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# Find the greatest number that will divide 55, 127 and 175 so as to lea

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Re: Find the greatest number that will divide 55, 127 and 175 so as to lea [#permalink]
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Bunuel wrote:
Find the greatest number that will divide 55, 127 and 175 so as to leave the same remainder in each case.

(A) 12
(B) 18
(C) 24
(D) 35
(E) 36

Say n is the greatest such value.

55 = na + R
127 = nb + R
175 = nc + R

72 = n(b - a)
48 = n(c - b)
120 = n(c - a)

So n is the greatest common factor of 72, 48 and 120.
n must be 24

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Find the greatest number that will divide 55, 127 and 175 so as to lea [#permalink]
Bunuel wrote:
Find the greatest number that will divide 55, 127 and 175 so as to leave the same remainder in each case.

(A) 12
(B) 18
(C) 24
(D) 35
(E) 36

based on range of answer choices,
assume difference between first two quotients=2
r=remainder
n=number
(127-r)/n-(55-r)/n=3
n=36
testing, 36 doesn't work on all three dividends
assume difference of 3 beween first two quotients
n=24
works on all three dividends
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Re: Find the greatest number that will divide 55, 127 and 175 so as to lea [#permalink]
Bunuel wrote:
Find the greatest number that will divide 55, 127 and 175 so as to leave the same remainder in each case.

(A) 12
(B) 18
(C) 24
(D) 35
(E) 36

I actually solved using plug in the answer choices:
Since the question has specifically asked for greatest no. so start with 36 , we get difference as 19,19, 31
35 , 20, 22, 0

whereas with 24, we get 7,7,7 hence correct.. option C
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Re: Find the greatest number that will divide 55, 127 and 175 so as to lea [#permalink]
saurabh9gupta wrote:
There is a trick to this question. I am not sure whether this is asked in the GMAT.

GCF of the difference among 3 numbers.

Differences are 72, 48 and 120

And HCF Is 24.

Basically this question hinges on the concept that if a number A is divisible by N
And
B is divisible by N

So A+B and A-B are also divisible by N

Posted from my mobile device

and the only reason why we took the difference is to get rid of the unknown R?
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Re: Find the greatest number that will divide 55, 127 and 175 so as to lea [#permalink]

72 = n(b - a)
48 = n(c - b)
120 = n(c - a)

VeritasKarishma - Thanks for the explanation.
Conceptual doubt: Why do we have to arrive to this step before we take the GCD. Why can we not take GCD directly with the 3 original numbers (55, 127, 175).
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Find the greatest number that will divide 55, 127 and 175 so as to lea [#permalink]
Bunuel wrote:
Find the greatest number that will divide 55, 127 and 175 so as to leave the same remainder in each case.

(A) 12
(B) 18
(C) 24
(D) 35
(E) 36

Even though it was a bit brute force i applied the same first the middle value

7 was the reminder when 12 was worked out
next was 24 and it worked
=24(2) +7
127=24(5) +7
175=24(7) +7

However i didn't stop worked out 35 and it was far off
and 36 didn't have a chance so does 35

Even though right answer took some time it's still right
Therefore IMO C
Find the greatest number that will divide 55, 127 and 175 so as to lea [#permalink]
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