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# Positive integers a and b are each less than 6. What is the smallest p

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Math Expert
Joined: 02 Sep 2009
Posts: 59728
Positive integers a and b are each less than 6. What is the smallest p  [#permalink]

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20 Mar 2019, 04:39
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Difficulty:

35% (medium)

Question Stats:

67% (01:27) correct 33% (01:52) wrong based on 52 sessions

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Positive integers a and b are each less than 6. What is the smallest possible value for 2a - ab ?

(A) -20
(B) -15
(C) -10
(D) 0
(E) 2

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Re: Positive integers a and b are each less than 6. What is the smallest p  [#permalink]

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20 Mar 2019, 06:58
Bunuel wrote:
Positive integers a and b are each less than 6. What is the smallest possible value for 2a - ab ?

(A) -20
(B) -15
(C) -10
(D) 0
(E) 2

a,b can be 0,1,2,3,4,5
so a*(2-b) will be min when a=b=5
so
5*(-3) ; -15
IMO B
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Re: Positive integers a and b are each less than 6. What is the smallest p  [#permalink]

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22 Mar 2019, 09:11
Bunuel wrote:
Positive integers a and b are each less than 6. What is the smallest possible value for 2a - ab ?

(A) -20
(B) -15
(C) -10
(D) 0
(E) 2

Since we want the smallest possible value of 2a - ab, we want b to be as large as possible. Therefore, b can be 5. We also want a to be as large as possible so that ab is the largest. Since the problem doesn’t say the integers are distinct, a can be 5 also. So we have 2(5) - 5(5) = -15 as the smallest possible value of 2a - ab.

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Re: Positive integers a and b are each less than 6. What is the smallest p   [#permalink] 22 Mar 2019, 09:11
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