Adam Family

This topic has expert replies
Master | Next Rank: 500 Posts
Posts: 156
Joined: Sun Jul 15, 2012 12:03 pm
Location: New York, USA
Thanked: 34 times
Followed by:1 members

Adam Family

by kartikshah » Sun Jul 22, 2012 11:41 am
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?

User avatar
Legendary Member
Posts: 520
Joined: Sat Apr 28, 2012 9:12 pm
Thanked: 339 times
Followed by:49 members
GMAT Score:770

by eagleeye » Sun Jul 22, 2012 12:57 pm
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.

User avatar
GMAT Instructor
Posts: 3225
Joined: Tue Jan 08, 2008 2:40 pm
Location: Toronto
Thanked: 1710 times
Followed by:614 members
GMAT Score:800

by Stuart@KaplanGMAT » Sun Jul 22, 2012 2:53 pm
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.
Image

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
BTG100 for $100 off a full course

User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Sun Jul 22, 2012 3:06 pm
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.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3