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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Sat Jul 14, 2012 9:41 am
AJWILL wrote:if a*b*c= 60, where a,b and c are integers greater than 1, a+b+c=?
1)a+b=8
2)Both a and b are odd numbers.
Please help..
Prime factorization comes in handy for this one.
60 = 2x2x3x5
Since a, b and c are integers greater than 1, there are only 3 cases that are possible.
case 1: the numbers are 2, 3, and 10 (sum = 15)
case 2: the numbers are 3, 4, and 5 (sum = 12)
case 3: the numbers are 2, 5, and 6 (sum = 13)

Statement 1: a+b=8
This could mean we have case 2 (a=3 and b=5) in which case a+b+c = 12.
Or it could mean we have case 3 (a=2 and b=6) in which case a+b+c = 13.
Since we can't answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: Both a and b are odd numbers.
Only case 2 features two odd numbers, so a+b+c must equal 12
So, statement 2 IS SUFFICIENT

The answer is B

Cheers,
Brent
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by kalpita123 » Sun Jul 15, 2012 3:53 pm
Brent@GMATPrepNow wrote:
AJWILL wrote:if a*b*c= 60, where a,b and c are integers greater than 1, a+b+c=?
1)a+b=8
2)Both a and b are odd numbers.
Please help..
Prime factorization comes in handy for this one.
60 = 2x2x3x5
Since a, b and c are integers greater than 1, there are only 3 cases that are possible.
case 1: the numbers are 2, 3, and 10 (sum = 15)
case 2: the numbers are 3, 4, and 5 (sum = 12)
case 3: the numbers are 2, 5, and 6 (sum = 13)

Statement 1: a+b=8
This could mean we have case 2 (a=3 and b=5) in which case a+b+c = 12.
Or it could mean we have case 3 (a=2 and b=6) in which case a+b+c = 13.
Since we can't answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: Both a and b are odd numbers.
Only case 2 features two odd numbers, so a+b+c must equal 12
So, statement 2 IS SUFFICIENT

The answer is B

Cheers,
Brent
Brent,

Although this will not change our current answer(B), another case can be the numbers 2,2 and 15 with sum=19, as the question doesn't say a,b, and c are different integers. Am i correct?
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by Brent@GMATPrepNow » Sun Jul 15, 2012 4:09 pm
kalpita123 wrote: Although this will not change our current answer(B), another case can be the numbers 2,2 and 15 with sum=19, as the question doesn't say a,b, and c are different integers. Am i correct?
You are 100% correct on both counts. The fourth case is that the numbers could by 2, 2, and 15, and the correct answer is still B.

My bad :-)

Cheers and thanks,
Brent
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