Is mn divisible by 40?
1.m is divisible by 10
2.n is divisible by 4
I saw this problem on Vimeo.Can anyone tell me again why 1 and 2 are insufficient.I want to understand the Prime Box method here.
Thanks
ConfusedNeed help here
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SOME BACKGROUND: A lot of integer property questions can be solved using prime factorization.dddanny2006 wrote:Is mn divisible by 40?
1) m is divisible by 10
2) n is divisible by 4
For questions involving divisibility, divisors, factors and multiples, we can say:
If N is divisible by k, then k is "hiding" within the prime factorization of N
Examples:
24 is divisible by 3 <> 24 = (2)(2)(2)(3)
70 is divisible by 5 <> 70 = (2)(5)(7)
330 is divisible by 6 <> 330 = (2)(3)(5)(11)
56 is divisible by 8 <> 56 = (2)(2)(2)(7)
Okay, now onto the question at hand . . .
Target question: Is mn divisible by 40?
Since 40 = (2)(2)(2)(5), we can rephrase the target question as . . .
REPHRASED target question: Are there three 2's and one 5 hiding in the prime factorization of mn?
Statement 1: m is divisible by 10
There are several values of m and n that satisfy this condition. Here are two possible cases:
Case a: m = 10 and n = 8, in which case mn is divisible by 40
Case b: m = 10 and n = 3, in which case mn is not divisible by 40
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: n is divisible by 4
There are several values of m and n that satisfy this condition. Here are two possible cases:
Case a: m = 10 and n = 4, in which case mn is divisible by 40
Case b: m = 3 and n = 4, in which case mn is not divisible by 40
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 1: Since 10 = (2)(5), statement 1 tells us that there is one 2 and one 5 hiding in the prime factorization of m.
Statement 2: Since 4 = (2)(2), statement 2 tells us that there are two 2's hiding in the prime factorization of n.
So, there must be three 2's and one 5 hiding in the prime factorization of mn
Since we can answer the target question with certainty, the combined statements are SUFFICIENT
Answer = C
Cheers,
Brent
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Here's one more approach . ..dddanny2006 wrote:Is mn divisible by 40?
1. m is divisible by 10
2. n is divisible by 4
Target question: Is mn divisible by 40?
Statement 1: m is divisible by 10
There are several values of m and n that satisfy this condition. Here are two possible cases:
Case a: m = 10 and n = 8, in which case mn is divisible by 40
Case b: m = 10 and n = 3, in which case mn is not divisible by 40
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: n is divisible by 4
There are several values of m and n that satisfy this condition. Here are two possible cases:
Case a: m = 10 and n = 4, in which case mn is divisible by 40
Case b: m = 3 and n = 4, in which case mn is not divisible by 40
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 1: If m is divisible by 10, then m = 10k (for some integer k)
Statement 2: If n is divisible by 4, then n = 4j (for some integer j)
So, mn = (10k)(4j) = 40kj
As we can see, mn is a multiple of 40, which means mn is definitely divisible by 40
Since we can answer the target question with certainty, the combined statements are SUFFICIENT
Answer = C
Cheers,
Brent

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Hey Brent,
Thanks for your reply.
Can you explain this problem in terms of
Statement one tells us 2 x 5...
Statement two tells us 2 x 2...
I want to prove insufficieny based on the above concept.
Thanks for your reply.
Can you explain this problem in terms of
Statement one tells us 2 x 5...
Statement two tells us 2 x 2...
I want to prove insufficieny based on the above concept.
Brent@GMATPrepNow wrote:SOME BACKGROUND: A lot of integer property questions can be solved using prime factorization.dddanny2006 wrote:Is mn divisible by 40?
1) m is divisible by 10
2) n is divisible by 4
For questions involving divisibility, divisors, factors and multiples, we can say:
If N is divisible by k, then k is "hiding" within the prime factorization of N
Examples:
24 is divisible by 3 <> 24 = (2)(2)(2)(3)
70 is divisible by 5 <> 70 = (2)(5)(7)
330 is divisible by 6 <> 330 = (2)(3)(5)(11)
56 is divisible by 8 <> 56 = (2)(2)(2)(7)
Okay, now onto the question at hand . . .
Target question: Is mn divisible by 40?
Since 40 = (2)(2)(2)(5), we can rephrase the target question as . . .
REPHRASED target question: Are there three 2's and one 5 hiding in the prime factorization of mn?
Statement 1: m is divisible by 10
There are several values of m and n that satisfy this condition. Here are two possible cases:
Case a: m = 10 and n = 8, in which case mn is divisible by 40
Case b: m = 10 and n = 3, in which case mn is not divisible by 40
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: n is divisible by 4
There are several values of m and n that satisfy this condition. Here are two possible cases:
Case a: m = 10 and n = 4, in which case mn is divisible by 40
Case b: m = 3 and n = 4, in which case mn is not divisible by 40
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 1: Since 10 = (2)(5), statement 1 tells us that there is one 2 and one 5 hiding in the prime factorization of m.
Statement 2: Since 4 = (2)(2), statement 2 tells us that there are two 2's hiding in the prime factorization of n.
So, there must be three 2's and one 5 hiding in the prime factorization of mn
Since we can answer the target question with certainty, the combined statements are SUFFICIENT
Answer = C
Cheers,
Brent
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Sure thing.dddanny2006 wrote:Hey Brent,
Thanks for your reply.
Can you explain this problem in terms of
Statement one tells us 2 x 5...
Statement two tells us 2 x 2...
I want to prove insufficiency based on the above concept.
Statement 1: m is divisible by 10
Since 10 = (2)(5), statement 1 tells us that there is one 2 and one 5 hiding in the prime factorization of m.
So, we can be certain that there is at least one 2 and one 5 hiding in the prime factorization of mn.
Can we then conclude that there MUST be three 2's and one 5 hiding in the prime factorization of mn? No.
It COULD be the case that three 2's and one 5 are hiding in the prime factorization of mn, but it COULD be the case that three 2's and one 5 are not hiding in the prime factorization of mn
As such, statement 1 is NOT SUFFICIENT
Statement 2: n is divisible by 4
Since 4 = (2)(2), statement 2 tells us that there are two 2's hiding in the prime factorization of n.
So, we can be certain that there are two 2's hiding in the prime factorization of mn.
Can we then conclude that there MUST be three 2's and one 5 hiding in the prime factorization of mn? No.
It COULD be the case that three 2's and one 5 are hiding in the prime factorization of mn, but it COULD be the case that three 2's and one 5 are not hiding in the prime factorization of mn
As such, statement 2 is NOT SUFFICIENT
Does that help?
Cheers,
Brent

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 Posts: 209
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Wow,brilliant.Thanks champ.Do you suggest testing values to be a better method than the prime factorization method?Which one's better and helpful in the longrun?Im not that comfortable with similar problems,whats the best way to master these?
Brent@GMATPrepNow wrote:Sure thing.dddanny2006 wrote:Hey Brent,
Thanks for your reply.
Can you explain this problem in terms of
Statement one tells us 2 x 5...
Statement two tells us 2 x 2...
I want to prove insufficiency based on the above concept.
Statement 1: m is divisible by 10
Since 10 = (2)(5), statement 1 tells us that there is one 2 and one 5 hiding in the prime factorization of m.
So, we can be certain that there is at least one 2 and one 5 hiding in the prime factorization of mn.
Can we then conclude that there MUST be three 2's and one 5 hiding in the prime factorization of mn? No.
It COULD be the case that three 2's and one 5 are hiding in the prime factorization of mn, but it COULD be the case that three 2's and one 5 are not hiding in the prime factorization of mn
As such, statement 1 is NOT SUFFICIENT
Statement 2: n is divisible by 4
Since 4 = (2)(2), statement 2 tells us that there are two 2's hiding in the prime factorization of n.
So, we can be certain that there are two 2's hiding in the prime factorization of mn.
Can we then conclude that there MUST be three 2's and one 5 hiding in the prime factorization of mn? No.
It COULD be the case that three 2's and one 5 are hiding in the prime factorization of mn, but it COULD be the case that three 2's and one 5 are not hiding in the prime factorization of mn
As such, statement 2 is NOT SUFFICIENT
Does that help?
Cheers,
Brent

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 Posts: 209
 Joined: Thu Jan 12, 2012 12:59 pm
@ Brent
Could you please help me out with this problem too,in the same method that you last solved the oter one for me.
Is m divisible by 8?
1.mn is divisible by 40
2.n is divisible by 5
Please solve it the same way you last did.
Thanks again.
Could you please help me out with this problem too,in the same method that you last solved the oter one for me.
Is m divisible by 8?
1.mn is divisible by 40
2.n is divisible by 5
Please solve it the same way you last did.
Thanks again.
Brent@GMATPrepNow wrote:Sure thing.dddanny2006 wrote:Hey Brent,
Thanks for your reply.
Can you explain this problem in terms of
Statement one tells us 2 x 5...
Statement two tells us 2 x 2...
I want to prove insufficiency based on the above concept.
Statement 1: m is divisible by 10
Since 10 = (2)(5), statement 1 tells us that there is one 2 and one 5 hiding in the prime factorization of m.
So, we can be certain that there is at least one 2 and one 5 hiding in the prime factorization of mn.
Can we then conclude that there MUST be three 2's and one 5 hiding in the prime factorization of mn? No.
It COULD be the case that three 2's and one 5 are hiding in the prime factorization of mn, but it COULD be the case that three 2's and one 5 are not hiding in the prime factorization of mn
As such, statement 1 is NOT SUFFICIENT
Statement 2: n is divisible by 4
Since 4 = (2)(2), statement 2 tells us that there are two 2's hiding in the prime factorization of n.
So, we can be certain that there are two 2's hiding in the prime factorization of mn.
Can we then conclude that there MUST be three 2's and one 5 hiding in the prime factorization of mn? No.
It COULD be the case that three 2's and one 5 are hiding in the prime factorization of mn, but it COULD be the case that three 2's and one 5 are not hiding in the prime factorization of mn
As such, statement 2 is NOT SUFFICIENT
Does that help?
Cheers,
Brent
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 Brent@GMATPrepNow
 GMAT Instructor
 Posts: 16207
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Target question: Is m divisible by 8?dddanny2006 wrote:@ Brent
Could you please help me out with this problem too,in the same method that you last solved the other one for me.
Is m divisible by 8?
1) mn is divisible by 40
2) n is divisible by 5
Since 8 = (2)(2)(2), we can rephrase the target question as follows:
REPHRASED target question: Are three 2's hiding in the prime factorization of 8?
Statement 1: mn is divisible by 40
Since 40 = (2)(2)(2)(5), this tells us that there are three 2's and one 5 hiding in the prime factorization of mn.
However, we can't be certain whether or not there are three 2's hiding in the prime factorization of m.
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT
Aside: we can also show that statement 2 is not sufficient by considering these two contradictory cases.
Case a: m = 8 and n = 5, in which case m is divisible by 8
Case b: m = 4 and n = 10, in which case m is not divisible by 8
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: n is divisible by 5
This tells us nothing about m
So, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Consider these two contradictory cases.
Case a: m = 8 and n = 5, in which case m is divisible by 8
Case b: m = 4 and n = 10, in which case m is not divisible by 8
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT
Answer = E
Cheers,
Brent

 Master  Next Rank: 500 Posts
 Posts: 209
 Joined: Thu Jan 12, 2012 12:59 pm
Hey Brent,
What if I change Statement 1 to mn is divisible by 8,everything else stays the same
Thanks
Dan
What if I change Statement 1 to mn is divisible by 8,everything else stays the same
Thanks
Dan
Brent@GMATPrepNow wrote:Target question: Is m divisible by 8?dddanny2006 wrote:@ Brent
Could you please help me out with this problem too,in the same method that you last solved the other one for me.
Is m divisible by 8?
1) mn is divisible by 40
2) n is divisible by 5
Since 8 = (2)(2)(2), we can rephrase the target question as follows:
REPHRASED target question: Are three 2's hiding in the prime factorization of 8?
Statement 1: mn is divisible by 40
Since 40 = (2)(2)(2)(5), this tells us that there are three 2's and one 5 hiding in the prime factorization of mn.
However, we can't be certain whether or not there are three 2's hiding in the prime factorization of m.
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT
Aside: we can also show that statement 2 is not sufficient by considering these two contradictory cases.
Case a: m = 8 and n = 5, in which case m is divisible by 8
Case b: m = 4 and n = 10, in which case m is not divisible by 8
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: n is divisible by 5
This tells us nothing about m
So, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Consider these two contradictory cases.
Case a: m = 8 and n = 5, in which case m is divisible by 8
Case b: m = 4 and n = 10, in which case m is not divisible by 8
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT
Answer = E
Cheers,
Brent
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 Brent@GMATPrepNow
 GMAT Instructor
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Hey Dan,dddanny2006 wrote:Hey Brent,
What if I change Statement 1 to mn is divisible by 8,everything else stays the same
Thanks
Dan
There are already a couple of different questions in this thread.
How about posting this one as a new thread.
Cheers,
Brent

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 Posts: 209
 Joined: Thu Jan 12, 2012 12:59 pm
Cool Brent.
Here are the links
https://www.beatthegmat.com/trickydsque ... tml#701946
Here are the links
https://www.beatthegmat.com/trickydsque ... tml#701946
Brent@GMATPrepNow wrote:Hey Dan,dddanny2006 wrote:Hey Brent,
What if I change Statement 1 to mn is divisible by 8,everything else stays the same
Thanks
Dan
There are already a couple of different questions in this thread.
How about posting this one as a new thread.
Cheers,
Brent