When positive integer p is divided by 7 the remainder is 2.

Question

When positive integer p is divided by 7, the remainder is 2. Is p divisible by 8?

(1) p is divisible by 2 and 3

(2) p<100

M05-20

KarishmaB · Accepted Answer

When you are given different remainders - 2 when divided by 7 and 0 when divided by 6 (using stmnt 1), you have to find the first such common number. Discussion on Division and Remainders here: https://www.youtube.com/watch?v=A5abKfUBFSc

x2suresh · Answer

p= 7k+2

p values when k=0,1,2,3,4,..

p=2,9,16,23,30,37,44,51,58,65,72,79,86,93,100
 
1) 
p is divided by 2 and 3 = p is dived by 6
possible values are 
30 -- remainder when divided by 8 --6
72-- remainder when divided by 8 --0.

not sufficient

2) 
p<100

not sufficient.

commbined not sufficient see statement1

E

wcgc · Answer

how did you get from this step:
p is divided by 2 and 3 = p is dived by 6
To this step:
possible values are
30 -- remainder when divided by 8 --6
72-- remainder when divided by 8 --0.

Could someone explain the logic behind it?

unplugged · Answer

wcgmat,

of the sample values mentioned, there are only 2 numbers - 30, 72, that are divisible by both 2 and 3

Cheers,
Unplugged

xALIx · Answer

Great explanation Suresh!!! I've always considered it 7p+2, but you're correct in noting it as 7k+2. 
Thanks!

wcgc · Answer

Ok, I see that in this example, 30 and 72 is obtained when we count out a bunch of numbers that fit the remainder equation that was provided. But when you encounter remainder type of problems like this, do you always just calculate out a bunch of sample numbers according to the equation provided? Is this the best strategy to use? Or are there mathematical ways to obtain numbers like 30 and 72?

seofah · Answer

As p is even, one can shorten the iteration by calculating p for even values of k. 
Any more shortcuts?

shelrod007 · Answer

I got the answer by listing down multiples of 6 and ( multiples of 7 ) + 2 till i found a match for 2 numbers is there a faster way of doing this ?

Since in the gmat time matters the most !!!

Bunuel · Answer

When positive integer  p  is divided by 7, the remainder is 2. Is  p  divisible by 8? 
 
When a positive integer  p  is divided by 7, the remainder is 2 can be expressed as  p=7q+2 , meaning that  p  can be: 2, 9,  16 , 23, 30, 37, 44, 51, 58, 65,  72 , and so forth.
 
(1)  p  is divisible by 2 and 3. 
 
This statement implies that  p  is a multiple of 6. Hence,  p  could be 30 (in which case the answer is NO) or 72 (in which case the answer is YES). This is not sufficient.
 
(2)  p < 100 . 
 
This statement is clearly insufficient by itself.
 
(1)+(2) Even when combining the two statements,  p  could still be either 30 (answer NO) or 72 (answer YES). Not sufficient.

Answer: E

AayushGMAT · Answer

if P is divided by 7 then remainder is 2, then what will be the remainder if p is divided by 8

Statement 1:

p is divisible by 2 and 3 
so we can say that p is divisible by all the multiples of 6

now we have to take the multiple of 6 which when divided by 7 gives remainder 2.
so the values are 30, 72 and so on

and when we divide 30 with 8 we get 6 as remainder but when we divide 72 with 8 we get o as remainder.

so this statement is clearly insufficient

Statement 2:   p < 100

clearly insufficient as p can be any value and thus can give any remainder from 0 to 9 when divided by 8

Combining both the statements

Clearly insufficient as we already know that there are 2 possible values of p under 100 and both are giving different remainder( i.e 6 and 0 resp.)

therefore the answer is   E

stonecold · Answer

Choose 72 and 30 as the two numbers and we can discard both the statements
Hence E

carma19 · Answer

p can be: 2, 9, 16, 23,  30 , 37, 44, 51, 58, 65,  72 , ...
(1) tells us that p is a multiple of 6. NS
(2) p<100 clearly insufficient
(1&2) if p=30 then NO; if p=72 then YES. Therefore, NS
( E )

gmatassassin88 · Answer

VeritasKarishma

link in not working. could you elaborate how finding common number can help reduce time.

KarishmaB · Answer

We were facing some technical difficulties with the blog. All links are working now. Please check.

CrackverbalGMAT · Answer

Information provided by Q. stem:
 
p is a positive integer

When p is divided by 7,the remainder is 2

Is p divisible by 8 or is p a multiple of 8?

St(1):p is divisible by 2 and 3

p is divisible by 6 and from the stem, p can be written as 7k + 2 where k is an integer

At k = 4, p is 30 is divisible by 6. Also the answer to the Q. stem is a No

At k=10, p is 72 and 72 is divisible by 6. Also the answer to the Q. stem is a Yes

(insufficient) Eliminate A,D

St(2):p<100

Clearly insufficient. p can be 72 & 30 providing answers of Yes & No to the Q.stem.

(insufficient) Eliminate B.

Combining 1 & 2,
p is divisible by 2 and 3 and <100

Using the same inputs,

If p = 30 answer to the Q. stem is a No

If p = 72 answer to the Q. stem is a Yes

(insufficient)
 (option e)

D.S
GMAT SME

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When positive integer p is divided by 7 the remainder is 2.

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When positive integer p is divided by 7 the remainder is 2.

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