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Kate is eight years older than her brother Jake. Four years ago, Kate

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Bunuel
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Kate is eight years older than her brother Jake. Four years ago, Kate [#permalink] New post   13 Jul 2020, 04:21
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E

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25% (medium)

Question Stats:

77% (01:19) correct 23% (01:38) wrong based on 31 sessions
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Kate is eight years older than her brother Jake. Four years ago, Kate was twice as old as Jake. How old is Jake now?

A. 4
B. 6
C. 8
D. 10
E. 12
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E
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Kinshook
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Re: Kate is eight years older than her brother Jake. Four years ago, Kate [#permalink] New post   13 Jul 2020, 04:24
Bunuel wrote:
Kate is eight years older than her brother Jake. Four years ago, Kate was twice as old as Jake. How old is Jake now?

A. 4
B. 6
C. 8
D. 10
E. 12


Given: Kate is eight years older than her brother Jake. Four years ago, Kate was twice as old as Jake.
Asked: How old is Jake now?

Let us assume that Kate is k years old and Jake is j years old now.

Kate is eight years older than her brother Jake.
k = j + 8

Four years ago, Kate was twice as old as Jake.
k - 4 = 2 (j -4)
k = 2j - 4 = j + 8
j = 12
k = 20

IMO E
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Re: Kate is eight years older than her brother Jake. Four years ago, Kate [#permalink] New post   13 Jul 2020, 04:25
Kate is eight years older than her brother Jake.
K = J+8 ------------(1)

Four years ago, Kate was twice as old as Jake.
(K-4) = 2(J-4) ---------(2)

J+8-4 = 2J-8
J+4 = 2J-8
12 = J
Answer is E

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Re: Kate is eight years older than her brother Jake. Four years ago, Kate [#permalink] New post   13 Jul 2020, 04:25
Current Age:
Jake = J
Kate = J+8

4 Years Ago:
J+8-4 = 2(J-4)
J + 4 = 2J - 8
J = 12

Answer: E
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Kate is eight years older than her brother Jake. Four years ago, Kate [#permalink] New post   13 Jul 2020, 05:38
Bunuel wrote:
Kate is eight years older than her brother Jake. Four years ago, Kate was twice as old as Jake. How old is Jake now?

A. 4
B. 6
C. 8
D. 10
E. 12


Let me pull out a unique approach for solving this question through POE by substitution.

From the question stem, we get two equations K = J+8 and (K-4) = 2(J-4)

Starting from option A,

If J = 4, K should be 12, it doesn't fit in the second equation, Hence, wrong.

Starting from option B,

If J = 6, K should be 14, it doesn't fit in the second equation, Hence, wrong.

Starting from option C,

If J = 8, K should be 16, it doesn't fit in the second equation, Hence, wrong.

Starting from option D,

If J = 10, K should be 18, it doesn't fit in the second equation, Hence, wrong.

Starting from option E,

If J = 12, K should be 20, it fits in the second equation, Hence, correct.

OA: E

This approach seems tough initially but gets easy on the go for tougher questions.

Hope my approach is worthy of a few kudos.
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Kate is eight years older than her brother Jake. Four years ago, Kate [#permalink]
13 Jul 2020, 05:38
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