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Math Expert V
Joined: 02 Sep 2009
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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 V
Joined: 02 Sep 2009
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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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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.
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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
BSchool Forum Moderator G
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I did not consider that the numbers could be both negatives. A mistake I need to avoid.
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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 V
Joined: 02 Sep 2009
Posts: 58347

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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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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 V
Joined: 02 Sep 2009
Posts: 58347

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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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