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

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Math Expert
Joined: 02 Sep 2009
Posts: 61301
The difference between integers a and b is 7, and a > b. What is a?  [#permalink]

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26 Nov 2019, 01:05
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75% (hard)

Question Stats:

40% (01:47) correct 60% (01:55) wrong based on 46 sessions

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

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

Are You Up For the Challenge: 700 Level Questions

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VP
Joined: 19 Oct 2018
Posts: 1301
Location: India
Re: The difference between integers a and b is 7, and a > b. What is a?  [#permalink]

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26 Nov 2019, 02:14
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) $$ab \geq 0$$

Are You Up For the Challenge: 700 Level Questions
VP
Joined: 24 Nov 2016
Posts: 1207
Location: United States
The difference between integers a and b is 7, and a > b. What is a?  [#permalink]

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26 Nov 2019, 04:04
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)
Senior Manager
Joined: 13 Feb 2018
Posts: 498
GMAT 1: 640 Q48 V28
The difference between integers a and b is 7, and a > b. What is a?  [#permalink]

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26 Nov 2019, 04:16
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
The difference between integers a and b is 7, and a > b. What is a?   [#permalink] 26 Nov 2019, 04:16
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