For integers p and q, if |p 9|

Question

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

e-GMAT     Question of the Week #44

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Rakesh1987 · Accepted Answer

|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) Required answer is 14-3-2=9. Therefore answer is A.

EgmatQuantExpert · Answer

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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nidhimohankamal · Answer

Why 9*8 not considered

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Bunuel · Answer

8*9 is counted, so no need to consider 9*8 because both give the same value for pq.

BrushMyQuant · Answer

↧↧↧ Detailed Video Solution to the Problem ↧↧↧

Given that p and q are integers and |p – 9| < 2 and |q – 7| ≤ 2, and we need to find how many values are possible for pq which are either multiple of only 3 or only 5?

Simplifying |p – 9| < 2
=> -2 < p - 9 < 2

Adding 9 on all the sides we get
-2 + 9 < p < 2 + 9
=> 7 < p < 11

Now, p is an integer
=> Possible values of p are 8, 9, 10

Simplifying |q – 7| ≤ 2
=> -2 ≤ q - 7 ≤ 2

Adding 7 on all the sides we get
-2 + 7 ≤ q ≤ 2 + 7
=> 5 ≤ q ≤ 9

Now, q is an integer
=> Possible values of q are 5, 6, 7, 8 , 9

Possible for pq which are either multiple of only 3 or only 5

For, p = 8,
q can be any number which is a multiple of 3 or 5
=> q = 5, 6, 9
=> 3 cases

For p = 9,
As p is a multiple of 3 so q can be any number which is NOT a multiple of 5 and which does not give any value of pq which is achieved above.
=> q = 6, 7, 9 (as q=8 will make pq=72, which is same as p = 8 and q = 9)
=> 3 cases

For p = 10,
As p is a multiple of 5, so q can be any number which is NOT a multiple of 3 and which does not give any value of pq which is achieved above.
=> q = 5, 7, 8
=> 3 cases

=> 9 cases in total

So, Answer will be A
Hope it helps!

Watch the following video to learn the Basics of Absolute Values

Kinshook · Answer

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?

-2 < p-9 < 2
7 < p < 11; p = {8,9,10}

-2 ≤ q -7 ≤ 2
5 ≤ q ≤ 9; q = {5,6,7,8,9}

Values of pq which are either multiple of only 3 or only 5 = {8*5 = 40, 8*6 = 48, 8*9=72, 9*6=54, 9*7=63, 9*9 = 81, 10*5 = 50, 10*7=70, 10*8=80}; 9 values

IMO A

For integers p and q, if |p 9| < 2 and |q 7| 2, then how many

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