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# s, t, and u are integers, and 10≤ s < t < u ≤ 20

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Founder
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s, t, and u are integers, and 10≤ s < t < u ≤ 20 [#permalink]  20 Dec 2017, 15:34
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74% (01:02) correct 25% (00:39) wrong based on 86 sessions
s, t, and u are integers, and 10≤ s < t < u ≤ 20

 Quantity A Quantity B $$s + \frac{t}{u}$$ 11

A. Quantity A is greater
B. Quantity B is greater.
C. The two quantities are equal
D. The relationship cannot be determined from the information given.

kudo for the right solution and explanation
[Reveal] Spoiler: OA

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Kudos [?]: 3 [1] , given: 1

Re: s, t, and u are integers, and 10≤ s < t < u ≤ 20 [#permalink]  20 Dec 2017, 20:38
1
KUDOS
we can deduce deduce the max value of A and min value of A
for Max value:
S=18
t=19
u=20
in this case A>B
for Min Value:
S=10
t=11
u=20
In that case A=10+(11/20)<11
So in this case B>A

Hence Ans D
Founder
Joined: 18 Apr 2015
Posts: 13719
GRE 1: Q160 V160
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Kudos [?]: 3553 [0], given: 12681

Re: s, t, and u are integers, and 10≤ s < t < u ≤ 20 [#permalink]  21 Dec 2017, 16:32
Expert's post
Added the OA. It is D.

Regards
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Intern
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Kudos [?]: 52 [0], given: 7

Re: s, t, and u are integers, and 10≤ s < t < u ≤ 20 [#permalink]  17 Feb 2018, 01:25
Such questions don't need any sort of calculation. What it need is just thinking. Here's how:
Minimum s can be 10. And the ratio of t to u is always less than 1. Thus the result will be between 10 and 11 i.e less than 11.
On other hand, s can be greater than 11, and thus Quantity A will become greater in that case because the ratio of t to u cannot be negative.

So, information is not sufficient to answer the question.
Choice D correct.
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Last edited by GREMasterBlaster on 04 Mar 2018, 01:55, edited 1 time in total.
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Kudos [?]: 2 [2] , given: 2

Re: s, t, and u are integers, and 10≤ s < t < u ≤ 20 [#permalink]  17 Feb 2018, 16:00
2
KUDOS
GREMasterBlaster wrote:
Such questions don't need any sort of calculation. What it need is just thinking. Here's how:
As minimum s can be 10. And the ration of t and u is always less than 1. Thus the result will be between 10 and 11 i.e less than 11.
On other hand, s can be greater than 11, and thus Quantity A will become greater in that case because the ratio of t and u cannot be negative.

So, information is not sufficient to answer the question.
Choice D correct.

I got this one wrong because I didn't look closely enough and see that it was either greater or equals, and only noticed the greater bit
Intern
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Kudos [?]: 16 [0], given: 15

Re: s, t, and u are integers, and 10≤ s < t < u ≤ 20 [#permalink]  04 Jun 2018, 19:16
Carcass wrote:
s, t, and u are integers, and 10≤ s < t < u ≤ 20

 Quantity A Quantity B $$s + \frac{t}{u}$$ 11

A. Quantity A is greater
B. Quantity B is greater.
C. The two quantities are equal
D. The relationship cannot be determined from the information given.

kudo for the right solution and explanation

For me, I calculated this by making s, t, & u equal by applying their Maximum and Minimum values of 20 and 10 respectively. Is this reasoning appropriate?
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Kudos [?]: 138 [1] , given: 22

Re: s, t, and u are integers, and 10≤ s < t < u ≤ 20 [#permalink]  05 Jun 2018, 17:19
1
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We assess the biggest and lowest possible amounts for A to be able to compare it with 11.

If we want to maximize A: u should be the lowest and t and s should be the biggest possible. But there might be a tradeoff between u and (s and t).
Minimum value for u can be 12 while t is 11 and s is 10. Then A=S+T/U= 10+11/12 which is less than B, but this equation can have a bigger value, for example when s=11 and t=12 and u is whatever between 13 to 20, the value of A is bigger than 11.
(The maximum value for A is when s is maximum, because u/t is always something less than 2 and doesn’t have so much effect. And it is when s has the minimum value. For u=20, t=19 and s=18 we have the maximum value of A which is 18+19/20.)

If we want to minimize A: u should be maximum value and t&s should be minimum. But again there might be a tradeoff between u and (s and t)
Maximum value that u can have is 20 (as it can be equal to the upper bound(20) and the minimum value for s can be 10 (as it can be equal to the lower bound(10) and t can’t be equal to 10, the Lowes possible value for t can be 11. Thus we have:
A = S+T/U = 10 + 11/20 that is less than 11 (B)

Answer is D. As A is between 10+11/20 and 18+19/20

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Re: s, t, and u are integers, and 10≤ s < t < u ≤ 20   [#permalink] 05 Jun 2018, 17:19
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