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The difference between integers a and b is 7, and a > b. What is a?

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Bunuel
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The difference between integers a and b is 7, and a > b. What is a? [#permalink] New post   26 Nov 2019, 02:05
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The difference between integers a and b is 7, and a > b. What is a?

(1) \(a^b=1\)
(2) \(ab \geq 0\)


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nick1816
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Re: The difference between integers a and b is 7, and a > b. What is a? [#permalink] New post   26 Nov 2019, 03:14
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a-b=7

Statement 1-

Case 1- a=7 and b=0

Case 2- a=1 and b=-6

Case 3 a=-1 and b=-8

Insufficient

Statement 2-

Case 1- a=7 and b=0

Case 2- a=-1 and b=-8

Insufficient

Even after combining both equations, a can be 7 or -1

Insufficient



Bunuel wrote:
The difference between integers a and b is 7, and a > b. What is a?

(1) \(a^b=1\)
(2) \(ab \geq 0\)


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exc4libur
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The difference between integers a and b is 7, and a > b. What is a? [#permalink] New post   26 Nov 2019, 05:04
Bunuel wrote:
The difference between integers a and b is 7, and a > b. What is a?

(1) \(a^b=1\)
(2) \(ab \geq 0\)


a>b: a-b=7

(1) \(a^b=1\) insufic

\(a^b=1:1^{any}=1…a=1,b=a-7=1-7=-6…(a,b)=(1,-6)…(a>b)\)
\(a^b=1:(-1)^{even}=1…a=-1,b=a-7=-1-7=-8…(a,b)=(-1,-8)…(a>b)\)
\(a^b=1:{any}^{0}=1…b=0…a=7+0=7…(a,b)=(7,0)…(a>b)\)

(2) \(ab \geq 0\) insufic

\((a,b)=(same.sign;or,0)\)

(1&2) insufic

\(a^b=1:(-1)^{even}=1…a=-1,b=a-7=-1-7=-8…(a,b)=(-1,-8)…(a>b)\)
\(a^b=1:{any}^{0}=1…b=0…a=7+0=7…(a,b)=(7,0)…(a>b)\)

Ans (E)
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The difference between integers a and b is 7, and a > b. What is a? [#permalink] New post   26 Nov 2019, 05:16
Let's play with numbers and dont forget that in the universe there are negative numbers as well

a=7; b=0 no conflict with the stem as a>b and a-b=7

a=-1; b=-8 no conflict with the stem as a>b and a-b=7

1) Both pairs satisfy, so no unique value for a. Insuff
2) Both pairs satisfy, so no unique value for a. Insuff

Even taken together we have both values valid

Circle that E and attack the next question
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Re: The difference between integers a and b is 7, and a > b. What is a? [#permalink] New post   05 Mar 2021, 09:07
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: The difference between integers a and b is 7, and a > b. What is a? [#permalink]
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