12 Days of Christmas GMAT Competition - Day 11: If p is a positive mul

Question

12 Days of Christmas GMAT Competition with Lots of Fun

If p is a positive integer divisible by 10, and r is the remainder when p is divided by 15, what is the value of r?

(1) p is not a multiple of 6
(2) When p + 7 is divided by 15, the remainder is less than r.

https://gmatclub.com/blog/wp-content/uploads/2020/12/12-days-of-christmas.jpg

M36-91

Bunuel · Accepted Answer

Official Solution:

If  p  is a positive integer divisible by 10, and  r  is the remainder when  p  is divided by 15, what is the value of  r ? 
 
 p  is a positive integer divisible by 10: 10, 20, 30, 40...
 
The remainder when  p  is divided by 15: 10, 5, 0, 10, ...
 
As we can see the remainder,  r , can be 10, 5, or 0.
 
(1)  p  is not a multiple of 6
 
If  p  is 10, the remainder is 10 but if  p  is 20, the remainder is 5. Not sufficient.
 
(2) When  p + 7  is divided by 15, the remainder is less than  r .
 
 p + 7=  17, 27, 37, 47, ...
 
 p + 7  divided by 15 gives the following remainders: 2, 12, 7, 2, ... The corresponding values of  r  are 10, 5, 0, 10, ...
 
As we can see the remainder is less than  r  when  r=10 . Sufficient.

Answer: B

zhanbo · Answer

My answer is  (B) . It took me 2 minutes. This is a relatively straightforward question.

If p is a positive integer divisible by 10, and r is the remainder when p is divided by 15, what is the value of r? 
Analysis:
P can be 10, 20, 30, 40, .... when divided by 15, 
remainder r is 10, 5, 0, 10, ... 
Notice the pattern: remainder r can be 10, 5, or 0. 
But exactly what r is?

(1) p is not a multiple of 6 
Meaning p cannot be 30, 60, 90, ... 
But p can still be 10 or 20
With r 10 or 5
INSUFFICIENT

(2) When p + 7 is divided by 15, the remainder is less than r. 
p+7 17, 27, 37, 47 ... 
remainder 2, 12, 7 , 2 ....
 r is 10, 5, 0, 10, ... 
Note: 2 < 10, but 12 > 5 and 7 > 0
We can determine that r is 10. 
SUFFICIENT.

bond001 · Answer

Answer B
p=10x
10x/15=some remainder R
from statment 1 
p=10,20,40,50...
r=10,5,10,5,...
from statement 2
p1=10,20,30,40,50,60,70,80,....
p2+7=17,27,37,47,57,67,77,87...
R1=10,5,0,10..
R2=2,12,7,2..
so the remainder is constant 10 sufficient

Green2k1 · Answer

If p is a positive integer divisible by 10, and r is the remainder when p is divided by 15, what is the value of r?
 p = 10k1 means 10,20, 30, 40, 50......
p = 15 k2 + r , Means r = 10, 5,0, ...........

(1) p is not a multiple of 6

means 30, 60, 90 ........ not possible. Means r= 10 or 5 not sufficient

(2) When p + 7 is divided by 15, the remainder is less than r.
 17, 27,37,47.........
the possible remainder - 2, 12, 7 is id less than r = 10, 5, 0

Which possible in the case where P= 10, 40, 70.......... therefore r= 10

Sufficient 
 
Correct Answer B

dep · Answer

If p is a positive integer divisible by 10, and r is the remainder when p is divided by 15, what is the value of r?
p=15n+r
p=10m
if n is odd then r =5
if n is even then r =10 or 0

(1) p is not a multiple of 6
p is not divisible by 3
Insufficient

(2) When p + 7 is divided by 15, the remainder is less than r.
if p+7 remainder is less than r then r >7
ie r =10 and n is even
Sufficient

IMO B

rocky620 · Answer

We can generalize that P is of the form 15n+5; 15n-5; 15n (when n is an even integer).

Case-1:  If P = 15n+5 the remainder (r) will be 5 (n is odd)
 Case-2: If P = 15n-5 the remainder (r) will be 10 (-5+15) (n is odd)
 Case-3: If P = 15n (when n is an even integer) the remainder (r) will be 0

Statement-1 
P is not a multiple of 6, so Case 3 will be eliminated. But we still have 2 values of r.
  Insufficient.

Statement-2 
In Case 1 - r will be 12
In Case 2 - r will be 2
In Case 3 - r will be 7

Only in Case 2 the remainder is less than r. So P will have a remainder 10 when divided by 15.

Sufficient.

IMO Option B

unraveled · Answer

If p is a positive integer divisible by 10, and r is the remainder when p is divided by 15, what is the value of r?

Thus r = 0 or 5 or 10

(1) p is not a multiple of 6
I: p = 10; r = 10
II: p = 20; r = 5

INSUFFICIENT.

(2) When p + 7 is divided by 15, the remainder is less than r.
Let remainder is r'.
p = 10 
p + 7 = 17;  r'= 2 and r = 10

p = 20
p + 7 = 27;  r'= 12 and r = 5

p = 30
p + 7 = 37;  r'= 7 and r = 0

p = 40
p + 7 = 47;  r'= 2 and r = 10

p = 50
p + 7 = 57;  r'= 12 and r = 5

p = 60
p + 7 = 67;  r'= 7 and r = 0

So, a pattern is formed where out of 3 remainders possible only 1 is applicable.
Hence r = 10

SUFFICIENT.

Answer B.

Nishant1795 · Answer

IMO Option B.

1. Insufficient
If p = 10, r = 10 and if p = 20, r = 5. We don't have a single value for r.

2. Sufficient
The pattern can be seen in the below table:

p r p+7 r2 r<r2?
10 10 17 2 No
20 5 27 12 No
30 0 37 7 Yes
40 10 47 2 No
50 5 57 12 No
60 0 67 7 Yes

As can be seen, statement 2 is true for values of p = 30, 60, 90, etc. Hence Sufficient.

Answer = B

ashu2526 · Answer

The value of r is 10
P is divisible by 10 = 10, 20, 30, 40, 50, 60, 70, 80, 90......
P when divided by 15 leaves a remainder = SO for remainder P will be excluded with (N*10 - LCM of 10, 15)
So, P consist of 10, 20, 40, 50, 70, 80

Statement 1: No not a multiple of 6, which we have already excluded during removal of LCM of 10,15
Statement 2: P+7/15, remainder is smaller than r

Cases1: 10/15 = r 10, 17/15 = 2
True
Case 2: 20/15 = r 5, 27/15 = 12
False
Case 3: 40/15 = r 10, 47/15 = 2
True
Case 4: 50/15 = r 5, 57/15 = 12

Pattern, only P as 10, 40, 70.... will satisfy 
So, r = 10

Answer 10

Kinshook · Answer

Asked: If p is a positive integer divisible by 10, and r is the remainder when p is divided by 15, what is the value of r?

p = 10k; where k is an integer
r = 0 when p=10k is divided by 15 when k = 3m
r = 10 when p=10k is divided by 15 when k = 3m + 1
r = 5 when p=10k is divided by 15 when k = 3m + 2

(1) p is not a multiple of 6
k is not = 3m
r = 10 when p=10k is divided by 15 when k = 3m + 1
r = 5 when p=10k is divided by 15 when k = 3m + 2
NOT SUFFICIENT

(2) When p + 7 is divided by 15, the remainder is less than r.
r = 0 when p=10k is divided by 15 when k = 3m: Not feasible since remainder can not be less than r=0: NOT FEASIBLE
r = 10 when p=10k is divided by 15 when k = 3m + 1; Remainder = 2 < r=10 when p + 7 = 30m + 17 when divided by 15 : FEASIBLE
r = 5 when p=10k is divided by 15 when k = 3m + 2; Remainder = 12 > r=5 when p + 7 = 30m + 27 when divided by 15: NOT FEASIBLE
r = 10
SUFFICIENT

IMO B

DinoPen · Answer

If p is a positive integer divisible by 10, and r is the remainder when p is divided by 15, what is the value of r?

p % 10 = 0
p % 15 = r
r = ?

(1) p is not a multiple of 6
p !% = 6
p = 10 r = 10
p = 20 r = 5
p = 40 r = 10
p = 50 r = 5 etc..
Hence, r = 5 or 10. 
Not sufficient.

(2) When p + 7 is divided by 15, the remainder is less than r.
p + 7 % 15 = R < r
p = 10 R = 2 < r, r = 10 Yes.
P = 20 R = 12 < r, r = 5 No.
Therefore, r = 10
sufficient.

carouselambra · Answer

IMO B

If p is a positive integer divisible by 10, and r is the remainder when p is divided by 15, what is the value of r?

(1) p is not a multiple of 6
Example :
a. p=20 and r=5
b. p=70 and r=10

Value of r is not consistent hence (A) is not sufficient

(2) When p + 7 is divided by 15, the remainder is less than r.
Example:
a. p=77 , r=2 (here p was 70)
b. p=107, r=2( here, p was 100)
c. p=47, r =2 (here, p was 40)
d. p=130 , r=2 (here, p was 130)

Value of r is consistent hence (B) is sufficient

winterschool · Answer

If p is a positive integer divisible by 10, and r is the remainder when p is divided by 15, what is the value of r?

(1) p is not a multiple of 6
(2) When p + 7 is divided by 15, the remainder is less than r.

p = 10, 20, 30, .......
p = 15 x + r, 
p =20, r = 5; 
p=30, r=0; 
p=40, r= 10
p=50, r=5,
...........

Statement 1:

p cant be 30, 60, 90.....
r can be 10 or 5
Not Sufficient

Statement 2:

p=27, r =12
p=37, r= 7
p=47, r=2
p=57, r=12

Sufficient
r=10

Answer B

minustark · Answer

1) p can be 40 or 50. In the first case, r is 10 and in the second, r is 5. Not sufficient.

2) When p = 10, p + 7 = 17, so the remainder when it is divided by 15 is 2, which is less than r = 10. Again when, p = 20, p + 7 = 27, which will violate the condition as 12 is greater than r = 5. Again when p =30, p + 7 = 37, which will produce remainder of 7, which will not fulfill the condition. So, p + 7 will produce a remainder less than r only when p is 10, 100, 1000 etc. r will be 10 then. Sufficient.

B is the answer.

Gmatfox · Answer

p = 10, 20, 30, ... p : 15 -- remainder r = ? Cycle of r is 10, 5, 0 1) p is not a multiple of 6 p = 10 then r = 10 p = 20 then r = 5 Insuff. 2) r((p + 7)/15) (r') < r(p/15) (r) . r = 10 then r' = 2 < r . r = 5 then r' = 12 > r. Then r cannot be 5 . r = 0 then r' = 7 > r. Then r cannot be 0 Finally, r can only be 10. Suff. Correct answer: B Posted from my mobile device

bumpbot · Answer

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.

12 Days of Christmas GMAT Competition - Day 11: If p is a positive mul

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 Data Sufficiency (DS) Questions

12 Days of Christmas GMAT Competition - Day 11: If p is a positive mul

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