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# Question of the Week 44 (For integers p and q, if |p – 9| < 2 and...)

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e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3142
Question of the Week 44 (For integers p and q, if |p – 9| < 2 and...)  [#permalink]

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17 May 2019, 04:33
00:00

Difficulty:

95% (hard)

Question Stats:

41% (02:57) correct 59% (03:00) wrong based on 88 sessions

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Question of the Week #44

For integers p and q, if |p – 9| < 2 and |q – 7| ≤ 2, then how many values are possible for pq which are either multiple of only 3 or only 5?

A. 9
B. 10
C. 11
D. 12
E. 13

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Schools: Stern '22 (II)
GMAT 1: 760 Q50 V44
Question of the Week 44 (For integers p and q, if |p – 9| < 2 and...)  [#permalink]

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Updated on: 23 May 2019, 21:11
2
EgmatQuantExpert wrote:
Question of the Week #44

For integers p and q, if |p – 9| < 2 and |q – 7| ≤ 2, then how many values are possible for pq which are either multiple of only 3 or only 5?

A. 9
B. 10
C. 11
D. 12
E. 13

$$|p – 9| < 2$$ => $$-2< p-9 <2$$ or $$7>p>11$$. As p is integer the possible values of p are 8,9,10.
$$|q – 7| ≤ 2$$ => $$-2\leq q-7\leq2$$ or $$5\leq q-7\leq9$$. As q is integer possible values of q are 5,6,7,8,9.

Question requires us to find values of pq which are either multiple of only 3 or only 5 are:

1) Total number of values of pq= 3 x 5=15 -1 (as 8*9=9*8=72)=14
2) number of multiple of both 3 and 5= 3 (9*5, 10*6, 10*9)
3) number of values which are not multiple of 3 or 5= 2 (8*7. 8*8)

Originally posted by Rakesh1987 on 17 May 2019, 05:20.
Last edited by Rakesh1987 on 23 May 2019, 21:11, edited 1 time in total.
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3142
Re: Question of the Week 44 (For integers p and q, if |p – 9| < 2 and...)  [#permalink]

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23 May 2019, 21:03

Solution

Given:
In this question, we are given that
• The integers p and q satisfy the inequalities |p – 9| < 2 and |q – 7| ≤ 2.

To find:
We need to determine
• The number of values possible for pq, which are either multiple of only 3 or only 5.

Approach and Working:
Let us simplify the inequalities first.
• |p – 9| < 2
Or, -2 < p – 9 < 2
Or, 7 < p < 11

As p is an integer, the values possible for p = 8, 9, 10

• |q – 7| ≤ 2
Or, -2 ≤ q – 7 ≤ 2
Or, 5 ≤ q ≤ 9

As q is an integer, the values possible for q = 5, 6, 7, 8, 9

Now, if pq is a multiple of only 3 or only 5, then the possible values of pq = 8 * 5, 8 * 6, 8 * 9, 9 * 6, 9 * 7, 9 * 9, 10 * 5, 10 * 7, 10 * 8 (9 values in total)

Hence, the correct answer is option A.

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Re: Question of the Week 44 (For integers p and q, if |p – 9| < 2 and...)   [#permalink] 23 May 2019, 21:03
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