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Eleven years ago Tina was half as old as Ike will be in 4 years.

Expert replies
by BTGModeratorVI » Fri May 29, 2020 6:45 am

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Answers

A

B

C

D

E

Stats

Difficulty—

Eleven years ago Tina was half as old as Ike will be in 4 years. If Ike is m years old now, how old is Tina now, in terms of m?

A. 4m - 11
B. m/2 + 13
C. 1/(2m - 22)
D. (4m + 11)/2
E. 2m-7

Answer: B
Source: Economist GMAT
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Source: — Problem Solving |

BTGModeratorVI wrote: ↑
Fri May 29, 2020 6:45 am
Eleven years ago Tina was half as old as Ike will be in 4 years. If Ike is m years old now, how old is Tina now, in terms of m?

A. 4m - 11
B. m/2 + 13
C. 1/(2m - 22)
D. (4m + 11)/2
E. 2m-7

Answer: B
Source: Economist GMAT
Given: m = Ike's PRESENT age
So, m + 4 = Ike's age IN 4 YEARS
So, (1/2)(m + 4) = Tina's age 11 YEARS AGO
So, (1/2)(m + 4) + 11 = Tina's PRESENT age

The answer does not appear among the answer choices. So, we'll need to SIMPLIFY the expression
Take: (1/2)(m + 4) + 11
Expand: m/2 + 2 + 11
Simplify: m/2 + 13

Answer: B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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This is how I approached it:

m = Ike's age
t = tina's age

The statement says that eleven years ago Tina was half of Ike's age four years from now. If you're having a hard time understanding this, just imagine that eleven years ago Tina was 10 and four years from now Ike is 20. Therefore we know that:

2*(t-11) = m+4
t = (m+4)/2 +11
t = m/2 + 2 + 11
t = m/2 + 13
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Easy problem to tackle, guys!

Start by assigning a variable to represent Ike's present age. The problem calls it M.
Next, we want to figure out Ike's age four years from now: M + 4 = Ike's age four years from now.
Ike's age four years from now is twice Tina's age eleven years ago. To put it mathematically, 0.5(M + 4) = Tina's age eleven years ago.
Finally, we need to get back to Tina's present age: 0.5(M + 4) + 11 = Tina's present age.
If we simplify:
Step 1: 0.5(M + 4) + 11 = Tina's present age
Step 2: 0.5M + 2 + 11 = Tina's present age
Step 3: 0.5M + 13 = Tina's present age --> this is B!
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Let Ike's present age = m
Therefore, m + 4 = Ike's age in 4 years

Tina's age 11 years ago = 1/2(m + 4)
Tina's present age = 1/2(m + 4 ) + 11

$$=\frac{\left(m+4\right)}{2}+\frac{11}{1}$$
$$\frac{m}{2}+\frac{4}{2}+\frac{11}{1}$$
$$\left(\frac{m}{2}\right)+\left(\frac{2}{1}+\frac{11}{1}\right)$$
$$=\frac{m}{2}+13$$

Answer = B
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