p, q, and r are integers such that |p|

Question

p, q, and r are integers such that  |p| < |q| < |r| < 40 . If  p + q + r = 20 , what is the maximum possible value of  p*q*r ?

A. 3610
B. 3600
C. 3510
D. 3500
E. 3490

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GMATinsight · Accepted Answer

For maximum value of p*q*r,  
1) they must have as big absolute values as possible for the given sum p + q + r = 20
2) Two of them may be negative and third positive for biggest absolute values
3) Biggest absolute value can be 39 i.e. sum of other two numbers must be -19 for the sum of them to be 20

i.e. p = -9, q = -10, r = 39

p*q*r = (-9)*(-10)*(39 = 3510

ANswer: Option C

yashikaaggarwal · Answer

Solve using options.
Factorization of options will get you no. Easily.

A) 3610=2*5*19*19 { Any combination of 3 no. will never lead to a sum of 20 }

B) 3600=2^4*3^2*5^2 { Any combination of 3 no. will never lead to a sum of 20 }

C) 3510=2*5*13*3^3 
{ (13*3),(3*3)(2*5)=> (39)(9)(10)=> put 9=-9 & 10=-10 
Sum will be 39-9-10=20 (verified)}

You don't have to solve further because we need maximum no. And rest two options are less than 3510, though you can check

D) 3500=2^2*5^3*7 { Any combination of 3 no. will never lead to a sum of 20 }

E) 3490=2*5*349 { Any combination of 3 no. will never lead to a sum of 20 }

Hence answer is C

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aryan440 · Answer

We need to maximise pqr. So,w e should shoot for either all three positive or two negative and one positive. Given p + q + r = 20, two positive and one negative works better. Let us say we choose p, q to be negative and r to be positive. Maximum value r can take is 39. p + q now becomes -19.

p = -9, q = -10 and r = 39 works best.

So, the product should be -9 * -10 * 39 = 3510.

p = -9, q = -10 and r = 39 works best.

So, the product should be -9 * -10 * 39 = 3510.

GunjanMadan1 · Answer

Whenever given in Modus, make you think about both positive and negative values. And they are mentioned as Integers, so if two of them are negative, it can maximize p*q*r.

Since P+q+r=20, and for maximum p*q*r, the positive number has to be maximum too, Hence r= 39

This makes the other two numbers p+q= -19 and hence p=-9 and q=-10

Therefore P*q*r= -9*-10*39= 3510.

Answer: Option C

Ninokh · Answer

Bunuel 
Hello Sir, can you please tell me where am I missing?
p*q*r=(-39)*(38)*(21)=31,122; the sum equals to 20. every number is different from each other and less than 40.

NK

Bunuel · Answer

(-39)*(38)*(21) = -31,122 NOT 31,122.

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p, q, and r are integers such that |p| < |q| < |r| < 40. If p + q + r

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