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The sum of two numbers is 216 and their H.C.F. is 27. The numbers are

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Bunuel
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The sum of two numbers is 216 and their H.C.F. is 27. The numbers are [#permalink] New post   Updated on: 04 Aug 2021, 09:02
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The sum of two positive integers is 216 and their highest common factor is 27. What are these numbers ?

(A) 27, 189
(B) 54, 162
(C) 81, 216
(D) 108, 118
(E) 116, 110
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A

Originally posted by Bunuel on 04 Aug 2021, 06:45.
Last edited by chetan2u on 04 Aug 2021, 09:02, edited 1 time in total.
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DHRJ0032
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The sum of two numbers is 216 and their H.C.F. is 27. The numbers are [#permalink] New post   Updated on: 04 Aug 2021, 09:29
Both A and C are the possible answers.

Posted from my mobile device
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File comment: bunuel has changed the option C from (81,135) to (81,216)

now, A will be the answer.
IMG_20210804_212406.jpg
IMG_20210804_212406.jpg [ 3.13 MiB | Viewed 2708 times ]


Originally posted by DHRJ0032 on 04 Aug 2021, 08:55.
Last edited by DHRJ0032 on 04 Aug 2021, 09:29, edited 1 time in total.
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chetan2u
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The sum of two numbers is 216 and their H.C.F. is 27. The numbers are [#permalink] New post   04 Aug 2021, 09:01
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Bunuel wrote:
The sum of two positive integers is 216 and their highest common factor is 27. What are these numbers ?

(A) 27, 189
(B) 54, 162
(C) 81, 135
(D) 108, 118
(E) 116, 110



Let the numbers be 27a and 27b, where a and b are co prime.
So 27a+27b=216………a+b=8
Now a and b are co-primes, so they can be 1 and 7 or 3 and 5

Thus, possible solutions
1) 27*1=27 and 27*7=189
2) 27*3=81 and 27*5=135

A is in the options.

Use options

As the HCF is 27, we cannot have both numbers even.
B, D and E are out.
The total in C does not come to 216. Eliminate


A
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Re: The sum of two numbers is 216 and their H.C.F. is 27. The numbers are [#permalink] New post   04 Aug 2021, 09:33
Bunuel has changed the option C from (81,135) to (81,216) after i posted the solution just to see my effort went into vain. :(
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chetan2u
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Re: The sum of two numbers is 216 and their H.C.F. is 27. The numbers are [#permalink] New post   04 Aug 2021, 09:41
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DHRJ0032 wrote:
Bunuel has changed the option C from (81,135) to (81,216) after i posted the solution just to see my effort went into vain. :(



A question cannot have two answers. So the options have been changed accordingly as there was an error in the options.
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Re: The sum of two numbers is 216 and their H.C.F. is 27. The numbers are [#permalink] New post   04 Aug 2021, 09:48
yeah for sure !
I said that because i checked my solution many times to arrive at the conclusion that both A and C are correct.
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Re: The sum of two numbers is 216 and their H.C.F. is 27. The numbers are [#permalink] New post   04 Aug 2021, 10:04
The sum of two positive integers is 216 and their highest common factor is 27. What are these numbers ?

a +b = 216 and 3^3 * (x+y) = 216
so, x +y = 8, now, x and y must have HCF as 1.

(A) 27, 189 -> x = 1 and y= 7. Possible.
(B) 54, 162 -> x =2 and y = 8, not possible as HCF = 2.
(C) 81, 216 -> Sum not equal to 216.
(D) 108, 118 -> x = 4, y not an integer.
(E) 116, 110 -> x and y both are not integers.

So, I think A. :)
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Re: The sum of two numbers is 216 and their H.C.F. is 27. The numbers are [#permalink] New post   07 Aug 2021, 09:55
DHRJ0032 wrote:
Both A and C are the possible answers.

Posted from my mobile device


Sum in case of C is more than 216
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DHRJ0032
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Re: The sum of two numbers is 216 and their H.C.F. is 27. The numbers are [#permalink] New post   07 Aug 2021, 19:36
ShaikhMoice wrote:
DHRJ0032 wrote:
Both A and C are the possible answers.

Posted from my mobile device


Sum in case of C is more than 216


Yeah you are right. But earlier option C was (81,135).refer to my solution. When I posted the solution then only Bunuel has changed the option C to (81,216).🙄
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Re: The sum of two numbers is 216 and their H.C.F. is 27. The numbers are [#permalink]
07 Aug 2021, 19:36
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