Last visit was: 14 Jul 2024, 06:59 It is currently 14 Jul 2024, 06:59
Toolkit
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

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.

# The integer P is greater than 7. If the integer P leaves a remainder

SORT BY:
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 94342
Own Kudos [?]: 640697 [16]
Given Kudos: 85011
Retired Moderator
Joined: 25 Feb 2013
Posts: 893
Own Kudos [?]: 1552 [8]
Given Kudos: 54
Location: India
GPA: 3.82
General Discussion
Manager
Joined: 15 Aug 2016
Posts: 168
Own Kudos [?]: 56 [0]
Given Kudos: 156
Location: India
Concentration: Technology, Operations
GMAT 1: 690 Q49 V35
GPA: 3.84
WE:Operations (Consulting)
Target Test Prep Representative
Joined: 04 Mar 2011
Affiliations: Target Test Prep
Posts: 3037
Own Kudos [?]: 6562 [0]
Given Kudos: 1646
Re: The integer P is greater than 7. If the integer P leaves a remainder [#permalink]
Bunuel wrote:
The integer P is greater than 7. If the integer P leaves a remainder of 4 when divided by 9, all of the following must be true EXCEPT

A. The number that is 4 less than P is a multiple of 9.
B. The number that is 5 more than P is a multiple of 9.
C. The number that is 2 more than P is a multiple of 3.
D. When divided by 3, P will leave a remainder of 1.
E. When divided by 2, P will leave remainder of 1.

We can create the following equation:

P = 9Q + 4

Thus, we see that P can be values such as:

13, 22, 31, 40, ...

A) The number that is 4 less than P is a multiple of 9.

P - 4 = 9Q + 4 - 4

P - 4 = 9Q

A is true.

B) The number that is 5 more than P is a multiple of 9.

P + 5 = 9Q + 4 + 5

P + 5 = 9Q + 9

B is true.

C) The number that is 2 more than P is a multiple of 3.

P + 2 = 9Q + 4 + 2

P + 2 = 9Q + 6

C is true.

D) When divided by 3, P will leave a remainder of 1.

(9Q + 4)/3 = (3Q + 1) + 1/3

D is true.

E) When divided by 2, P will leave remainder of 1.

(9Q + 2)/2 = (4Q + 1) + Q/2

We can’t be certain what the remainder is. If Q = 1, then the remainder is 1; however, if Q is 2, then the remainder is 0.

Alternate solution:

Since the problem says all of the answer choices must be true except one of them, we can use any integer > 7 that satisfies the condition “when it is divided by 9, it will leave a remainder of 4” to check the answer choices. Since 13 is one such number, we will use that.

A) 13 - 4 = 9 and 9 is a multiple of 9. This is true.

B) 13 + 5 = 18 and 18 is a multiple of 9. This is true.

C) 13 + 2 = 15 and 15 is a multiple of 3. This is true.

D) 13/3 = 4 R 1. This is true.

E) 13/2 = 6 R 1. This is true.

Since 13 makes all answer choices true, we need to use another number. Another number we can use is 13 + 9 = 22.

Instead of checking each answer choice again, we can see that choice E is not true, since when 22 is divided by 2, the remainder is 0, not 1.

Manager
Joined: 06 Jun 2013
Posts: 120
Own Kudos [?]: 37 [0]
Given Kudos: 339
Location: India
Concentration: Finance, Economics
Schools: Tuck
GMAT 1: 640 Q49 V30
GPA: 3.6
WE:Engineering (Computer Software)
Re: The integer P is greater than 7. If the integer P leaves a remainder [#permalink]
E is the correct option .

P = 9k + 4

k= 1,2,3 ....

P1 = 9*1 + 4 = 13, when divided by 2, remainder is 1

P2 = 9*2 + 4 = 22, when divided by 2, remainder is 0
VP
Joined: 07 Dec 2014
Posts: 1068
Own Kudos [?]: 1606 [0]
Given Kudos: 27
The integer P is greater than 7. If the integer P leaves a remainder [#permalink]
Bunuel wrote:
The integer P is greater than 7. If the integer P leaves a remainder of 4 when divided by 9, all of the following must be true EXCEPT

A. The number that is 4 less than P is a multiple of 9.
B. The number that is 5 more than P is a multiple of 9.
C. The number that is 2 more than P is a multiple of 3.
D. When divided by 3, P will leave a remainder of 1.
E. When divided by 2, P will leave remainder of 1.

if P+4 is even, e.g., 22,40,58...
then P/2 will leave no remainder
E

Originally posted by gracie on 29 Nov 2017, 20:36.
Last edited by gracie on 29 Mar 2020, 20:45, edited 1 time in total.
Non-Human User
Joined: 09 Sep 2013
Posts: 33969
Own Kudos [?]: 851 [0]
Given Kudos: 0
Re: The integer P is greater than 7. If the integer P leaves a remainder [#permalink]
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Re: The integer P is greater than 7. If the integer P leaves a remainder [#permalink]
Moderator:
Math Expert
94342 posts