Abigail is 4 times as old as Bonnie. In 6 years, Bonnie will

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pm; Followed by:23 members

Abigail is 4 times as old as Bonnie. In 6 years, Bonnie will

by BTGmoderatorDC » Fri Aug 23, 2019 3:52 pm

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Abigail is 4 times as old as Bonnie. In 6 years, Bonnie will be twice as old as Candice. If, 4 years from now, Abigail will be 36 years old, how old will Candice be in 6 years?

A. 5
B. 6
C. 7
D. 8
E. 9

OA C

Source: Manhattan Prep

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Source: Beat The GMAT — Problem Solving | Fri Aug 23, 2019 3:52 pm

swerve: Legendary Member; Posts: 2499; Joined: Sun Oct 29, 2017 2:04 pm; Followed by:6 members

by swerve » Sat Aug 24, 2019 2:52 pm

BTGmoderatorDC wrote:Abigail is 4 times as old as Bonnie. In 6 years, Bonnie will be twice as old as Candice. If, 4 years from now, Abigail will be 36 years old, how old will Candice be in 6 years?

A. 5
B. 6
C. 7
D. 8
E. 9

OA C

Source: Manhattan Prep

Let the age of Bonnie $= x$
$\Rightarrow$ Age of Abigail $= 4x$ and Candice $= C$

$\begin{array}{|c|c|c|c|}
\hline
A & B & C & \textrm{Time} \\ \hline
4x & x & C & \textrm{Present} \\ \hline
4x+6 & x+6 & C+6 & \textrm{After $6$ years} \\ \hline
4x+4 & x+4 & C+4 & \textrm{After $4$ years}\\ \hline
\end{array}$

Given,
In 6 years, Bonnie will be twice as old as Candice
$\Rightarrow x+6 = 2(C+6)$
$\Rightarrow C = \frac{x}{2} - 3$

4 years from now, Abigail will be 36 years old
$\Rightarrow 4x+4 = 36$.
$\Rightarrow x = 8 $
$\Rightarrow C = \frac{8}{2} - 3 = 1$

In 6 years, age of Candice $= 1 + 6 = 7$

Therefore, option __C__

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Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 am; Location: Montreal; Thanked: 1090 times; Followed by:355 members; GMAT Score:780

by Ian Stewart » Sun Aug 25, 2019 8:13 am

Abigail will be 36 in four years, so Abigail is 32. She is 4 times as old as Bonnie, so Bonnie is 8. In six years, Bonnie will be 14, and will be twice as old as Candice, so in six years, Candice will be 7, which is what the question asked us to find.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Tue Aug 27, 2019 5:19 pm

BTGmoderatorDC wrote:Abigail is 4 times as old as Bonnie. In 6 years, Bonnie will be twice as old as Candice. If, 4 years from now, Abigail will be 36 years old, how old will Candice be in 6 years?

A. 5
B. 6
C. 7
D. 8
E. 9

OA C

Source: Manhattan Prep

We can let A, B, and C be the current ages of Abigail, Bonnie, and Candice, respectively, and create the equations:

A = 4B,

B + 6 = 2(C + 6),

and

A + 4 = 36

From the third equation, we see that A = 32. Therefore, B = 8 (from the first equation). Now, substituting 8 for B in the second equation, we have:

8 + 6 = 2(C + 6)

14 = 2C + 12

2 = 2C

1 = C

Therefore, in 6 years, Candice will be 1 + 6 = 7 years old.

Answer: C

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