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Number to be doubled to halve the expression

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Number to be doubled to halve the expression

by gmattesttaker2 » Thu Feb 20, 2014 10:50 pm
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
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by Uva@90 » Thu Feb 20, 2014 11:35 pm
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.
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by [email protected] » Fri Feb 21, 2014 12:38 am
Hi Sri,

This question is based on an arithmetic Number Property: what do you have to do to HALVE a fraction?

Under normal circumstances, there are 2 ways to halve a fraction:
1) Halve the numerator
2) Double the denominator

The prompt gives us the extra piece of information that we need to DOUBLE one of the 5 variables. This means that we should be looking in the denominator.

The denominator is (D/E), so what do we have to DOUBLE to double the value of this fraction?....The D... By doubling that value, the denominator will double and the overall fraction will be halved.

Final Answer: D

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by Abhishek009 » Sun Feb 23, 2014 9:54 am
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...
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by Nupur.nk » Mon Feb 24, 2014 1:07 pm
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
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by gmattesttaker2 » Wed Feb 26, 2014 10:40 pm
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
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