Gita is 12 years older than Harvey. In 4 years, Gita will be twice as old as Harvey. How old will Harvey be in 3 years?

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Magoosh

Gita is 12 years older than Harvey. In 4 years, Gita will be twice as old as Harvey. How old will Harvey be in 3 years?

A. 5
B. 11
C. 15
D. 19
E. 23

OA B

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AAPL wrote:
Thu Feb 18, 2021 10:35 am
Magoosh

Gita is 12 years older than Harvey. In 4 years, Gita will be twice as old as Harvey. How old will Harvey be in 3 years?

A. 5
B. 11
C. 15
D. 19
E. 23

OA B
Gita is 12 years older than Harvey.
Let x = Harvey's PRESENT age
Let x + 12 = Gita's PRESENT age

In 4 years, . . . .
x + 4 = Harvey's age IN FOUR YEARS
(x + 12) + 4 = Gita's age IN FOUR YEARS

. . . Gita will be twice as old as Harvey.
So: (Gita's age IN 4 YEARS) = 2(Harvey's age IN 4 YEARS)
In other words: (x + 12) + 4 = 2(x + 4)
Simplify: x + 16 = 2x + 8
Subtract x from both sides: 16 = x + 8
Subtract 8 from both sides: 8 = x

So, Harvey's PRESENT age is 8 years old

How old will Harvey be in 3 years?
Harvey will be 11 years old in 3 years.

Answer: B

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AAPL wrote:
Thu Feb 18, 2021 10:35 am
Magoosh

Gita is 12 years older than Harvey. In 4 years, Gita will be twice as old as Harvey. How old will Harvey be in 3 years?

A. 5
B. 11
C. 15
D. 19
E. 23
An alternate approach is to PLUG IN THE ANSWERS, which represent Harvey's age in 3 years.
When the correct answer is plugged in, Gina in 4 years will be twice as old as Harvey.

D: 19, implying that Harvey's current age = 19-3 = 16
Since Gina is 12 years older than Harvey, Gina = 16+12 = 28.
Harvey in 4 years = 16+4 = 20
Gina in 4 years = 28+4 = 32
Since Gina in 4 years is not twice as old as Harvey, eliminate D.

B: 11, implying that Harvey's current age = 11-3 = 8
Since Gina is 12 years older than Harvey, Gina = 8+12 = 20.
Harvey in 4 years = 8+4 = 12
Gina in 4 years = 20+4 = 24
Success!
Gina in 4 years is twice as old as Harvey.

The. correct answer is B.
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