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# M27-15

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Math Expert
Joined: 02 Sep 2009
Posts: 58347

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16 Sep 2014, 01:27
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Difficulty:

75% (hard)

Question Stats:

49% (01:12) correct 51% (01:13) wrong based on 230 sessions

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If $$a$$ and $$b$$ are integers and $$ab=2$$, is $$a=2$$?

(1) $$b+3$$ is not a prime number

(2) $$a \gt b$$

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Math Expert
Joined: 02 Sep 2009
Posts: 58347

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16 Sep 2014, 01:27
3
1
Official Solution:

Notice that we are not told that $$a$$ and $$b$$ are positive.

There are the following possible integer pairs of $$(a, b)$$: (1, 2), (-1, -2), (2, 1) and (-2, -1). Basically, we are asked whether we have the third case.

(1) $$b+3$$ is not a prime number. This statement rules out 1st and 4th options. Not sufficient.

(2) $$a \gt b$$. This statement also rules out 1st and 4th options. Not sufficient.

(1)+(2) Still two options are left: (-1, -2) and (2, 1). Not sufficient.

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Joined: 07 Jan 2017
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08 Mar 2018, 15:40
There are the following possible integer pairs of (a,b)(a,b): (1, 2), (-1, -2), (2, 1) and (-2, -1). Basically, we are asked whether we have the third case.

(1) b+3b+3 is not a prime number. This statement rules out 1st and 4th options. Not sufficient.

Yes but, option one also rules out (-1,-2), as 3 + -2 = 1, which is a prime number. It rules out options 1, 2, and 4.
Intern
Joined: 09 Sep 2018
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27 Sep 2018, 06:00
1
deloitter wrote:
There are the following possible integer pairs of (a,b)(a,b): (1, 2), (-1, -2), (2, 1) and (-2, -1). Basically, we are asked whether we have the third case.

(1) b+3b+3 is not a prime number. This statement rules out 1st and 4th options. Not sufficient.

Yes but, option one also rules out (-1,-2), as 3 + -2 = 1, which is a prime number. It rules out options 1, 2, and 4.

That is not true. Number 1 is not prime
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Joined: 23 May 2018
Posts: 531
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28 Sep 2018, 02:58
I did not consider that the numbers could be both negatives. A mistake I need to avoid.
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Joined: 01 Feb 2018
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Location: India
Concentration: Entrepreneurship, Marketing
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27 Oct 2018, 04:45
Bunuel wrote:
Official Solution:

Notice that we are not told that $$a$$ and $$b$$ are positive.

There are the following possible integer pairs of $$(a, b)$$: (1, 2), (-1, -2), (2, 1) and (-2, -1). Basically, we are asked whether we have the third case.

(1) $$b+3$$ is not a prime number. This statement rules out 1st and 4th options. Not sufficient.

(2) $$a \gt b$$. This statement also rules out 1st and 4th options. Not sufficient.

(1)+(2) Still two options are left: (-1, -2) and (2, 1). Not sufficient.

If $$a$$ and $$b$$ are integers and $$ab=2$$, is $$a=2$$?

Question here is whether A is 2 or not??

Considering situation (1) and from your explanation (1, 2) and (-2, -1) can be values.. neither values has a=2, so its clear "a" is not 2, in that case i think its clear that a is not 2 hence, statement 1 is sufficient.

though there are multiple values of a, but we have to answer whether a is 2 or not,, which is clear that it is not under statement 1.

if m wrong pls help me.
Math Expert
Joined: 02 Sep 2009
Posts: 58347

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27 Oct 2018, 05:44
GMAT215 wrote:
Bunuel wrote:
Official Solution:

Notice that we are not told that $$a$$ and $$b$$ are positive.

There are the following possible integer pairs of $$(a, b)$$: (1, 2), (-1, -2), (2, 1) and (-2, -1). Basically, we are asked whether we have the third case.

(1) $$b+3$$ is not a prime number. This statement rules out 1st and 4th options. Not sufficient.

(2) $$a \gt b$$. This statement also rules out 1st and 4th options. Not sufficient.

(1)+(2) Still two options are left: (-1, -2) and (2, 1). Not sufficient.

If $$a$$ and $$b$$ are integers and $$ab=2$$, is $$a=2$$?

Question here is whether A is 2 or not??

Considering situation (1) and from your explanation (1, 2) and (-2, -1) can be values.. neither values has a=2, so its clear "a" is not 2, in that case i think its clear that a is not 2 hence, statement 1 is sufficient.

though there are multiple values of a, but we have to answer whether a is 2 or not,, which is clear that it is not under statement 1.

if m wrong pls help me.

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29 Oct 2018, 02:55
Bunuel wrote:
GMAT215 wrote:
Bunuel wrote:
Official Solution:

Notice that we are not told that $$a$$ and $$b$$ are positive.

There are the following possible integer pairs of $$(a, b)$$: (1, 2), (-1, -2), (2, 1) and (-2, -1). Basically, we are asked whether we have the third case.

(1) $$b+3$$ is not a prime number. This statement rules out 1st and 4th options. Not sufficient.

(2) $$a \gt b$$. This statement also rules out 1st and 4th options. Not sufficient.

(1)+(2) Still two options are left: (-1, -2) and (2, 1). Not sufficient.

If $$a$$ and $$b$$ are integers and $$ab=2$$, is $$a=2$$?

Question here is whether A is 2 or not??

Considering situation (1) and from your explanation (1, 2) and (-2, -1) can be values.. neither values has a=2, so its clear "a" is not 2, in that case i think its clear that a is not 2 hence, statement 1 is sufficient.

though there are multiple values of a, but we have to answer whether a is 2 or not,, which is clear that it is not under statement 1.

if m wrong pls help me.

Math Expert
Joined: 02 Sep 2009
Posts: 58347

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29 Oct 2018, 03:59
Bunuel wrote:
GMAT215 wrote:
Bunuel wrote:
Official Solution:

Notice that we are not told that $$a$$ and $$b$$ are positive.

There are the following possible integer pairs of $$(a, b)$$: (1, 2), (-1, -2), (2, 1) and (-2, -1). Basically, we are asked whether we have the third case.

(1) $$b+3$$ is not a prime number. This statement rules out 1st and 4th options. Not sufficient.

(2) $$a \gt b$$. This statement also rules out 1st and 4th options. Not sufficient.

(1)+(2) Still two options are left: (-1, -2) and (2, 1). Not sufficient.

If $$a$$ and $$b$$ are integers and $$ab=2$$, is $$a=2$$?

Question here is whether A is 2 or not??

Considering situation (1) and from your explanation (1, 2) and (-2, -1) can be values.. neither values has a=2, so its clear "a" is not 2, in that case i think its clear that a is not 2 hence, statement 1 is sufficient.

though there are multiple values of a, but we have to answer whether a is 2 or not,, which is clear that it is not under statement 1.

if m wrong pls help me.

I think you did not re-read the solution.

The solution clearly says that from statement (1) 1st and 4th options are NOT possible: This statement rules out 1st and 4th options. So, from (1) only (-1, -2) and (2, 1) are possible, NOT (1, 2) and (-2, -1).
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Re: M27-15   [#permalink] 29 Oct 2018, 03:59
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# M27-15

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