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Anke has 5 fewer candies than Conrad. If Anke gives Conrad 5

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Joined: 07 Jun 2014
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GRE 1: Q167 V156
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Anke has 5 fewer candies than Conrad. If Anke gives Conrad 5 [#permalink]  14 Jun 2018, 14:25
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Question Stats:

80% (01:19) correct 20% (01:52) wrong based on 5 sessions
Anke has 5 fewer candies than Conrad. If Anke gives Conrad 5 candies, Conrad will then have 4 times as many candies as Anke. How many candies does Anke have?

(A) 5
(B) 10
(C) 15
(D) 20
(E) 25
[Reveal] Spoiler: OA

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Sandy
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Re: Anke has 5 fewer candies than Conrad. If Anke gives Conrad 5 [#permalink]  02 Jul 2018, 22:16
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sandy wrote:
Anke has 5 fewer candies than Conrad. If Anke gives Conrad 5 candies, Conrad will then have 4 times as many candies as Anke. How many candies does Anke have?

(A) 5
(B) 10
(C) 15
(D) 20
(E) 25

Here;

Let Anke = A and Conrad = C

Therefore;

A = C - 5 (since Anke has 5 candies fewer than Conard)

and 4(A - 5) = C + 5 (Since Anke gives Conrad 5 candies, Conrad will then have 4 times as many candies as Anke)

or 4A - 20 = C + 5

or 4A - 20 = A + 5 + 5 (since A = C - 5)

or 3A = 30

or A =10 i.e. Anke have 10 candies
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GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4856
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 102

Kudos [?]: 1741 [0], given: 397

Re: Anke has 5 fewer candies than Conrad. If Anke gives Conrad 5 [#permalink]  05 Jul 2018, 03:10
Expert's post
Explanation

First, translate the problem into two equations, writing “Anke after she gave Conrad 5 candies” as (A – 5) and “Conrad after receiving 5 more candies” as (C + 5):

$$A = C - 5$$

$$4(A - 5) = C + 5$$

Since A = C – 5, plug C – 5 in for A in the second equation:

$$4(C - 5 - 5) = C + 5$$

$$4(C - 10) = C + 5$$

$$4C - 40 = C + 5$$

$$4C = C + 45$$

$$3C = 45$$

$$C = 15$$

If C = 15, then, since Anke has 5 fewer candies, she has A = 10.

Check the answer. If Anke starts with 10 candies, after giving 5 to Conrad she has 5. If Conrad starts with 15 candies, he has 20 after receiving 5 from Anke. It is true that 20 is 4 times 5.
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Re: Anke has 5 fewer candies than Conrad. If Anke gives Conrad 5   [#permalink] 05 Jul 2018, 03:10
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