If a and b are positive integers, what is the remainder when ab is divided by 40?
(1) b is 60% greater than a.
(2) Each of a^2b and ab^2 is divisible by 40.
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a and b are positive integer
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j_shreyans
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[email protected]
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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
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
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jaspreetsra
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GMATGuruNY
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Statement 1: b is 60% greater than ajaspreetsra wrote:A MUST be a multiple of 5 and B must be the equivalent multiple of 8.Why? didn't get it.
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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I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
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j_shreyans
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Hi Rich ,[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
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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Matt@VeritasPrep
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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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j_shreyans
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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
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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GMATGuruNY
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Since b = (8/5)a -- and b is an integer -- a must be a multiple of 5, as in the following cases: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
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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My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
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nikhilgmat31
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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
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
