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# If a and b are positive integers, a^(1/2) > 3, b^(1/2) > 2, and a is

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Joined: 12 Feb 2015
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If a and b are positive integers, a^(1/2) > 3, b^(1/2) > 2, and a is  [#permalink]

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17 Dec 2018, 10:47
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Question Stats:

64% (01:19) correct 36% (01:34) wrong based on 99 sessions

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If a and b are positive integers, $$\sqrt{a} > 3$$, $$\sqrt{b} > 2$$, and $$a$$ is a multiple of 7, then what is the smallest possible value of $$ab$$?

A) 35
B) 56
C) 70
D) 81
E) 84

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Manish

"Only I can change my life. No one can do it for me"
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Joined: 11 Dec 2018
Posts: 24
Re: If a and b are positive integers, a^(1/2) > 3, b^(1/2) > 2, and a is  [#permalink]

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20 Dec 2018, 04:26
2
√a>3
Which means,
a>9 and also a multiple of 7 (given)
Therefore, it can be 14
√b>2
Which means,
a>4 and can be 5
As we need the minimum value for ab, we take the minimum value for both.
Hence, 14*5=70
Ans-C

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Re: If a and b are positive integers, a^(1/2) > 3, b^(1/2) > 2, and a is  [#permalink]

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20 Dec 2018, 04:50
Given that a>0 & b>0

As per the question, √a>3 i.e. a>9 (Since a is positive, we can square both sides without impacting the greater than sign)
Now again a is a multiple of 7. Hence the possible values of a are 14, 21, 35, 42, 49, .....

As per the question, √b>2 i.e. b>4 (Since b is positive, we can square both sides without impacting the greater than sign)
Hence the possible values of b are 5, 6, 7, 8, 9, ......

Smallest possible value of a as per conditions = 14
Smallest possible value of b as per conditions = 5
For the product ab to be smallest, both a and b must be smallest possible values, i.e. a = 14, and b = 5
Hence ab = 70.
Correct answer is option C. 70
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Director
Joined: 12 Feb 2015
Posts: 875
If a and b are positive integers, a^(1/2) > 3, b^(1/2) > 2, and a is  [#permalink]

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Updated on: 10 Jan 2019, 22:22
If a and b are positive integers, $$\sqrt{a} > 3$$, $$\sqrt{b} > 2$$, and $$a$$ is a multiple of 7, then what is the smallest possible value of $$ab$$?

A) 35
B) 56
C) 70
D) 81
E) 84
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Originally posted by CAMANISHPARMAR on 10 Jan 2019, 13:19.
Last edited by Bunuel on 10 Jan 2019, 22:22, edited 2 times in total.
Renamed the topic and edited the question.
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Joined: 07 Dec 2014
Posts: 1206
Re: If a and b are positive integers, a^(1/2) > 3, b^(1/2) > 2, and a is  [#permalink]

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10 Jan 2019, 13:34
CAMANISHPARMAR wrote:
If a and b are positive integers, $$\sqrt{a}$$ > 3, $$\sqrt{b}$$ > 2, and $$a$$ is a multiple of 7, then what is the smallest possible value of $$ab$$?

A) 35
B) 56
C) 70
D) 81
E) 84

14 is least multiple of 7 with square root>3
5 is least integer with square root>2
ab=14*5=70
C
Math Expert
Joined: 02 Sep 2009
Posts: 56256
Re: If a and b are positive integers, a^(1/2) > 3, b^(1/2) > 2, and a is  [#permalink]

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10 Jan 2019, 22:31
1
CAMANISHPARMAR wrote:
If a and b are positive integers, $$\sqrt{a} > 3$$, $$\sqrt{b} > 2$$, and $$a$$ is a multiple of 7, then what is the smallest possible value of $$ab$$?

A) 35
B) 56
C) 70
D) 81
E) 84

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Re: If a and b are positive integers, a^(1/2) > 3, b^(1/2) > 2, and a is   [#permalink] 10 Jan 2019, 22:31
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