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

Question

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.

niks18 · Accepted Answer

P = 9k+4 , where  k  is any positive integer and since  P>7  so  k  is not equal to  0

A. The number that is 4 less than P is a multiple of 9.  =>9k+4-4=9k . clearly a multiple of  9 .  True

B. The number that is 5 more than P is a multiple of 9.  =>9k+4+5=9k+9 . clearly a multiple of  9 .  True

C. The number that is 2 more than P is a multiple of 3.  =>9k+4+2=9k+6=3(3k+2) . clearly a multiple of  3 .  True

D. When divided by 3, P will leave a remainder of 1.  =>\frac{9k+4}{3}=3k+\frac{4}{3} . This will leave a remainder  1 .  True

E. When divided by 2, P will leave remainder of 1.  =>9k+4 , if  k  is even then it will be divisible by  2  but if  k  is odd then it will leave a remainder of  1  when divided by  2 . Hence Not True always

Option  E

Mick1005 · Answer

We can Make different cases in this question.
For example lets take P which satisfies the conditions given in the questions i.e multiple of 9 plus 4.
So it can be 31,40,49
a)Always True (27,36,45 are multiples of 9)
b)Always true(Negative remainder , so this will also be true)
c)Always true( 33,42,51 are multiples of 3)
d)Always true( Leaving remainder 1) (Also remainder 4 in the question divide by 3 also leaves 1 as remainder)
e)Not always True. (40 is divisible by 2)

Thus OA= E .
Please correct me if I am wrong.

JeffTargetTestPrep · Answer

We can create the following equation:

P = 9Q + 4

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

13, 22, 31, 40, ...

Let’s review the answer choices.

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.

Answer: E

brs1cob · Answer

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

gracie · Answer

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

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards