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a and b are positive integer

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Source: — Data Sufficiency |

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by [email protected] » Tue Oct 07, 2014 10:00 am
Hi j_shreyans,

Before I work through the explanation for this question, you should really put a bit more detail into your posts. Any prompt that involves exponents, multi-variable division, etc. requires details so that the Experts and other users answer the actual question that's asked. If you're going to use carats (the "^" symbol), then you MUST use parentheses to clarify the information. In this prompt, we have unclear information in Fact 2...

When you type a^2b, do you mean....(a^2)(b) or do you mean a^(2b)? These are different math terms and will affect the question in different ways.
The same goes for ab^2....do you mean (a)(b^2) or do you mean (ab)^2?

Since this information is unclear, I'm not going to work through Fact 2. As for the rest of the prompt:

We're told that A and B are POSITIVE INTEGERS. We're asked for the remainder when (A)(B) is divided by 40.

This question is perfect for TESTing VALUES....

Fact 1:B is 60% greater than A

Since both variables must be positive integers, we're really restricted by what we can TEST.

If....
A = 5
B = 8
AB = (5)(8) = 40 and 40/40 = 1r0 so the answer is 0.

A = 10
B = 16
AB = (10)(16) = 160 and 160/40 = 4r0 so the answer is 0.

The answer will ALWAYS = 0 because A MUST be a multiple of 5 and B must be the equivalent multiple of 8. This is the only way for A and B to BOTH be positive integers and for B to be 60% greater than A.
Fact 1 is SUFFICIENT.

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by jaspreetsra » Tue Oct 07, 2014 5:59 pm
A MUST be a multiple of 5 and B must be the equivalent multiple of 8.Why? didn't get it.
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by GMATGuruNY » Tue Oct 07, 2014 7:04 pm
jaspreetsra wrote:A MUST be a multiple of 5 and B must be the equivalent multiple of 8.Why? didn't get it.
Statement 1: b is 60% greater than a
In other words:
b is 160% of a.

Translated into math:
b = (160/100)a
b/a = 160/100 = 8/5.

Since b and a are INTEGERS in a ratio of 8 to 5, b must be a multiple of 8, while a must be a multiple of 5.
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by j_shreyans » Tue Oct 07, 2014 9:38 pm
[email protected] wrote:Hi j_shreyans,

Before I work through the explanation for this question, you should really put a bit more detail into your posts. Any prompt that involves exponents, multi-variable division, etc. requires details so that the Experts and other users answer the actual question that's asked. If you're going to use carats (the "^" symbol), then you MUST use parentheses to clarify the information. In this prompt, we have unclear information in Fact 2...

When you type a^2b, do you mean....(a^2)(b) or do you mean a^(2b)? These are different math terms and will affect the question in different ways.
The same goes for ab^2....do you mean (a)(b^2) or do you mean (ab)^2?

Since this information is unclear, I'm not going to work through Fact 2. As for the rest of the prompt:

We're told that A and B are POSITIVE INTEGERS. We're asked for the remainder when (A)(B) is divided by 40.

This question is perfect for TESTing VALUES....

Fact 1:B is 60% greater than A

Since both variables must be positive integers, we're really restricted by what we can TEST.

If....
A = 5
B = 8
AB = (5)(8) = 40 and 40/40 = 1r0 so the answer is 0.

A = 10
B = 16
AB = (10)(16) = 160 and 160/40 = 4r0 so the answer is 0.

The answer will ALWAYS = 0 because A MUST be a multiple of 5 and B must be the equivalent multiple of 8. This is the only way for A and B to BOTH be positive integers and for B to be 60% greater than A.
Fact 1 is SUFFICIENT.

GMAT assassins aren't born, they're made,
Rich
Hi Rich ,

Well noted , next time i will be more care full.Pls see the below statement 2.

2) Each of (a^2)(b) and (a)(b^2) is divisible by 40

I hope this is clear.
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by Matt@VeritasPrep » Sun Oct 12, 2014 10:04 pm
Another way to make this legible is to use superscripts. You can copy and paste them from the list given here. Pretty much every instructor except Rich does this, and it makes math much easier to read: to my eyes, (a²b)(b²a) versus a^2bb^2a is kinda of like "Are you doing anything tonight?" vs "r U doin n e thing 2nite??"
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by j_shreyans » Thu May 28, 2015 9:18 am
Hi ,

Small doubt in the below question .

Statement 1 says b=160a/100 or 8a/5

so can we put b in the ab/40 then find out the remainder, doing this will get a^2/25 and a is positive integers so by this statement 1 is not sufficient.

Please advise and correct me .

Thanks
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by GMATGuruNY » Thu May 28, 2015 9:32 am
j_shreyans wrote:Hi ,

Small doubt in the below question .

Statement 1 says b=160a/100 or 8a/5

so can we put b in the ab/40 then find out the remainder, doing this will get a^2/25 and a is positive integers so by this statement 1 is not sufficient.

Please advise and correct me .

Thanks
Since b = (8/5)a -- and b is an integer -- a must be a multiple of 5, as in the following cases:
a=5, b = (8/5)(5) = 8.
a=10, b = (8/5)(10) = 16.
a=15, b = (8/5)(15) = 24.
And so on.

Since a is a multiple of 5, a² must be a multiple of 25, implying that dividing a² by 25 will leave a remainder of 0.
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by nikhilgmat31 » Tue Jun 02, 2015 2:12 am
2) Each of (a^2)(b) and (a)(b^2) is divisible by 40

doesn't seems to be sufficient

a*a*b/40

Exp-

Part 1 ==> a= 2 b=10 (a*a*b)/40 2*2*10/40 = 1 is divisible (a*b*b)/40 ==> 2*10*10/40 is divisible OK where as (2*10)/40 is not divisible.

Part 2 ==> a=4 b =10 (a*a*b)/40 4*4*10/40 = 4 OK and (a*b*b)/40 ==> 10*10*4/40 = 10 is divisible where as (4*10)/40 =1 is divisible


B is not sufficient
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