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If r and s are positive integers and r-s=6, which of the following has

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zatspeed
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If r and s are positive integers and r-s=6, which of the following has [#permalink] New post  Updated on: 12 Mar 2015, 06:16
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If r and s are positive integers and r-s=6, which of the following has the greatest value?

A. 2r
B. 2s
C. r +s
D. 2r-s
E. 2s-r

I am not entirely sure of the method I used and I got
D and E have answer value of 12
B has answer value of 12-r
A has answer value of 12+s
C, I am not even sure how to input the values for this one
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Originally posted by zatspeed on 11 Mar 2015, 22:57.
Last edited by Bunuel on 12 Mar 2015, 06:16, edited 1 time in total.
Renamed the topic and edited the question.
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EMPOWERgmatRichC
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Re: If r and s are positive integers and r-s=6, which of the following has [#permalink] New post  11 Mar 2015, 23:04
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Hi zatspeed,

You can answer this question by using Number Properties and logic or by TESTing VALUES.

We're told that R and S are POSITIVE INTEGERS and that R-S = 6. We're asked which of the 5 answers has the GREATEST value.

IF....
R = 8
S = 2

Answer A: 2R = 2(8) = 16
Answer B: 2S = 2(2) = 4
Answer C: R+S = 8+2 = 10
Answer D: 2R-S = 2(8) - 2 = 14
Answer E: 2S-R = 2(2) - 8 = -4

Final Answer:
Show Spoiler
A


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zatspeed
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Re: If r and s are positive integers and r-s=6, which of the following has [#permalink] New post  11 Mar 2015, 23:45
EMPOWERgmatRichC wrote:
Hi zatspeed,

You can answer this question by using Number Properties and logic or by TESTing VALUES.

We're told that R and S are POSITIVE INTEGERS and that R-S = 6. We're asked which of the 5 answers has the GREATEST value.

IF....
R = 8
S = 2

Answer A: 2R = 2(8) = 16
Answer B: 2S = 2(2) = 4
Answer C: R+S = 8+2 = 10
Answer D: 2R-S = 2(8) - 2 = 14
Answer E: 2S-R = 2(2) - 8 = -4

Final Answer:
Show Spoiler
A


GMAT assassins aren't born, they're made,
Rich


That makes great sense. Thanks

I tried inputting the values for example as it says r-s=6. I input answer D as 2(r-s=6)= 12. But guess this method is wrong.
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EMPOWERgmatRichC
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Re: If r and s are positive integers and r-s=6, which of the following has [#permalink] New post  12 Mar 2015, 11:42
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Hi zatspeed,

The problem with what you tried to do is that it does not follow "Order of Operations" rules.

2R - S means "the product of 2 and R.......minus S"; the multiplication has to happen before the subtraction. That's why....

2R-S is different from 2(R-S) = 2R - 2S. These are subtle rules, but important ones - they govern how math "works."

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zatspeed
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Re: If r and s are positive integers and r-s=6, which of the following has [#permalink] New post  12 Mar 2015, 20:43
EMPOWERgmatRichC wrote:
Hi zatspeed,

The problem with what you tried to do is that it does not follow "Order of Operations" rules.

2R - S means "the product of 2 and R.......minus S"; the multiplication has to happen before the subtraction. That's why....

2R-S is different from 2(R-S) = 2R - 2S. These are subtle rules, but important ones - they govern how math "works."

GMAT assassins aren't born, they're made,
Rich


Oh ya, ofcourse. Not sure how I overlooked that method. Practice gets to ya at times :p

Thanks
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Re: If r and s are positive integers and r-s=6, which of the following has [#permalink] New post  12 Mar 2015, 22:51
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zatspeed wrote:
If r and s are positive integers and r-s=6, which of the following has the greatest value?

A. 2r
B. 2s
C. r +s
D. 2r-s
E. 2s-r

I am not entirely sure of the method I used and I got
D and E have answer value of 12
B has answer value of 12-r
A has answer value of 12+s
C, I am not even sure how to input the values for this one


The simplest way to do this is to assume values.
We are told that r and s are positive integers.
Also, r-s = 6 => r = 6+s
Hence r is 6 more than s.
Let s be 10. Hence r = 16.

Option A: 2r = 2*16 = 32
Option B: 2s = 2 * 10 = 20
Option C: r + s = 16 + 10 = 26
Option D: 2r - s = 2(16) - 10 = 32 - 10 = 22
Option E: 2s - r = 2(10) - 16 = 20 - 16 = 4

Hence option A is the greatest.

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Re: If r and s are positive integers and r-s=6, which of the following has [#permalink] New post  01 Jan 2020, 19:36
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zatspeed wrote:
If r and s are positive integers and r-s=6, which of the following has the greatest value?

A. 2r
B. 2s
C. r +s
D. 2r-s
E. 2s-r



We can let r = 7 and s = 1. Testing each answer choice, we have:

A) 2r = 14

B) 2s = 2

C) r + s = 8

D) 2r - s = 13

E) 2s - r = -5

We see that choice A produces the largest value.

Answer: A
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Re: If r and s are positive integers and r-s=6, which of the following has [#permalink] New post  07 Jun 2021, 01:48
zatspeed wrote:
If r and s are positive integers and r-s=6, which of the following has the greatest value?

A. 2r
B. 2s
C. r +s
D. 2r-s
E. 2s-r

I am not entirely sure of the method I used and I got
D and E have answer value of 12
B has answer value of 12-r
A has answer value of 12+s
C, I am not even sure how to input the values for this one


The problem can be solved without picking any numbers, only by using logic to eliminate wrong answer choices.

Since both r and s are positive integers, option A > D, and B > E. [Eliminate D & E]

Again, since r-s = 6, r > s. So A > B. [Eliminate B]

Again, 2r = r+r. And r+r > r+s. So A > C [Eliminate C]

Option A is the right answer.
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Re: If r and s are positive integers and r-s=6, which of the following has [#permalink]
07 Jun 2021, 01:48
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