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# Of the numbers r+s, r-s, r x s, and r/s, which is greatest?

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Intern
Joined: 08 Feb 2015
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Of the numbers r+s, r-s, r x s, and r/s, which is greatest?  [#permalink]

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15 Nov 2016, 13:47
1
9
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15% (low)

Question Stats:

73% (01:08) correct 27% (01:17) wrong based on 255 sessions

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Of the numbers r+s, r-s, r x s, and r/s, which is greatest?

1) r=s=1

2)r-s is the least of the numbers
Status: Preparing for GMAT
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Re: Of the numbers r+s, r-s, r x s, and r/s, which is greatest?  [#permalink]

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16 Nov 2016, 03:08
9
5
S1 - r=s=1, therefore r+s=2; r-s=0; r x s=1; r/s = 1
hence greatest is r+s.

S2 - r-s is the least.
When r=s=1, r+s is greatest.
Suppose, when r=3,s=2
r+s=5; r-s=1; r x s=6; r/s = 3/2 which gives r x s as the greatest.
Since we get two different values, so B not sufficient.

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Re: Of the numbers r+s, r-s, r x s, and r/s, which is greatest?  [#permalink]

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28 Jul 2018, 09:49
1
the best way to solve the problem will be to assume numbers and A fits nicely
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Re: Of the numbers r+s, r-s, r x s, and r/s, which is greatest?  [#permalink]

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28 Aug 2018, 08:12
Hi, correct Answer is option D. Even though I don't know why. I was reviewing my answers on the mock test and it showed option A as wrong answer. Anyone here who knows the reason why D is the right answer? (P.s. can't upload image because I'm a new user)
Status: Preparing for GMAT
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Re: Of the numbers r+s, r-s, r x s, and r/s, which is greatest?  [#permalink]

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28 Aug 2018, 08:19
shivamsharma wrote:
Hi, correct Answer is option D. Even though I don't know why. I was reviewing my answers on the mock test and it showed option A as wrong answer. Anyone here who knows the reason why D is the right answer? (P.s. can't upload image because I'm a new user)

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Re: Of the numbers r+s, r-s, r x s, and r/s, which is greatest?  [#permalink]

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30 Aug 2018, 08:21
souvonik2k wrote:
shivamsharma wrote:
Hi, correct Answer is option D. Even though I don't know why. I was reviewing my answers on the mock test and it showed option A as wrong answer. Anyone here who knows the reason why D is the right answer? (P.s. can't upload image because I'm a new user)

Yup, my bad. A is correct. Thanks!
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Re: Of the numbers r+s, r-s, r x s, and r/s, which is greatest?  [#permalink]

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09 Nov 2018, 09:34
1) r=s=1
clearly r+s is greatest for these values

2)r-s is the least of the numbers
cant say
eg r=s=0.5 r=s is greatest
r=s=3 r*s is the greatest
not sufficient
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Re: Of the numbers r+s, r-s, r x s, and r/s, which is greatest?  [#permalink]

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19 Apr 2019, 09:52
Is there a better way to solve the second statement? Using numbers as examples takes time and leaves rool for making error
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Re: Of the numbers r+s, r-s, r x s, and r/s, which is greatest?  [#permalink]

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13 Aug 2019, 01:13
jyotsnamahajan wrote:
Is there a better way to solve the second statement? Using numbers as examples takes time and leaves rool for making error

For Statement 1, solving for r+s, r-s, rs and r/s clearly indicates r+s as the largest number.

For Statement 2, lets assume the following cases.

Case 1: r is +ve, and s is +ve
=> r+s and r*s is definitely bigger than r-s
=> but its hard to discern which one will be the largest.
=>Please note, you can only take cases where r-s is < than r/s because r/s may or may not be bigger than r-s
eg: if r=4 and s=1, r-s<r/s; but if r=6 and s=2, r-s>r/s

Case 2: r is +ve and s is -ve
=> r-s will always be greater than r+s
=> since this case does not satisfy the condition in Statement 2 (r-s is the least number), we can disregard this case.

Case 3: r is -ve and s is -ve
=> Here too r+s will always be greater than r-s
=> since this case does not satisfy the condition in Statement 2 (r-s is the least number), we can disregard this case.

Case 4: r is -ve and s is +ve
=> analysing the r+s, r-s, rs and r/s no particular pattern is discernible.
=> so we can choose numbers to find cases where r-s is the least but there are different answers for the max

All in all, after looking at the cases, Case 2 and Case 3 can be disregarded and Case 1 and Case 4 does not give you a constant maximum.
During the test, If you start with Case 1, given that case 1 does not give you a number which will always be maximum, you can strike Statement 2 as insufficient
Re: Of the numbers r+s, r-s, r x s, and r/s, which is greatest?   [#permalink] 13 Aug 2019, 01:13
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