"Length of integer" (prime number properties)

Expert replies

JohnRapp: Newbie | Next Rank: 10 Posts; Posts: 9; Joined: Thu Sep 15, 2011 9:41 am

by JohnRapp » Sun Nov 13, 2011 9:48 am

For any integer k > 1, the term "length of an integer" refers to the number of positive prime factors, not necessarily distinct, whose product is equal to k. For example, if k = 24, the length of k is equal to 4, since 24 = 2 Ã— 2 Ã— 2 Ã— 3. If x and y are positive integers such that x > 1, y > 1, and x + 3y < 1000, what is the maximum possible sum of the length of x and the length of y?

A. 5
B. 6
C. 15
D. 16
E. 18

I'm hoping this post can provide alternative explanations to the OA explanation.

OA = [spoiler](D) 16[/spoiler]

Like this post

Source: Beat The GMAT — Problem Solving | Sun Nov 13, 2011 9:48 am

rijul007: Legendary Member; Posts: 588; Joined: Sun Oct 16, 2011 9:42 amFollowed by: 9 members; Location: New Delhi, India; Thanked: 130 times; GMAT Score:720

by rijul007 » Sun Nov 13, 2011 10:14 am

for a number to have maximum length.. it should have the highest no of prime factors not necessarily distinct

this number n should have max nuber of 2s as a prime factor

x>1
y>1

x = 2^a [a is the length of x]
y = 2^b

x+3y<1000
2^a + 3(2)^b <1000

highest value of 2^a that can fit into this is 512

2^a = 512
a = 9

3(2)^b <1000-512
2^b < 488/3
2^b < 162
highest value of 2^b can be 128
b = 7

Maximum sum of length of a and length of b = a + b =9+7 = 16

Option D

Like this post

rijul007: Legendary Member; Posts: 588; Joined: Sun Oct 16, 2011 9:42 amFollowed by: 9 members; Location: New Delhi, India; Thanked: 130 times; GMAT Score:720

by rijul007 » Sun Nov 13, 2011 10:15 am

for a number to have maximum length.. it should have the highest no of prime factors not necessarily distinct

a number should have max nuber of 2s as a prime factor for the max length..

x>1
y>1

x = 2^a [a is the length of x]
y = 2^b

x+3y<1000
2^a + 3(2)^b <1000

highest value of 2^a that can fit into this is 512

2^a = 512
a = 9

3(2)^b <1000-512
2^b < 488/3
2^b < 162
highest value of 2^b can be 128
b = 7

Maximum sum of length of x and length of y = a + b =9+7 = 16

Option D

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review