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The difference of two integers is 30. Which of the following is a poss
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13 Sep 2021, 01:48

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Question Stats:

The difference of two integers is 30. Which of the following is a possible ratio of the larger to the smaller integer?

Indicate all such ratios.

(A) 5:2

(B) 7:3

(C) 8:5

(D) 9:4

(E) 11:1

_________________

Indicate all such ratios.

(A) 5:2

(B) 7:3

(C) 8:5

(D) 9:4

(E) 11:1

_________________

The difference of two integers is 30. Which of the following is a poss
[#permalink]
13 Sep 2021, 02:15

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Subtract num and denominator and check if it is divisible by 3.

For eg:

5 :2

5x - 2x = 30

Therefore 3x = 30 , x = 10.

For eg:

5 :2

5x - 2x = 30

Therefore 3x = 30 , x = 10.

Re: The difference of two integers is 30. Which of the following is a poss
[#permalink]
20 Sep 2021, 09:25

2

Let bid number be a and small be b

a-b=30

(A) 5/2=a/b -> a=5/2b

a-b=30 -> 5/2b-b=30 -> 3/2b=30 -> b=20

Hence possible

Do it for all options

a-b=30

(A) 5/2=a/b -> a=5/2b

a-b=30 -> 5/2b-b=30 -> 3/2b=30 -> b=20

Hence possible

Do it for all options

Re: The difference of two integers is 30. Which of the following is a poss
[#permalink]
18 Jul 2023, 14:57

1

Let the big integer be "a" and small integer be "b".

thus given a - b= 30

now we have the answer choices in the ratio form , we can use that ratio form to put in our original equation to check if we can get a valid value .

E.g. option A states 5:2 so let the ratio be x between them , thus a =5x and b=2x

and a - b = 30 --> 5x-2x=30 --> 3x=30 or x=10 , thus we get a valid ratio and the option choice is correct, in case we do not get an integer ratio we can deem that answer choice to be incorrect

Option B --> 7:3 i.e. a=7x and b =3x and 7x-3x=30 --> 4x= 30 , thus we will not get a valid ratio for our integers , option incorrect

Option C --> a=8x , b =5x , thus 8x-5x=30 --> 3x=10 , x=10 , valid , correct

Option D --> a = 9x , b =4x , thus 9x-4x=30 --> 5x=30 , x=6 , valid ratio , correct

Option E --> a = 11x, b = x, thus 11x-x=30 --> 10x=30 , x=3 , valid ratio , correct

Answers A,C,D,E

thus given a - b= 30

now we have the answer choices in the ratio form , we can use that ratio form to put in our original equation to check if we can get a valid value .

E.g. option A states 5:2 so let the ratio be x between them , thus a =5x and b=2x

and a - b = 30 --> 5x-2x=30 --> 3x=30 or x=10 , thus we get a valid ratio and the option choice is correct, in case we do not get an integer ratio we can deem that answer choice to be incorrect

Option B --> 7:3 i.e. a=7x and b =3x and 7x-3x=30 --> 4x= 30 , thus we will not get a valid ratio for our integers , option incorrect

Option C --> a=8x , b =5x , thus 8x-5x=30 --> 3x=10 , x=10 , valid , correct

Option D --> a = 9x , b =4x , thus 9x-4x=30 --> 5x=30 , x=6 , valid ratio , correct

Option E --> a = 11x, b = x, thus 11x-x=30 --> 10x=30 , x=3 , valid ratio , correct

Answers A,C,D,E

The difference of two integers is 30. Which of the following is a poss
[#permalink]
08 Sep 2023, 09:44

1

Take the difference of numerator and denominator in each option , 30 should be the multiple of the difference. Therefore, a,c,d,e is the answer

gmatclubot

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