integers - divisibility

Expert replies

arocks: Master | Next Rank: 500 Posts; Posts: 127; Joined: Tue Oct 02, 2007 9:35 am; Thanked: 1 times

by arocks » Sun Oct 14, 2007 6:04 am

When positive integer x is divided by 5, the remainder is 3; and when x is divided by 7, the remainder is 4. When positive integer y is divided by 5, the remainder is 3; and when y is divided by 7, the remainder is 4. If x > y, which of the following must be a factor of x - y?

A. 12
B. 15
C. 20
D. 28
E. 35

Please explain. Thanks. OA - E

One of the numbers could be 18 -
18 divided by 5 leaves 3 as remainder;
18 divided by 7 leaves 4 as remainder;

Not sure which the other number is...How do we find such numbers?

Source: Beat The GMAT — Problem Solving | Sun Oct 14, 2007 6:04 am

Suyog: Master | Next Rank: 500 Posts; Posts: 315; Joined: Thu Aug 17, 2006 10:43 pm; Thanked: 23 times

by Suyog » Sun Oct 14, 2007 7:10 am

Integer x is divided by 5, the remainder is 3;

Here the first integer will be 3 just go on adding 5 to it and write down 10-12 such numbers:

3 8 13 18 23 28 33 38 43 48 53 58

when y is divided by 7, the remainder is 4;

Here the first integer will be 4 just go on adding 7 to it and write down 10-12 such numbers:

4 11 18 25 32 39 46 53..... we got 2 common numbers....18 and 53

since x > y; x = 53 and y = 18
x - y = 53 - 18 = 35

Ans E.

arocks: Master | Next Rank: 500 Posts; Posts: 127; Joined: Tue Oct 02, 2007 9:35 am; Thanked: 1 times

by arocks » Sun Oct 14, 2007 7:14 am

Perfect...thanks!

samirpandeyit62: Master | Next Rank: 500 Posts; Posts: 460; Joined: Sun Mar 25, 2007 7:42 am; Thanked: 27 times

by samirpandeyit62 » Sun Oct 14, 2007 7:23 am

When positive integer x is divided by 5, the remainder is 3; and when x is divided by 7, the remainder is 4. When positive integer y is divided by 5, the remainder is 3; and when y is divided by 7, the remainder is 4. If x > y, which of the following must be a factor of x - y?

so when x-y is divided by 5 the remainder is 0 (3-3 =0)

also when x-y is divided by 7 remainder is 0 (4-4 =0)

so 5&7 are factors of x-y

i.e 5*7= 35 is a factor of x-y

E

Regards
Samir

Featured schoolRound 2 closes Jan 7, 2027 54 days left

Chicago Booth

Since 1982, 10 Booth faculty members have received the Nobel Prize in Economic Sciences, more than any other business school.

#3
U.S. News rank: $175,000
Median base salary: 670
Average GMAT Focus: 635
Students in the class

Apply to Booth Visit chicagobooth.edu See the full profile

Photo: Warren LeMay, CC BY-SA 2.0

GMAT Course Reviews

563 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (563 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