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If p and q are two positive integers and p/q = 1.15

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If p and q are two positive integers and p/q = 1.15  [#permalink]

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New post 06 Feb 2016, 11:45
1
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A
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C
D
E

Difficulty:

  25% (medium)

Question Stats:

71% (01:15) correct 29% (01:35) wrong based on 308 sessions

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If p and q are two positive integers and p/q = 1.15, then p can equal which one of the following?

(A) 15
(B) 18
(C) 20
(D) 22
(E) 23

Source: GMAT math Bible

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Re: If p and q are two positive integers and p/q = 1.15  [#permalink]

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New post 06 Feb 2016, 11:57
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BrainLab wrote:
If p and q are two positive integers and p/q = 1.15, then p can equal which one of the following?

(A) 15
(B) 18
(C) 20
(D) 22
(E) 23

Source: GMAT math Bible

p/q = 1.15 = 115/100 = 23/20

So, p COULD equal 23
Answer: E

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Re: If p and q are two positive integers and p/q = 1.15  [#permalink]

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New post 06 Feb 2016, 12:58
1
BrainLab wrote:
If p and q are two positive integers and p/q = 1.15, then p can equal which one of the following?

(A) 15
(B) 18
(C) 20
(D) 22
(E) 23

Source: GMAT math Bible


This is a classic question utilizing the definition of a divisor, quotient and dividend relation.

Dividend = divisor * quotient + remainder

Thus, p/q = 1.15 ---> p = 1.15q = q + 0.15q

Now, remainder can only be integer. Thus lets say 0.15q = I (an integer) ---> q=20*I/3. Thus I must be a multiple of 3 , making q as a multiple of 20. As the minimum value of q can be 20, eliminate A,B ,C .

Coming back to the question and the remaining options. If the divisor is 20, the remainder must be = 3 (based on the fact that I is a multiple of 3), giving you Dividend = 20+3=23.

E is thus the correct answer.

Hope this helps.
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If p and q are two positive integers and p/q = 1.15  [#permalink]

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New post 07 Feb 2016, 12:02
These are sub 600 level questions.
I don't fool myself
These sets of GMAT math bible questions aren't your typical GMAT 600-700 level questions.
One must have never reviewed a GMAT CAT to describe the question above as 600level.
It's simply ridiculous and delusional to rank it 600-700level.
I'm sorry but that's the truth.
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Re: If p and q are two positive integers and p/q = 1.15  [#permalink]

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New post 07 Feb 2016, 12:32
Nez wrote:
These are sub 600 level questions.
I don't fool myself
These sets of GMAT math bible questions aren't your typical GMAT 600-700 level questions.
One must have never reviewed a GMAT CAT to describe the question above as 600level.
It's simply ridiculous and delusional to rank it 600-700level.
I'm sorry but that's the truth.


Might be, but relax... Based on the responses one can evaluate better the difficulty level of this question, and I'll update it accordingly.
BTW there's no difficulty level given for GMATprep questions and even respected GMAT Tutors avoid classifying those ;)
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Re: If p and q are two positive integers and p/q = 1.15  [#permalink]

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New post 14 Apr 2017, 04:45
1
BrainLab wrote:
If p and q are two positive integers and p/q = 1.15, then p can equal which one of the following?

(A) 15
(B) 18
(C) 20
(D) 22
(E) 23


This problem will be best solved using the remainder formula. Let’s first state the remainder formula:

When positive integer x is divided by positive integer y, if integer Q is the quotient and r is the remainder, then x/y = Q + r/y.

We are given that p and q are two positive integers and p/q = 1.15. Thus:

p/q = 1 + 15/100, or Q + r/q = 1 + 15/100

Since 15/100 = 3/20, r/q = 3/20 or r/q = 3k/20k for some positive integer k. We can see that r is 3 or a multiple of 3.

If r = 3, then q = 20 and p = 23.

Since 23 is one of the answer choices, choice E is the correct answer.

Alternate Solution:

Let’s convert the decimal 1.15 to a mixed number and then to an improper fraction:

1.15 = 1 15/100 = 1 3/20 = 23/20

We know that p/q = 1.15, so p/q = 23/20. Thus, one possible value for p is 23.

Answer: E
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Re: If p and q are two positive integers and p/q = 1.15  [#permalink]

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New post 14 Apr 2017, 06:31
BrainLab wrote:
If p and q are two positive integers and p/q = 1.15, then p can equal which one of the following?

(A) 15
(B) 18
(C) 20
(D) 22
(E) 23

Source: GMAT math Bible


\(\frac{p}{q} = 1.15\)

Or, \(\frac{p}{q} = 115/100\)

Or, \(\frac{p}{q} = 23/50\)

So the answer is p can be (E) 23
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Re: If p and q are two positive integers and p/q = 1.15  [#permalink]

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New post 21 Jan 2019, 17:27
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Re: If p and q are two positive integers and p/q = 1.15   [#permalink] 21 Jan 2019, 17:27
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