OG2015 PS Lois has x dollars

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lionsshare: Senior | Next Rank: 100 Posts; Posts: 62; Joined: Wed Aug 09, 2017 3:54 pm

by lionsshare » Wed Sep 13, 2017 9:34 pm

Lois has x dollars more than Jim has, and together they have a total of y dollars. Which of the following represents the number of dollars that Jim has?

(A) (y - x)/2
(B) y - x/2
(C) y/2 - x
(D) 2y - x
(E) y - 2x

OA: A

Hi, Experts. Please share the solution to this problem. Thanks.

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Source: Beat The GMAT — Problem Solving | Wed Sep 13, 2017 9:34 pm

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

by Jay@ManhattanReview » Wed Sep 13, 2017 9:43 pm

lionsshare wrote:Lois has x dollars more than Jim has, and together they have a total of y dollars. Which of the following represents the number of dollars that Jim has?

(A) (y - x)/2
(B) y - x/2
(C) y/2 - x
(D) 2y - x
(E) y - 2x

OA: A

Hi, Experts. Please share the solution to this problem. Thanks.

Say Lois has $L, and Jim has $J.

Thus, as per the condition: "Lois has x dollars more than Jim has," we get

L - J = x ---(1)

As per the second condition: "together they have a total of y dollars," we get

L + J = y ---(2)

Since we want to find out the amount of money Jim has, let's subtract (1) from (2).

We get (L + J = y) - (L - J = x)

L + J - L + J = y - x

2J = y - x

J = (y - x)/2

The correct answer: A

Hope this helps!

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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 » Thu Sep 14, 2017 6:36 am

lionsshare wrote:Lois has x dollars more than Jim has, and together they have a total of y dollars. Which of the following represents the number of dollars that Jim has?

(A) (y - x)/2
(B) y - x/2
(C) y/2 - x
(D) 2y - x
(E) y - 2x

Let J = number of dollars that Jim has

Lois has x dollars more than Jim has
So, J + x = number of dollars that Lois has

Together they have a total of y dollars
So, (Jim's $) + (Lois' $) = y
Or: J + (J+x) = y
Simplify: 2J + x = y

Which of the following represents the number of dollars that Jim has?
Solve 2J + x = y for J
Subtract x from both sides to get: 2J = y - x
Divide both sides by 2 to get: (y-x)/2

Answer: A

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Thu Sep 14, 2017 11:19 am

Hi lionsshare,

We're told that Lois has X dollars MORE than Jim has and together they have a TOTAL of Y dollars. We're asked for the number of dollars that Jim has. This question can be solved by TESTing VALUES.

IF....
Lois has 5 dollars and Jim has 2 dollars, then X = 3 and Y = 7. So we're looking for an answer that equals 2 when we plug in X = 3 and Y = 7... There's only one answer that matches:

Final Answer: A

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

Contact Rich at [email protected]

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Tue Sep 19, 2017 2:54 pm

lionsshare wrote:Lois has x dollars more than Jim has, and together they have a total of y dollars. Which of the following represents the number of dollars that Jim has?

(A) (y - x)/2
(B) y - x/2
(C) y/2 - x
(D) 2y - x
(E) y - 2x

OA: A

To solve, we will set up two equations. Let's start by defining two variables.

J = number of dollars Jim has

L = number of dollars Lois has

We are given that Lois has x dollars more than Jim. We set up the following equation:

L = x + J

We are next given that together they have a total of y dollars. We can set up our second equation:

J + L = y

Since we know that L = x + J, we can substitute x + J for L in the second equation, J + L = y.

Notice that after the substitution, we will only have variables of J, x, and y. Thus, we have:

J + x + J = y

2J + x = y

2J = y - x

J = (y - x)/2

Answer: A

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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