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

Question

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

Poorvi05 · Answer

√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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DisciplinedPrep · Answer

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

gracie · Answer

14 is least multiple of 7 with square root>3
5 is least integer with square root>2
ab=14*5=70
C

bumpbot · Answer

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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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