It is currently 12 Dec 2018, 14:04
My Tests

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

When p is divided by 7, the remainder is 4. When p is divide

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Senior Manager
Senior Manager
Joined: 20 May 2014
Posts: 282
Followers: 15

Kudos [?]: 49 [0], given: 220

CAT Tests
When p is divided by 7, the remainder is 4. When p is divide [#permalink] New post 05 Nov 2017, 01:58
00:00

Question Stats:

83% (02:51) correct 16% (00:01) wrong based on 6 sessions
When p is divided by 7, the remainder is 4. When p is divided by 4, the remainder is 1. How many different values of p are less than 120?

(A) 2

(B) 4

(C) 5

(D) 11

(E) 18

Kudos for correct solution.
[Reveal] Spoiler: OA
1 KUDOS received
Director
Director
Joined: 03 Sep 2017
Posts: 521
Followers: 1

Kudos [?]: 330 [1] , given: 66

Re: When p is divided by 7, the remainder is 4. When p is divide [#permalink] New post 05 Nov 2017, 06:56
1
This post received
KUDOS
Here we can notice that if a number divided by 7 leaves a remainder of 4, it means that if we sum 3 to it it becomes divisible by 7. The same holds for the division by 4: since the remainder is 1 when dividing by 4, if we sum 3, we get a number divisible by 4.

Since the number we have to sum to make the number divisible by 7 and 4 is the same, it means that the number is divisible by the product of 7 and 4, i.e. 28. Thus, we have to look for the number of numbers less than 120 which are multiples of 28.

Then, using the formula and given the first multiple equal to 28 and the highest one equal to 112, we get \(\frac{112-28}{28}+1 = 4\).

Answer B
1 KUDOS received
Target Test Prep Representative
User avatar
Status: Head GRE Instructor
Affiliations: Target Test Prep
Joined: 09 May 2016
Posts: 161
Location: United States
Followers: 4

Kudos [?]: 117 [1] , given: 0

Re: When p is divided by 7, the remainder is 4. When p is divide [#permalink] New post 09 Jan 2018, 10:11
1
This post received
KUDOS
Expert's post
Bunuel wrote:
When p is divided by 7, the remainder is 4. When p is divided by 4, the remainder is 1. How many different values of p are less than 120?

(A) 2

(B) 4

(C) 5

(D) 11

(E) 18


We have the following two equations:

p = 7Q + 4 where Q is a whole number.

So, p can be values such as 4, 11, 18, 25, …, 7(16) + 4 = 116.

and

p = 4S + 1 where S is a whole number.

So, p can be values such as 1, 5, 13, 14, 21, 25, …, 4(29) + 1 = 117.

We see that 25 is the first matching value of p. Since the LCM of 7 and 4 is 28, the next will be 25 + 28 = 53, and the next will be 53 + 28 = 81, and the final matching value will be 81 + 28 = 109, so there are a total of 4 values of p less than 120 that satisfy the two criteria.

Alternate Solution:

We have

p = 7Q + 4

for some Q and

p = 4S + 1

for some S.

Then, p + 3 = 7Q + 7 = 4S + 4 is divisible by both 7 and 4. Let’s list the numbers less than 120 that are divisible by 7 and 4, i.e., by 28: 0, 28, 56, 84, 112. However, these are values for p + 3; thus, the corresponding values for p are -3, 25, 53, 81, and 109. p can take any value in this list except for -3; therefore, there are four values in total.

Answer: B
_________________

Jeffery Miller
Head of GRE Instruction

GRE Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Re: When p is divided by 7, the remainder is 4. When p is divide   [#permalink] 09 Jan 2018, 10:11
Display posts from previous: Sort by

When p is divided by 7, the remainder is 4. When p is divide

  Question banks Downloads My Bookmarks Reviews Important topics  


GRE Prep Club Forum Home| About| Terms and Conditions and Privacy Policy| GRE Prep Club Rules| Contact

Powered by phpBB © phpBB Group

Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.