Is p/7 and Integer? 1) When p is divided by 35, the remainder is 7 2)

Question

Is p/7 and Integer? 1) When p is divided by 35, the remainder is 7 2) When p is divided by 6, the remainder is 1 Source: www.GMATinsight.com

fskilnik · Answer

{p \over 7}\,\,\,\mathop = \limits^? \,\,\,{\mathop{\rm int}}

\left( 1 \right)\,\,p = 35M + 7\,\,,\,\,M\,\,{\mathop{\rm int}}

?\,\,\,:\,\,\,{p \over 7} = 5M + 1\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\,\,\,\,\,\,\,\left( {5 \cdot {\mathop{\rm int}} \,\, + 1 = {\mathop{\rm int}} } \right)

\left( 2 \right)\,\,\,p = 6N + 1\,\,\,,\,\,\,N\,\,{\mathop{\rm int}} \,\,\,\,\,\,\left\{ \matrix{
 \,{\rm{Take}}\,\,N = 0\,\,\, \Rightarrow \,\,\,p = 1\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\, \hfill \cr 
 \,{\rm{Take}}\,\,N = 1\,\,\, \Rightarrow \,\,\,p = 7\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\, \hfill \cr} \right.

This solution follows the notations and rationale taught in the GMATH method.

Regards, 
Fabio.

Salsanousi · Answer

Statement 1)

p/35 = q + 7/35

p = 35q + 7
p will always be a multiple of 7

Sufficient.

Statement 2)

p/6 = q + 1/6

p = 6q + 1

P can be a multiple of 7 if q = 1
And is not a multiple of 7 if q = 0

Two different answers.

Insufficient.

Answer choice A

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KrishnakumarKA1 · Answer

Hi,

Question: Is p/7 an (not and) integer?

That is, whether is “p” is a multiple of 7 or not?

Remainder questions are popular in GMAT, all you require to do is write down the few initial values according to the information provided and you will get to the see pattern or different values.

Statement I is sufficient:

When p is divided by 35, the remainder is 7

Using division rule, we can write the above statement as,

p = 35q + 7, where q is the quotient value.

We can write down few initial values here which satisfies the above statement.

p = 7, 42, 77, 112, etc …

We can clearly see that all the values are divisible by 7.

Because p = 35q + 7, where 35q is a multiple of 7 and also the 7 in the expression is of course divisible by 7.

So, p is divisible by 7. Statement I is sufficient.

Statement II is insufficient:

When p is divided by 6, the remainder is 1

Again, using the division rule,

We can write it as,

p = 6q + 1

So,

p = 1,7,13,20,27, 34,41,49….

We can see that, 7 and 49 are divisible by 7

But 1, 13 ,20 etc are not divisible.

So this statement is insufficient to answer the question.

So the answer is I only(Statement I alone sufficient).

bumpbot · Answer

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Is p/7 and Integer? 1) When p is divided by 35, the remainder is 7 2)

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Is p/7 and Integer? 1) When p is divided by 35, the remainder is 7 2)

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