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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # s, t, and u are integers, and 10≤ s < t < u ≤ 20  Question banks Downloads My Bookmarks Reviews Important topics
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Moderator  Joined: 18 Apr 2015
Posts: 5860
Followers: 94

Kudos [?]: 1147 , given: 5456

s, t, and u are integers, and 10≤ s < t < u ≤ 20 [#permalink]
Expert's post 00:00

Question Stats: 72% (01:01) correct 27% (00:39) wrong based on 61 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

_________________ Intern Joined: 04 Jun 2016
Posts: 3
Followers: 0

Kudos [?]: 3  , given: 1

Re: s, t, and u are integers, and 10≤ s < t < u ≤ 20 [#permalink]
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
Moderator  Joined: 18 Apr 2015
Posts: 5860
Followers: 94

Kudos [?]: 1147 , given: 5456

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

Regards
_________________
Intern Joined: 11 Jan 2018
Posts: 44
Followers: 0

Kudos [?]: 33 , given: 7

Re: s, t, and u are integers, and 10≤ s < t < u ≤ 20 [#permalink]
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.
_________________

Persistence >>>>>>> Success

Don't say thanks, just give KUDOS.
1 kudos = 1000 Thanks

Last edited by GREMasterBlaster on 04 Mar 2018, 01:55, edited 1 time in total. Intern Joined: 17 Feb 2018
Posts: 9
Followers: 0

Kudos [?]: 2  , given: 2

Re: s, t, and u are integers, and 10≤ s < t < u ≤ 20 [#permalink]
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 Joined: 08 Apr 2018
Posts: 44
Followers: 0

Kudos [?]: 15 , given: 16

Re: s, t, and u are integers, and 10≤ s < t < u ≤ 20 [#permalink]
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?
Manager Joined: 22 Feb 2018
Posts: 159
Followers: 2

Kudos [?]: 100 , given: 22

Re: s, t, and u are integers, and 10≤ s < t < u ≤ 20 [#permalink]
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

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