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Tom’s Mom is five times as old as him. In 6 years, Tom’

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by Max@Math Revolution » Wed Oct 03, 2018 1:11 am

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[Math Revolution GMAT math practice question]

Tom's Mom is five times as old as him. In 6 years, Tom's Mom will be three times as old as him. How old is Tom now?

A. 3
B. 4
C. 5
D. 6
E. 7
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by fskilnik@GMATH » Wed Oct 03, 2018 4:28 am
Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

Tom's Mom is five times as old as him. In 6 years, Tom's Mom will be three times as old as him. How old is Tom now?

A. 3
B. 4
C. 5
D. 6
E. 7
$$? = T$$
$$\left\{ \matrix{
M = 5T \hfill \cr
M + 6 = 3\left( {T + 6} \right) \hfill \cr} \right.\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,5T + 6 = 3T + 18\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,? = 6$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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Portuguese-speakers :: https://www.gmath.com.br
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by Brent@GMATPrepNow » Wed Oct 03, 2018 8:48 am
Max@Math Revolution wrote: Tom's Mom is five times as old as him. In 6 years, Tom's Mom will be three times as old as him. How old is Tom now?
A. 3
B. 4
C. 5
D. 6
E. 7
Tom's Mom is five times as old as him.
Let T = Tom's PRESENT age
So, 5T = Mom's PRESENT age

This also means:
Let T + 6= Tom's age IN 6 YEARS
and 5T + 6 = Mom's age IN 6 YEARS

In 6 years, Tom's Mom will be three times as old as Tom.
In other words: (Mom's age IN 6 YEARS) = 3(Tom's age IN 6 YEARS)
Or we can write: 5T + 6 = 3(T + 6)
Expand: 5T + 6 = 3T + 18
Subtract 3T from both sides: 2T + 6 = 18
So: 2T = 12
T = 6

Answer: D

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by GMATGuruNY » Wed Oct 03, 2018 10:06 am
Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

Tom's Mom is five times as old as him. In 6 years, Tom's Mom will be three times as old as him. How old is Tom now?

A. 3
B. 4
C. 5
D. 6
E. 7
An alternate approach is to PLUG IN THE ANSWERS, which represents Tom's current age.
When the correct answer is plugged in, Mom's age in 6 years will be 3 times Tom's age in 6 years.

D: Tom = 6
Since Mom is currently 5 times as old as Tom, Mom = 5*6 = 30.
Tom's age in 6 years = 6+6 = 12.
Mom's age in 6 years = 30+6 = 36.
Success!
The value in green is 3 times the value in blue.

The correct answer is D.
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by Max@Math Revolution » Fri Oct 05, 2018 12:19 am
=>

We can set up this question using the IVY approach. "Is"
can be converted to "=" and "times" can be converted to the multiplication sign "x".

Let m and t be Tom's Mom's age and Tom's age now, respectively.
Then m = 5t since Tom's mom is five times as old as Tom.
We also have
m + 6 = 3(t + 6) since Tom's mom will be three times as old as Tom in 6 years.

Plugging m = 5t into the second equation yields
5t + 6 = 3t + 18 or 2t = 12.
So, t = 6.

Therefore, the answer is D.
Answer: D
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by Scott@TargetTestPrep » Sun Oct 07, 2018 6:31 pm
Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

Tom's Mom is five times as old as him. In 6 years, Tom's Mom will be three times as old as him. How old is Tom now?

A. 3
B. 4
C. 5
D. 6
E. 7
We can let T = Tom's present age and M = his Mom's present age and create the equation:

5T = M

In 6 years, we see that Tom will be (T + 6) years old, and his Mom will be (M + 6) years old. We are told that at that time (6 years from now) Tom's Mom's age will be 3 times Tom's age. Thus, we have:

M + 6 = 3(T + 6)

M + 6 = 3T + 18

M = 3T + 12

Substituting 5T for M, we have:

5T = 3T + 12

2T = 12

T = 6

Answer: D

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