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# If a and b are both positive integers such that a < b, which of the fo

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Math Expert
Joined: 02 Sep 2009
Posts: 47037
If a and b are both positive integers such that a < b, which of the fo [#permalink]

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07 Jul 2018, 09:25
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73% (01:28) correct 27% (01:56) wrong based on 26 sessions

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If a and b are both positive integers such that a < b, which of the following must be true?

(A) $$a < \sqrt{ab} <b$$

(B) $$\sqrt{a} < \sqrt{ab} < \sqrt{b}$$

(C) $$\sqrt{a} < \sqrt{b} < \sqrt{ab}$$

(D) $$\sqrt{ab}<a<b$$

(D) $$a<\sqrt{ab}<\sqrt{b}$$

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Math Expert
Joined: 02 Aug 2009
Posts: 6219
If a and b are both positive integers such that a < b, which of the fo [#permalink]

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07 Jul 2018, 10:15
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Bunuel wrote:
If a and b are both positive integers such that a < b, which of the following must be true?

(A) $$a < \sqrt{ab} <b$$

(B) $$\sqrt{a} < \sqrt{ab} < \sqrt{b}$$

(C) $$\sqrt{a} < \sqrt{b} < \sqrt{ab}$$

(D) $$\sqrt{ab}<a<b$$

(D) $$a<\sqrt{ab}<\sqrt{b}$$

$$a=\sqrt{aa}$$ and b=$$\sqrt{bb}$$since a<b...... $$\sqrt{aa}<\sqrt{ab}<\sqrt{bb}.......................a<\sqrt{ab}<b$$

A
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: If a and b are both positive integers such that a < b, which of the fo [#permalink]

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07 Jul 2018, 10:35
Bunuel wrote:
If a and b are both positive integers such that a < b, which of the following must be true?

(A) $$a < \sqrt{ab} <b$$

(B) $$\sqrt{a} < \sqrt{ab} < \sqrt{b}$$

(C) $$\sqrt{a} < \sqrt{b} < \sqrt{ab}$$

(D) $$\sqrt{ab}<a<b$$

(D) $$a<\sqrt{ab}<\sqrt{b}$$

Let a=4 & b=16 (a<b)
(A) $$a < \sqrt{ab} <b$$: 4<8<16 (True)
(B) $$\sqrt{a} < \sqrt{ab} < \sqrt{b}$$: 2<8<4 (False)
(C) $$\sqrt{a} < \sqrt{b} < \sqrt{ab}$$: 2<4<8 (False)
(D) $$\sqrt{ab}<a<b$$: 8<4<16 (False)
(E) $$a<\sqrt{ab}<\sqrt{b}$$: 2<8<4 (False)

Ans. (A)

P.S.- Perfect square are chosen for checking purpose since square roots are involved in the answer choices.
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Re: If a and b are both positive integers such that a < b, which of the fo   [#permalink] 07 Jul 2018, 10:35
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