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Bunuel
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If the value of the expression above is to be halved by doubling exact 03 May 2018, 02:34
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D
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85% (01:00) correct 15% (01:01) wrong based on 103 sessions

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\(\frac{a + \frac{b}{c}}{\frac{d}{e}}\)

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
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D
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If the value of the expression above is to be halved by doubling exact Updated on: 03 May 2018, 15:47
Originally posted by u1983 on 03 May 2018, 04:50.
Last edited by u1983 on 03 May 2018, 15:47, edited 1 time in total.
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Bunuel
\(\frac{a + \frac{b}{c}}{\frac{d}{e}}\)

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
Show more


\(\frac{a + \frac{b}{c}}{\frac{d}{e}}\) = \(\frac{\frac{(ab+c)}{c}}{\frac{d}{e}}\) = \(\frac{(ab+c)}{c} *\frac{e}{d}\) = \(\frac{{(ab+c)e}}{{c d}}\)

As per the Q-stem : the expression is to be halved by doubling one of the five numbers
Thus , the variable should be in the denominator...... either \(c\) or \(d\)
Now if we take c , as the same has its presence in numerator ... the exact doubling will not happen.
But in case of d, as it donot have numerator presence, the resulting expression ( after doubling d) will become 1/2 of the previous.

\(\frac{{(ab+c)e}}{{c 2 d}}\)

Thus I would go for D
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If the value of the expression above is to be halved by doubling exact 03 May 2018, 12:24
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(ac+b)(e/cd); hence d should be doubled to get half value
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If the value of the expression above is to be halved by doubling exact 03 May 2018, 15:21
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Bunuel
\(\frac{a + \frac{b}{c}}{\frac{d}{e}}\)

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
Show more

We need to halve this expression:
\(\frac{a + \frac{b}{c}}{\frac{d}{e}}\)

So we multiply by 1/2:

\(\frac{a + \frac{b}{c}}{\frac{d}{e}}*\frac{1}{2}\)

Which number gets doubled? d

Answer: D
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If the value of the expression above is to be halved by doubling exact 04 May 2018, 10:25
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Bunuel
\(\frac{a + \frac{b}{c}}{\frac{d}{e}}\)

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
Show more

Notice that (a + b/c)/(d/c) = (a + b/c)(c/d) = ac/d + b/d.

If we double d we have:

(a + b/c)/(2d/c) = (a + b/c)(c/(2d)) = ac/(2d) + b/(2d) = (1/2)(ac/d) + (1/2)(b/d) = (1/2)(ac/d + b/d)

So we see that by doubling d, the entire expression is halved.

Alternate Solution:

Let’s initially set all five variables equal to 1. We would have:

[1+ (1/1)] /(1/1) = 2/1 = 2

Our goal is to determine which of the 1’s must be doubled so that the value of the entire expression is halved (i.e., equal to 1 instead of 2).

If a is doubled, we have: [2+ (1/1)] /(1/1) = 3/1 = 3 This is not correct.

If b is doubled, we have [1+ (2/1)] /(1/1) = 3/1 = 3 This is not correct.

If c is doubled, we have [1+ (1/2)] /(1/1) = (1.5/1 = 1.5 This is not correct.

If d is doubled, we have [1+ (1/1)] /(2/1) = 2/2 = 1 This is correct.

If e is doubled, we have [1+ (1/1)] /(1/2) = 2/(1/2) = 4 This is not correct.

Answer: D
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If the value of the expression above is to be halved by doubling exact 17 Nov 2021, 10:30
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if D is doubled, then the expression d/e is also doubled, meaning the denominator is doubled, therefore halving the whole expression.
Ans=D
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Bunuel
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