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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)  [#permalink]

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New post 11 Oct 2018, 10:15
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Difficulty:

  25% (medium)

Question Stats:

77% (01:15) correct 23% (01:30) wrong based on 59 sessions

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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

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Re: Is p/7 and Integer? 1) When p is divided by 35, the remainder is 7 2)  [#permalink]

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New post 11 Oct 2018, 11:53
GMATinsight wrote:
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: http://www.GMATinsight.com

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

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

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


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


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

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Re: Is p/7 and Integer? 1) When p is divided by 35, the remainder is 7 2)  [#permalink]

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New post 11 Oct 2018, 13:08
GMATinsight wrote:
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: http://www.GMATinsight.com


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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Re: Is p/7 and Integer? 1) When p is divided by 35, the remainder is 7 2)  [#permalink]

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New post 11 Oct 2018, 21:03
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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).
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Re: Is p/7 and Integer? 1) When p is divided by 35, the remainder is 7 2)   [#permalink] 11 Oct 2018, 21:03
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