Number to be doubled to halve the expression

gmattesttaker2 wrote:Hello,

Can you please tell me how to solve this:

[ a + (b/c) ] / [ d/e ]

If the value of the expression above is to be halved by doubling exactly one of the five numbers a, b, c, d, or e, which should be doubled?

(A) a
(B) b
(C) c
(D) d
(E) e

OA: D

When I simplify [ a + (b/c) ] / [ d/e ] I get:

[ ( (ac + b)e ) / (cd) ] x [ 1/2 ]

However, I was not sure how to solve from here.


Thanks for your help,
Sri

Sri,

Does question has additional info as "all numbers are integers" ?

Let me assume as integers,

(a+ b/c) * (e/d) => (ae/d + be/cd)
check for the common denominator.(Since multiplying the denominator twice will end up halved)

So Ans is D

Cross Verify,
Let a=e=d=c=1
then,
1/d +1/d = 2/d
If d=1 then 2/1 = 2
if d=2 then 2/2 = 1

Hence d is correct.

Regards,
Uva.

gmattesttaker2 wrote:Hello,

Can you please tell me how to solve this:

[ a + (b/c) ] / [ d/e ]

If the value of the expression above is to be halved by doubling exactly one of the five numbers a, b, c, d, or e, which should be doubled?

(A) a
(B) b
(C) c
(D) d
(E) e

OA: D

When I simplify [ a + (b/c) ] / [ d/e ] I get:

[ ( (ac + b)e ) / (cd) ] x [ 1/2 ]

However, I was not sure how to solve from here.


Thanks for your help,
Sri

Pleased to put my inputs for this question based on pure Number theory -


First of all remember an Important rule , if the Denominator of a fraction is increased then the fraction as a decreases in magnitude and vice versa.

Eg -

1/2 ----> 1/4

1/3 ----> 1/4


Further if Denominator is increased by a factor " D " then the fraction gets reduced by " D "

1/2 ===> 1/4

0.5 ===> 0.25


Now with the current problem in hand -

I have worked out with the problem and reduced the complex looking algebraic expression into simple understandable form.

Upon careful observation one can find that the denominator consists of 2 variables C and D

Now carefully observe the variable C can be our answer but it is already present in the Numerator , so if we select it as answer it will not help us..

Example -

15 / 3 ==== > ( 5 * 3 ) / 3

45 /9 ======> ( 5 * 3 * 3 ) / 3 *3

Observe that both Numerator and Denominator when multiplied by same factor results in no change of the Fraction. ( This is another rule of Number System)

So we can Ignore (C)

Now we are left with only d , if we multiple d by 2 then the original fraction will reduce by 1/2

Hence IMO (D) as the correct answer...

gmattesttaker2 wrote:Hello,

Can you please tell me how to solve this:

[ a + (b/c) ] / [ d/e ]

If the value of the expression above is to be halved by doubling exactly one of the five numbers a, b, c, d, or e, which should be doubled?

(A) a
(B) b
(C) c
(D) d
(E) e

OA: D

When I simplify [ a + (b/c) ] / [ d/e ] I get:

[ ( (ac + b)e ) / (cd) ] x [ 1/2 ]

However, I was not sure how to solve from here.


Thanks for your help,
Sri

You can also simply pick numbers, such as the following:

a = 1
b = 2
c = 3
d = 4
e = 5

Plug the numbers in the expression given and you will get simplified expression as such:

(2ea/d) + (2eb/dc)
which equals = (5/3)(5/4)
= 25/12.

Now to get half of this, multiply by
1/2...and you get 25/24

So the way we got 24 was, 4 * 2 = 8
8 * 3 = 24

Thus the answer is D

Nupur.nk wrote:

gmattesttaker2 wrote:Hello,

Can you please tell me how to solve this:

[ a + (b/c) ] / [ d/e ]

If the value of the expression above is to be halved by doubling exactly one of the five numbers a, b, c, d, or e, which should be doubled?

(A) a
(B) b
(C) c
(D) d
(E) e

OA: D

When I simplify [ a + (b/c) ] / [ d/e ] I get:

[ ( (ac + b)e ) / (cd) ] x [ 1/2 ]

However, I was not sure how to solve from here.


Thanks for your help,
Sri

You can also simply pick numbers, such as the following:

a = 1
b = 2
c = 3
d = 4
e = 5

Plug the numbers in the expression given and you will get simplified expression as such:

(2ea/d) + (2eb/dc)
which equals = (5/3)(5/4)
= 25/12.

Now to get half of this, multiply by
1/2...and you get 25/24

So the way we got 24 was, 4 * 2 = 8
8 * 3 = 24

Thus the answer is D

Hello Nupur,

Thanks for your explanation with the example. I was clear till the following:

So the way we got 24 was, 4 * 2 = 8
8 * 3 = 24

I was thinking that since we just multiply the denominator of 25/12 by 2, how we arrive at the above.

Thanks,
Sri