weight problem

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sportypk: Junior | Next Rank: 30 Posts; Posts: 15; Joined: Mon Mar 31, 2008 11:01 amFollowed by: 1 member

by sportypk » Fri May 30, 2008 8:57 am

If Jake loses 8 pounds, he will weigh twice as much as his
sister. Together they now weigh 278 pounds. What is Jakeï¿½s
present weight, in pounds?
(A) 131
(B) 135
(C) 139
(D) 147
(E) 188

the OA is 188. how?

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Source: Beat The GMAT — Problem Solving | Fri May 30, 2008 8:57 am

DavidP: Site Admin; Posts: 387; Joined: Sun Feb 17, 2008 4:25 pmFollowed by: 29 members; Thanked: 17 times

by DavidP » Fri May 30, 2008 9:00 am

x = weight of Jake's sister

2x + 8 = Jake's weight

278 = Jake's sister's weight + Jake's weight

278 = x + (2x + 8)

278 = 3x + 8

270 = 3x

x = 90

Thus, Jake's weight = 2x + 8 = 2*90 + 8 = 188

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egybs: Master | Next Rank: 500 Posts; Posts: 178; Joined: Wed May 14, 2008 3:51 pmFollowed by: 1 member; Thanked: 16 times; GMAT Score:99%+

by egybs » Fri May 30, 2008 9:08 am

Even easier -

we know that

J-8 = 2S
Therefore S = (J-8 )/2

So J + .5J -4 = 278

(3/2)J = 282
J = 188

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sportypk: Junior | Next Rank: 30 Posts; Posts: 15; Joined: Mon Mar 31, 2008 11:01 amFollowed by: 1 member

thanks

by sportypk » Fri May 30, 2008 9:19 am

wow i feel like the queen of silly mistakes...thanks guys...

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8138; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Wed Jun 24, 2015 3:21 am

sportypk wrote:If Jake loses 8 pounds, he will weigh twice as much as his
sister. Together they now weigh 278 pounds. What is Jakeï¿½s
present weight, in pounds?
(A) 131
(B) 135
(C) 139
(D) 147
(E) 188

the OA is 188. how?

Solution:

This problem can be solved as a simple word problem in which we must convert words to math. Before we create our equations, we want to define some variables.

J = Jake's current weight, in pounds

S = Sister's current weight, in pounds

We are told that "If Jake loses 8 pounds, he will weigh twice as much as his sister." We put this into an equation:

J - 8 = 2S

We can isolate J by adding 8 to 2S:

J = 2S + 8 (Equation 1)

Next, we are told that "Together they now weigh 278 pounds." We can also put this into an equation.

J + S = 278 (Equation 2)

To solve this equation, we can substitute 2S + 8 from Equation 1 for the variable J in Equation 2:

2S + 8 + S = 278

3S = 270

S = 90

We now know that the sister weighs S = 90 pounds, and we can plug that value into either equation to determine J. Let's plug 90 for S into equation 2:

J + 90 = 278

J = 188

Answer: E

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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 » Wed Jun 24, 2015 6:15 am

sportypk wrote:If Jake loses 8 pounds, he will weigh twice as much as his
sister. Together they now weigh 278 pounds. What is Jakeï¿½s
present weight, in pounds?
(A) 131
(B) 135
(C) 139
(D) 147
(E) 188

Here's a solution that uses one variable.

Let x = Jake's present weight in pounds
So, x - 8 = Jake's hypothetical weight IF he were to lose 8 pounds

If Jake loses 8 pounds, he will weigh twice as much as his sister.
In other words, the sister weighs HALF as much as Jake's hypothetical weight of x - 8 pounds
So, (x - 8)/2 = sister's present weight

Together they NOW weigh 278 pounds.
So, Jake's present weight + sister's present weight = 278
So, x + (x - 8)/2 = 278
Eliminate fractions by multiplying both sides by 2 to get: 2x + (x - 8) = 556
Simplify: 3x - 8 = 556
Add 8 to both sides: 3x = 564
Solve: x = [spoiler]188 = E[/spoiler]

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Wed Jun 24, 2015 6:40 am

sportypk wrote:If Jake loses 8 pounds, he will weigh twice as much as his
sister. Together they now weigh 278 pounds. What is Jakeï¿½s
present weight, in pounds?
(A) 131
(B) 135
(C) 139
(D) 147
(E) 188

ALWAYS KEEP YOUR EYE ON THE ANSWER CHOICES.

If Jake loses 8 pounds, he will weigh twice as much as his sister.
j-8 = 2s
j = 2s + 8 = even + even = even.

Since Jake's weight must be an EVEN VALUE, the correct answer is E.

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egybs: Master | Next Rank: 500 Posts; Posts: 178; Joined: Wed May 14, 2008 3:51 pmFollowed by: 1 member; Thanked: 16 times; GMAT Score:99%+

by egybs » Wed Jun 24, 2015 7:10 am

GMAT 'experts', I still like my solution from 7 years ago better.

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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 » Wed Jun 24, 2015 7:17 am

GMATGuruNY wrote:
sportypk wrote:If Jake loses 8 pounds, he will weigh twice as much as his
sister. Together they now weigh 278 pounds. What is Jakeï¿½s
present weight, in pounds?
(A) 131
(B) 135
(C) 139
(D) 147
(E) 188
ALWAYS KEEP YOUR EYE ON THE ANSWER CHOICES.

If Jake loses 8 pounds, he will weigh twice as much as his sister.
j-8 = 2s
j = 2s + 8 = even + even = even.

Since Jake's weight must be an EVEN VALUE, the correct answer is E.

Sweeeeeeeeeet!

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] » Wed Jun 24, 2015 9:37 am

Hi All,

The answer choices in this question are 'spread out' in such a way that we can get to the correct answer with just a bit of logical thinking.

We're told that the total weight of Jake and his sister = 278 pounds. We're also told that if Jake LOST 8 pounds, he would TWICE as much as his sister....

This means that Jake weighs MORE than twice his sister RIGHT NOW. Since the total is 278 pounds, Jake's weight MUST make up MOST of that total weight (a lot more than half). There's only one answer that fits....

Final Answer: E

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

Contact Rich at [email protected]

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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 » Wed Jun 24, 2015 1:28 pm

[email protected] wrote:Hi All,

The answer choices in this question are 'spread out' in such a way that we can get to the correct answer with just a bit of logical thinking.

We're told that the total weight of Jake and his sister = 278 pounds. We're also told that if Jake LOST 8 pounds, he would TWICE as much as his sister....

This means that Jake weighs MORE than twice his sister RIGHT NOW. Since the total is 278 pounds, Jake's weight MUST make up MOST of that total weight (a lot more than half). There's only one answer that fits....

Final Answer: E

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

Another sweeeeet answer!
And here I'm using algebra like some sucker!!

I love seeing how many approaches one can take with a GMAT math question!!!

I've already reached my exclamation mark quota for the day, so I hope no one else presents more awesome approaches.

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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

by Ian Stewart » Wed Jun 24, 2015 3:15 pm

Mitch's solution is obviously fastest, but there is a no-variable solution we can use if the answer choices don't allow for any trick: if Jake loses 8 pounds, then together they'll weigh 270 pounds, and if Jake would then weigh twice as much as his sister, the ratio of their weights is 2 to 1, so Jake would weigh 2/3 of 270, or 180 pounds. Add back the 8, and 188 is the answer.

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

ianstewartgmat.com

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