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If Jake loses 8 pounds, he will weigh twice as much as his sister. Together they now weigh 278 pounds. What is Jake's

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by M7MBA » Thu Jan 07, 2021 10:25 am

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If Jake loses 8 pounds, he will weigh twice as much as his sister. Together they now weigh 278 pounds. What is Jake's present weight, in pounds?

(A) 131
(B) 135
(C) 139
(D) 147
(E) 188

Answer: E

Source: Official Guide
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Re: If Jake loses 8 pounds, he will weigh twice as much as his sister. Together they now weigh 278 pounds. What is Jake'

by Brent@GMATPrepNow » Mon Jan 11, 2021 7:41 am
M7MBA wrote: ↑
Thu Jan 07, 2021 10:25 am
 If Jake loses 8 pounds, he will weigh twice as much as his sister. Together they now weigh 278 pounds. What is Jake's present weight, in pounds?

(A) 131
(B) 135
(C) 139
(D) 147
(E) 188

Answer: E

Source: Official Guide
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 the fraction 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 = 564/3 = 188

Answer: E

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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Re: If Jake loses 8 pounds, he will weigh twice as much as his sister. Together they now weigh 278 pounds. What is Jake'

by Scott@TargetTestPrep » Tue Jan 19, 2021 6:23 am
M7MBA wrote: ↑
Thu Jan 07, 2021 10:25 am
 If Jake loses 8 pounds, he will weigh twice as much as his sister. Together they now weigh 278 pounds. What is Jake's present weight, in pounds?

(A) 131
(B) 135
(C) 139
(D) 147
(E) 188

Answer: E

Source: Official Guide
Solution:

We let J = Jake’s current weight and S = Sister’s current weight, in pounds, and create the equations:

J – 8 = 2S

J = 2S + 8 (Equation 1)

and

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

Alternate Solution:

From the answer choices, we understand that Jake’s weight is an integer and since the sum of Jake and his sister’s weights is an integer, it follows that Jake’s sister’s weight is an integer, too. Since Jake’s weight is 8 less than twice that of his sister’s, Jake’s weight must be an even integer (if sister’s weight is n, then Jake’s weight is 2n - 8, which is always even). The only even number among the given answer choices is 188.

Answer: E

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