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# If Harry's age is exactly three times Bill's age, what is Harry's age?

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Math Expert
Joined: 02 Sep 2009
Posts: 47157
If Harry's age is exactly three times Bill's age, what is Harry's age?  [#permalink]

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05 Apr 2017, 03:25
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Difficulty:

15% (low)

Question Stats:

93% (00:46) correct 7% (02:36) wrong based on 44 sessions

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If Harry's age is exactly three times Bill's age, what is Harry's age?

(1) Six years ago, Harry's age was fifteen times Bill's age
(2) Seven years from now, Harry's age will be twice Bill's age

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If Harry's age is exactly three times Bill's age, what is Harry's age?  [#permalink]

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05 Apr 2017, 04:20
If Harry's age is exactly three times Bill's age, what is Harry's age?

(1) Six years ago, Harry's age was fifteen times Bill's age
(2) Seven years from now, Harry's age will be twice Bill's age

Let.

Harry age=H
Bill's age=B

Given that: H=3B

We have to find H.

Statement 1:

H-6= 15 * (B-6) --> H-6=15B-90 --> H=15B-84
Given, H=3B

2 equation and 2 variables can be solved.

Sufficient!

Statement 2:

H+7 = 2 * (B+7) --> H+7 = 2B+14 --> H=2B+7

Given, H=3B

2 equation and 2 variables can be solved.

Sufficient!

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Re: If Harry's age is exactly three times Bill's age, what is Harry's age?  [#permalink]

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05 Apr 2017, 06:29
Hi,

H = 3B Given ; H=?
St-1 :
H-6 = 15(B-6)
Substitute H = 3B in above equation, we will get H= 21, Suff
St-2 :
H+7 = 2(B+7)
Substitute H = 3B in above equation, we will get H= 21, Suff

Ans : Option D;
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Re: If Harry's age is exactly three times Bill's age, what is Harry's age?  [#permalink]

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14 Apr 2017, 05:57
Bunuel wrote:
If Harry's age is exactly three times Bill's age, what is Harry's age?

(1) Six years ago, Harry's age was fifteen times Bill's age
(2) Seven years from now, Harry's age will be twice Bill's age

We can let Harry’s age today = h and Bill’s age today = b.

Since Harry's age is exactly three times Bill's age, we know that h = 3b.

We need to determine h.

Statement One Alone:

Six years ago, Harry's age was fifteen times Bill's age. If we go back in time six years, Harry’s age was (h - 6) and Bill’s age was (b - 6). We can create the following equation:

h - 6 = 15(b - 6)

h - 6 = 15b - 90

h = 15b - 84

Since h = 3b, we have:

3b = 15b - 84

84 = 12b

b = 7

Thus, h = 3 x 7 = 21.

Statement one alone is sufficient to answer the question.

Statement Two Alone:

Seven years from now, Harry's age will be twice Bill's age. If we go forward in time seven years, Harry’s age will be (h + 7), and Bill’s age will be (b + 7). We can create the following equation:

h + 7 = 2(b + 7)

h + 7 = 2b + 14

h = 2b + 7

Since h = 3b, we have:

3b = 2b + 7

b = 7

Thus, h = 3 x 7 = 21.

Statement two alone is sufficient to answer the question.

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Re: If Harry's age is exactly three times Bill's age, what is Harry's age? &nbs [#permalink] 14 Apr 2017, 05:57
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