Adam Family

kartikshah wrote:In the Adams family there are 7 boys. Each boy is twice as heavy as his next younger brother. If the sum of the boys' weights is 127 pounds, then how much, in pounds, does the oldest boy weigh?

(A) 10

(B) 20

(C) 34

(D) 58

(E) 64

Source: Master GMAT

I set up an equation x+2x+4x+....64x = 127

Any quicker way to solve?

You did it correctly and I am guessing quick enough.

This may be faster:

Since the weight doubles, it is a geometric progression with r=2.
Let the first boys weight be x.
The for 7 boys, heaviest =x* 2^(7-1)=64x

Sum of GP= x*(2^7-1)/(2-1) =127 (given)
=> x*127 =127
x=1

Hence heaviest = 64.

kartikshah wrote:In the Adams family there are 7 boys. Each boy is twice as heavy as his next younger brother. If the sum of the boys' weights is 127 pounds, then how much, in pounds, does the oldest boy weigh?

(A) 10

(B) 20

(C) 34

(D) 58

(E) 64

Source: Master GMAT

I set up an equation x+2x+4x+....64x = 127

Any quicker way to solve?

Hi!

You can solve this almost instantaneously if you understand what the question is asking.

Since each brother is double the weight of the previous brother, the correct answer has to be divisible by 2 many times. The only answer that has lots of factors is 2 is 64... choose E!

The question would have been a bit more interesting if 32 were one of the choices, since then we'd have two viable options. If that had been the case, then we could have just tested either 32 or 64 (no need to test both!) to validate/eliminate one of the last two choices.

kartikshah wrote:In the Adams family there are 7 boys. Each boy is twice as heavy as his next younger brother. If the sum of the boys' weights is 127 pounds, then how much, in pounds, does the oldest boy weigh?

(A) 10

(B) 20

(C) 34

(D) 58

(E) 64

Source: Master GMAT

I set up an equation x+2x+4x+....64x = 127

Any quicker way to solve?

ALWAYS LOOK AT THE ANSWER CHOICES.
The sum of the weights is an integer.
The answers represent the weight of the oldest boy.
Since each boy is twice as heavy at the next youngest boy, the correct answer must be a value that can be divided by 2 six times.
Since 2� = 64, the only viable answer choice is E:
64+32+16+8+4+2+1 = 127.
Success!

The correct answer is E.