Seven years ago Bob was $k$ times as old as Ann. If Ann is

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Gmat_mission: Legendary Member; Posts: 1622; Joined: Thu Mar 01, 2018 7:22 amFollowed by: 2 members

by Gmat_mission » Sat Dec 14, 2019 6:03 am

Seven years ago Bob was $k$ times as old as Ann. If Ann is now 11 years old, what is Bob's present age in terms of $k?$

A. $7 + 4k$
B. $\dfrac{11}k + 7$
C. $11 - \dfrac7k$
D. $11 - \dfrac{k}7$
E. $4k - 7$

[spoiler]OA=A[/spoiler]

Source: Magoosh

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Source: Beat The GMAT — Problem Solving | Sat Dec 14, 2019 6:03 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sat Dec 14, 2019 6:27 am

Gmat_mission wrote:Seven years ago Bob was $k$ times as old as Ann. If Ann is now 11 years old, what is Bob's present age in terms of $k?$

A. $7 + 4k$
B. $\dfrac{11}k + 7$
C. $11 - \dfrac7k$
D. $11 - \dfrac{k}7$
E. $4k - 7$

[spoiler]OA=A[/spoiler]

Source: Magoosh

If Ann is NOW 11 years old, then 7 YEARS AGO, Ann was 4 years old.

Seven years ago Bob was k times as old as Ann.
So, 7 YEARS AGO, Bob's age was 4k

What is Bob's present age in terms of k?
To find Bob's present age, we need to add 7 to his age 7 years ago.
So, Bob's PRESENT age = 4k + 7

Answer: A

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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by [email protected] » Sat Dec 14, 2019 3:11 pm

Hi gmat_mission,

Most Test Takers would approach this question using a "system" of equations, which is fine. As long as you handle the "time shift" correctly, then you'll get to the correct answer. This question can also be solved by TESTing VALUES - you just have to note that Ann was 4 years old seven years ago....

We're told that 7 years ago, Bob was K times as old as Ann. Then we're told that Ann is NOW 11 years old. Thus, seven years ago, Ann was 11-7 = 4 years old....

Seven Years Ago:
Ann = 4 years old

Let's say that K = 2
Bob = 2(4) = 8 old

Present Day:
Ann = 11 years old
Bob = 8+7 = 15 years old

The question asks for Bob's age NOW, relative to K...

Answer A: 7 + 4(2) = 15 This IS a match
Answer B: 11/2 + 7 = 12.5 NOT a match
Answer C: 11 - 7/2 = Less than 15
Answer D: 11 - 2/7 = Less than 15
Answer E: 8 - 7 = Less than 15

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8154; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Sun Dec 22, 2019 7:31 pm

Gmat_mission wrote:Seven years ago Bob was $k$ times as old as Ann. If Ann is now 11 years old, what is Bob's present age in terms of $k?$

A. $7 + 4k$
B. $\dfrac{11}k + 7$
C. $11 - \dfrac7k$
D. $11 - \dfrac{k}7$
E. $4k - 7$

[spoiler]OA=A[/spoiler]

Source: Magoosh

Letting B and A equal Bob's and Ann's current ages, respectively, we can create the equation:

B - 7 = k(A - 7)

Since A = 11, we have:

B - 7 = k(11 - 7)

B - 7 = 4k

B = 4k + 7

Answer: A

Scott Woodbury-Stewart
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[email protected]

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