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

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

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New post 26 Nov 2019, 02:05
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

38% (01:35) correct 62% (01:51) wrong based on 32 sessions

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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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New post 26 Nov 2019, 03:14
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) \(ab \geq 0\)


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

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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]

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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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The difference between integers a and b is 7, and a > b. What is a?   [#permalink] 26 Nov 2019, 05:16
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