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

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Math Expert
Joined: 02 Sep 2009
Posts: 58381
Find the greatest number that will divide 55, 127 and 175 so as to lea  [#permalink]

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26 Nov 2018, 05:12
12
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Difficulty:

65% (hard)

Question Stats:

61% (02:14) correct 39% (02:09) wrong based on 177 sessions

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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

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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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26 Nov 2018, 06:55
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3
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
##### General Discussion
Intern
Joined: 24 Nov 2018
Posts: 6
Find the greatest number that will divide 55, 127 and 175 so as to lea  [#permalink]

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Updated on: 26 Nov 2018, 08:30
1
I got A. Luckily the strategy of plugging in the lowest and highest option, followed by the middle value worked out swimmingly!

Thanks to the others responses I have revised my solution...
ORIGINAL
55=12(4) + R7
127= 12(10) + R7
175= 12(14) + R7

After re-reading the question and seeing "greatest"...
REVISION
55=24(2) +7
127=24(5) +7
175=24(7) +7

Originally posted by sarajkluz on 26 Nov 2018, 07:07.
Last edited by sarajkluz on 26 Nov 2018, 08:30, edited 2 times in total.
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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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26 Nov 2018, 07:11
1
1
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]

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26 Nov 2018, 13:31
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]

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26 Nov 2018, 17:37
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]

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01 Dec 2018, 06:03
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]

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04 Jan 2019, 05:55

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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Re: Find the greatest number that will divide 55, 127 and 175 so as to lea   [#permalink] 04 Jan 2019, 05:55
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# Find the greatest number that will divide 55, 127 and 175 so as to lea

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