I would quickly write down different numbers satisfying statement 1 (variable n) and then come up with 2 numbers for variable t and check the remainder of the product nt in both cases and try to eliminate choices.
n can take values such as 2,5,8,11,14,17
t can take values such as 3,8,13,18, etc.
you can see you can get remainder as 6 (if n= 2, t =3) or 1 (n=17, t =18), no definite answer even after combining statements, mark E and move on...
not a solid approach, but it'll work (and not so time consuming <- my opinion)
hope this helps.
Question from Prep
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Source: Beat The GMAT — Data Sufficiency |
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gmatboost
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This is a hard question.
From the question prompt:
n can be written as 3k+2
t can be written as 5j+3
This is because we know they are a certain amount (2, 3) more than a multiple of some number (3, 5)
Statement 1:
n - 2 is divisible by 5 means that n is 2 more than a multiple of 5
Recall that n is also 2 more than a multiple of 3 (from the prompt)
Putting those together, n is 2 more than a multiple of 3 and 5, which is also known as a multiple of 15
So, n is 2 more than a multiple of 15 and can be written as 15k + 2
Multiply this by t: (15k+2)(5j+3) = 75kj + 45k + 10j + 6
The first two terms are each evenly divisible by 15, but 10j is not necessarily, and we do not know anything more about j. Insufficient.
Statement 2:
t is divisible by 3
Recall that t is also 3 more than a multiple of 5 (from the prompt)
This is perhaps the hardest step of all:
Putting those together, t is 3 more than a multiple of 15 (it cannot be 8 more or 13 more, because then it would satisfy being 3 more than a multiple of 5, but would not satisfy being a multiple of 3)
So, t can be written as 15j + 3
Multiply this by n: (3k+2)(15j+3) = 45kj + 30j + 9k + 6
The first two terms are again each evenly divisible by 15, but 9k is not necessarily, and we do not know anything more about k. Insufficient.
Combined:
n = 15k+2
t = 15j+3
nt = (15k + 2)(15j + 3) = 225jk + 30j + 45k + 6
Now, the first three terms are each evenly divisible by 15. All we have left is +6, so the remainder when nt is divided by 15 is always 6. Sufficient.
From the question prompt:
n can be written as 3k+2
t can be written as 5j+3
This is because we know they are a certain amount (2, 3) more than a multiple of some number (3, 5)
Statement 1:
n - 2 is divisible by 5 means that n is 2 more than a multiple of 5
Recall that n is also 2 more than a multiple of 3 (from the prompt)
Putting those together, n is 2 more than a multiple of 3 and 5, which is also known as a multiple of 15
So, n is 2 more than a multiple of 15 and can be written as 15k + 2
Multiply this by t: (15k+2)(5j+3) = 75kj + 45k + 10j + 6
The first two terms are each evenly divisible by 15, but 10j is not necessarily, and we do not know anything more about j. Insufficient.
Statement 2:
t is divisible by 3
Recall that t is also 3 more than a multiple of 5 (from the prompt)
This is perhaps the hardest step of all:
Putting those together, t is 3 more than a multiple of 15 (it cannot be 8 more or 13 more, because then it would satisfy being 3 more than a multiple of 5, but would not satisfy being a multiple of 3)
So, t can be written as 15j + 3
Multiply this by n: (3k+2)(15j+3) = 45kj + 30j + 9k + 6
The first two terms are again each evenly divisible by 15, but 9k is not necessarily, and we do not know anything more about k. Insufficient.
Combined:
n = 15k+2
t = 15j+3
nt = (15k + 2)(15j + 3) = 225jk + 30j + 45k + 6
Now, the first three terms are each evenly divisible by 15. All we have left is +6, so the remainder when nt is divided by 15 is always 6. Sufficient.
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It's a total of 20+ hours of expert instruction for an introductory price of just $10.
View sample questions and tips without signing up, or sign up now for full access.
Also, check out the most useful GMAT Math blog on the internet here.
dont know what I was thinking-
navami
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Precisely ..
From Question we get . n = a*3 + 2
t = b*5 + 3
n*t = 15 * a * b + 6 + 10b + 9a
6 + 10b + 9a / 15 = ?
1) statement 1 says n - 2 is multiple of 5 . and n = a*3 + 2 so n-2 = a*2 +2 -2 = a*3 is multiple of 5. or a is multiple of 5.
2) statement 2 says ( likewise) b is multiple of 3
so now we need to find if 6 + 10b + 9a / 15 = ?
10b and 9a would be divisible by 15 { From statement 1 + statement 2}
but what about 6 ??????
so we know that (6 + 10b + 9a / 15 = NO)
From Question we get . n = a*3 + 2
t = b*5 + 3
n*t = 15 * a * b + 6 + 10b + 9a
6 + 10b + 9a / 15 = ?
1) statement 1 says n - 2 is multiple of 5 . and n = a*3 + 2 so n-2 = a*2 +2 -2 = a*3 is multiple of 5. or a is multiple of 5.
2) statement 2 says ( likewise) b is multiple of 3
so now we need to find if 6 + 10b + 9a / 15 = ?
10b and 9a would be divisible by 15 { From statement 1 + statement 2}
but what about 6 ??????
so we know that (6 + 10b + 9a / 15 = NO)
This time no looking back!!!
Navami
Navami
