Nov 2016, 06:53
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 Answer: Option C Check solution
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Re: For the students in class A, the range of their heights is r centimete
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18 Apr 2017, 16:20
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 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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Re: For the students in class A, the range of their heights is r centimete
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14 Oct 2017, 03:14
Bunuel wrote: 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 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. Hi can we Subtract the two inequalities given in the statements 1. r<s 2. g>h 1+2 combined : Subtracting 1 from 2 : gr>hs ...means Min of A > Min of B ...so C is my steps correct?



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Re: For the students in class A, the range of their heights is r centimete
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14 Oct 2017, 03:40
shoumodip wrote: Bunuel wrote: 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 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. Hi can we Subtract the two inequalities given in the statements 1. r<s 2. g>h 1+2 combined : Subtracting 1 from 2 : gr>hs ...means Min of A > Min of B ...so C is my steps correct? ADDING/SUBTRACTING INEQUALITIES1. 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 \(<\)) > \(ac>bd\) (take the sign of the inequality you subtract from). Example: \(3<4\) and \(5>1\) > \(35<41\). Check for more the links below: Inequalities Made Easy!
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Re: For the students in class A, the range of their heights is r centimete
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18 Sep 2019, 06:57
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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Re: For the students in class A, the range of their heights is r centimete
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