Math Expert Joined: 02 Sep 2009 Posts: 87541
The sum of two numbers is 216 and their H.C.F. is 27. The numbers are [#permalink]
00:00
Difficulty:
Question Stats: Hide Show timer StatisticsThe 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 _________________
Originally posted by Bunuel on 04 Aug 2021, 05:45. Edited
Manager Joined: 27 Feb 2020 Posts: 110 Location: United States Concentration: Finance, Operations GPA: 4 WE:Operations (Aerospace and Defense)
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. Posted from my mobile device
Attachments
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.
Math Expert Joined: 02 Aug 2009 Posts: 10654
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 _________________
Manager Joined: 27 Feb 2020 Posts: 110 Location: United States Concentration: Finance, Operations GPA: 4 WE:Operations (Aerospace and Defense)
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.
Math Expert Joined: 02 Aug 2009 Posts: 10654
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.
Manager Joined: 27 Feb 2020 Posts: 110 Location: United States Concentration: Finance, Operations GPA: 4 WE:Operations (Aerospace and Defense)
Re: The sum of two numbers is 216 and their H.C.F. is 27. The numbers are [#permalink] yeah for sure !
SVP Joined: 14 Jul 2020 Posts: 1857 Location: India
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.
Manager Joined: 25 Jan 2021 Posts: 103
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
Manager Joined: 27 Feb 2020 Posts: 110 Location: United States Concentration: Finance, Operations GPA: 4 WE:Operations (Aerospace and Defense)
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 |
If the HCF of two numbers is 27 and their sum is 216 find these numbers
zusammenhängende Posts
Urheberrechte © © 2024 frojeostern Inc.
