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Hansel is 7 years older than Gretel. If the product of their ages (in

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Bunuel
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Hansel is 7 years older than Gretel. If the product of their ages (in [#permalink] New post   24 May 2022, 08:15
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Hansel is 7 years older than Gretel. If the product of their ages (in years) is 60, then how old is Gretel ?

A. 5
B. 6
C. 7
D. 12
E. 14
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A
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Abhishek009
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Re: Hansel is 7 years older than Gretel. If the product of their ages (in [#permalink] New post   24 May 2022, 08:18
Bunuel wrote:
Hansel is 7 years older than Gretel. If the product of their ages (in years) is 60, then how old is Gretel ?

A. 5
B. 6
C. 7
D. 12
E. 14

12 - 5 = 7 & 12*5 = 60

Hence, Gretel (Younger one) will be 5 Years, Answer must be (A)
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Re: Hansel is 7 years older than Gretel. If the product of their ages (in [#permalink] New post   24 May 2022, 08:37
Say, Gretel is X years old.
Hansel=X+7
If the product of their ages 60, then if option (A) 5 is used we find the answer.
If Gretel is 5, Hansel is X+7, putting 5 in X we get 5+7=12.
Now the product becomes 5×12=60

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Re: Hansel is 7 years older than Gretel. If the product of their ages (in [#permalink] New post   24 May 2022, 09:35
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Bunuel wrote:
Hansel is 7 years older than Gretel. If the product of their ages (in years) is 60, then how old is Gretel ?

A. 5
B. 6
C. 7
D. 12
E. 14


As the two posters above me have shown, the fastest approach here is to test the answer choices.
If you didn't spot that approach, here is an algebraic solution.

Let G = Gretel's age
So, G + 7 = Hansel's age

Since the product of their ages is 60, we can write: (G)(G + 7) = 60
Expand: G² + 7G = 60
Since we have a quadratic equation, we'll set it equal to zero by subtracting 60 from both sides: G² + 7G - 60 = 0
Factor to get: (G + 12)(G - 5) = 0
So, either G = -12 or G = 5

Since Gretel's age can't be negative, we know that battle must be 5 years old

Answer: A
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Re: Hansel is 7 years older than Gretel. If the product of their ages (in [#permalink] New post   24 May 2022, 11:10
Hansel is 7 years older than Gretel. If the product of their ages (in years) is 60, then how old is Gretel ?

A. 5
B. 6
C. 7
D. 12
E. 14

IMO A
x*(x+7) = 60
x=5 , thus Gretel is 5 years old.
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Re: Hansel is 7 years older than Gretel. If the product of their ages (in [#permalink]
24 May 2022, 11:10
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