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If i, a and b are integers, is 4(3b + 2) = 5a?

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If i, a and b are integers, is 4(3b + 2) = 5a?  [#permalink]

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If i, a and b are integers, is 4(3b + 2) = 5a?

(1) If i is divided by 5 the quotient is a and the remainder is 3
(2) If i is divided by 12 the quotient is b and the remainder is 11

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Originally posted by reto on 17 May 2015, 10:00.
Last edited by reto on 23 May 2015, 02:25, edited 2 times in total.
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Re: If i, a and b are integers, is 4(3b + 2) = 5a?  [#permalink]

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New post 17 May 2015, 18:23
Cool question, and somewhat abstract. My first inclination on this problem was to think about primes, but then I realized that the problem is actually simpler than that. Distributing out the 4 to reorganize the given question stem, we have the question: "is 12b + 8 = 5a? " Statement 1 shows us that if we multiply 5*a, we will end up with "i - 3," because when "i" is divided by 5 you end up with a and then 3 more (remainder 3). The same concept applies to statement 2, where we see that 12*b will give us "i - 11." So substituting these expressions back into the initial question, we have "Is i - 11 + 8 = i - 3?" It then becomes apparent that they are equal, because "i-3 = i-3."

This entire problem revolved around putting everything in terms of "i." The biggest hint to do this was the fact that "i" was not even present in the initial questioned formula, so we had to incorporate it into the problem.

I hope this helps!
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Re: If i, a and b are integers, is 4(3b + 2) = 5a?  [#permalink]

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New post 12 Dec 2016, 09:43
We have to just find if 4(3b+2)=5a or not.

Statement 1: i=5a+3
No info. about b to prove the relation to be true.
Insufficient.

Statement 2: i=12b+11
Same as st.1
Insufficient.

Both statements together give us

5a+3=12b+11
5a=4(3b+2)

Hence C
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If i, a and b are integers, is 4(3b + 2) = 5a?  [#permalink]

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New post 25 May 2017, 06:01
reto wrote:
If i, a and b are integers, is 4(3b + 2) = 5a?

(1) If i is divided by 5 the quotient is a and the remainder is 3
(2) If i is divided by 12 the quotient is b and the remainder is 11


My solution is

Statement 1 : i = (5a + 3) .

now a could be 1 , 2 , 3 ,4 and so on .

now if a would be 1 , 5a would be 5
a would be 2 , 5a would be 10 .

Therefore 5a of the equation 4(3b+2) = 5a could be odd or even , but the left hand side 4( 3b +2 ) would be always even .
Hence the equation could be equal in case a =2 , could not be equal (sure shot) when a = 1 .

Statement 2 : i = 12 b + 11

b could be 1,2,3,4 you can add 0 also

but it does not matter what is the value of b is as long as we dont know the value of a , the statement is insufficient .

combined together , we will use algebraic approach to prove their equality .

12 b + 8 = 5a

i-11 + 8 = i -3

i-3 = i-3 , Hence the solution is C
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Re: If i, a and b are integers, is 4(3b + 2) = 5a?  [#permalink]

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New post 21 Oct 2017, 04:39
VeritasPrepBrandon wrote:
Cool question, and somewhat abstract. My first inclination on this problem was to think about primes, but then I realized that the problem is actually simpler than that. Distributing out the 4 to reorganize the given question stem, we have the question: "is 12b + 8 = 5a? " Statement 1 shows us that if we multiply 5*a, we will end up with "i - 3," because when "i" is divided by 5 you end up with a and then 3 more (remainder 3). The same concept applies to statement 2, where we see that 12*b will give us "i - 11." So substituting these expressions back into the initial question, we have "Is i - 11 + 8 = i - 3?" It then becomes apparent that they are equal, because "i-3 = i-3."

This entire problem revolved around putting everything in terms of "i." The biggest hint to do this was the fact that "i" was not even present in the initial questioned formula, so we had to incorporate it into the problem.

I hope this helps!


Pl see if my approach is correct, VeritasPrepBrandon

We have to prove, if 4(3b+2) = 5a
(1) says, i=5a+3, we don’t know the value of b. INSUFFICIENT
(2) says, i=12b+11, we don’t know the value of a. INSUFFICIENT
Now, (1) + (2), 12b+11 = 5a+3 => 12b+8=5a => 4(3b+2) = 5a. Option C correct
Re: If i, a and b are integers, is 4(3b + 2) = 5a? &nbs [#permalink] 21 Oct 2017, 04:39
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