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The sum of two numbers is 216 and their H.C.F. is 27. The numbers are [#permalink]
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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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Originally posted by Bunuel on 04 Aug 2021, 05:45.
Last edited by chetan2u on 04 Aug 2021, 08:02, edited 1 time in total.
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The sum of two numbers is 216 and their H.C.F. is 27. The numbers are [#permalink]
Both A and C are the possible answers.
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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 [ 3.13 MiB | Viewed 1341 times ]
Originally posted by DHRJ0032 on 04 Aug 2021, 07:55.
Last edited by DHRJ0032 on 04 Aug 2021, 08:29, edited 1 time in total.
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The sum of two numbers is 216 and their H.C.F. is 27. The numbers are [#permalink]
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=8Now a and b are co-primes, so they can be 1 and 7 or 3 and 5Thus, possible solutions1) 27*1=27 and 27*7=1892) 27*3=81 and 27*5=135A 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]
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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Re: The sum of two numbers is 216 and their H.C.F. is 27. The numbers are [#permalink]
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.
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Re: The sum of two numbers is 216 and their H.C.F. is 27. The numbers are [#permalink]
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]
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]
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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Re: The sum of two numbers is 216 and their H.C.F. is 27. The numbers are [#permalink]
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).🙄
Re: The sum of two numbers is 216 and their H.C.F. is 27. The numbers are [#permalink]
07 Aug 2021, 18:36