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If p and q are positive integers, each of the following can be the val

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Sajjad1994
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If p and q are positive integers, each of the following can be the val [#permalink] New post   Updated on: 24 May 2023, 14:31
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If p and q are positive integers, each of the following can be the value of \(\sqrt{200pq}\) except.

A. \(20\sqrt{q}\)

B. \(20\sqrt{p}\)

C. \(20\sqrt{2p}\)

D. \(30\sqrt{q}\)

E. \(300\sqrt{q}\)
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D

Originally posted by Sajjad1994 on 20 Oct 2018, 05:17.
Last edited by Bunuel on 24 May 2023, 14:31, edited 5 times in total.
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Re: If p and q are positive integers, each of the following can be the val [#permalink] New post   10 Nov 2020, 07:30
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Sajjad1994 wrote:
If p and q are positive integers, each of the following can be the value of \(\sqrt{200pq}\) except.

A. 20\(\sqrt{q}\)
B. 20\(\sqrt{p}\)
C. 20\(\sqrt{2p}\)
D. 30\(\sqrt{q}\)
E. 300\(\sqrt{q}\)


Solution:

If we square the given expression, we have 200pq. Now, if we square the expressions in the given choices, we have:

A) 400q

B) 400p

C) 400(2p) = 800p

D) 900q

E) 90,000q

We see that, in order for 200pq to become 900q, p must be 4.5. However, since p is a positive integer, we see that 200pq can’t be 900q, i.e., √(200pq) can’t be 30√q.

Answer: D
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Re: If p and q are positive integers, each of the following can be the val [#permalink] New post   20 Oct 2018, 06:29
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SajjadAhmad wrote:
If p and q are positive integers, each of the following can be the value of \(\sqrt{200pq}\) except.

A. 20\(\sqrt{q}\)
B. 20\(\sqrt{p}\)
C. 2\(\sqrt{2p}\)
D. 30\(\sqrt{q}\)
E. 300\(\sqrt{q}\)

EG


Let us see what MINIMUM quantity should each choice have..
\(\sqrt{200pq}=10\sqrt{2pq}\)

Let us see the choices..

A. 20\(\sqrt{q}\).......yes,p could be 2
B. 20\(\sqrt{p}\)......yes, q could be 2
C. 2\(\sqrt{2p}\).....NO, it has to be 20√(2p) and not 2√(2p)
D. 30\(\sqrt{q}\).....NO, it has to be 30√(2q) atleast
E. 300\(\sqrt{q}\)...yes

So some flaw in one of the two choices C and D, as there cannot be 2 answers
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Re: If p and q are positive integers, each of the following can be the val [#permalink] New post   21 Oct 2018, 02:58
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If p and q are positive integers, each of the following can be the value of 200pq‾‾‾‾‾‾√200pq except.

A. 20q‾√q
B. 20p‾√p
C. 22p‾‾‾√2p
D. 30q‾√q
E. 300q‾√

Upon doing the factorising 200 : we get 2*10^2

We can say : 10 (2pg)^1/2

From all the answer options the one which wont be correct would be the one without '0' therefore C is right..
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Re: If p and q are positive integers, each of the following can be the val [#permalink] New post   21 Oct 2018, 03:20
Archit3110 wrote:
If p and q are positive integers, each of the following can be the value of 200pq‾‾‾‾‾‾√200pq except.

A. 20q‾√q
B. 20p‾√p
C. 22p‾‾‾√2p
D. 30q‾√q
E. 300q‾√

Upon doing the factorising 200 : we get 2*10^2

We can say : 10 (2pg)^1/2

From all the answer options the one which wont be correct would be the one without '0' therefore C is right..

For D , 900/200 = 4.5. Also incorrect

C & D are both incorrect
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Re: If p and q are positive integers, each of the following can be the val [#permalink] New post   24 Mar 2019, 08:03
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SajjadAhmad wrote:
If p and q are positive integers, each of the following can be the value of \(\sqrt{200pq}\) except.

A. 20\(\sqrt{q}\)
B. 20\(\sqrt{p}\)
C. 2\(\sqrt{2p}\)
D. 30\(\sqrt{q}\)
E. 300\(\sqrt{q}\)

Source: Experts Global GMAT
Difficulty Level: 700


Hi, Bunuel
\(2\sqrt{2p}\) should be corrected to \(20\sqrt{2p}\)
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Re: If p and q are positive integers, each of the following can be the val [#permalink] New post   24 Mar 2019, 08:05
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Mahmoudfawzy83 wrote:
SajjadAhmad wrote:
If p and q are positive integers, each of the following can be the value of \(\sqrt{200pq}\) except.

A. 20\(\sqrt{q}\)
B. 20\(\sqrt{p}\)
C. 2\(\sqrt{2p}\)
D. 30\(\sqrt{q}\)
E. 300\(\sqrt{q}\)

Source: Experts Global GMAT
Difficulty Level: 700


Hi, Bunuel
\(2\sqrt{2p}\) should be corrected to \(20\sqrt{2p}\)


Edited. Thank you.
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Re: If p and q are positive integers, each of the following can be the val [#permalink] New post   24 Mar 2019, 08:49
this is actually easy and 550 level Question
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Re: If p and q are positive integers, each of the following can be the val [#permalink] New post   24 May 2023, 14:28
ScottTargetTestPrep wrote:
We see that, in order for 200pq to become 900q, p must be 4.5. However, since p is a positive integer, we see that 200pq can’t be 900q, i.e., √(200pq) can’t be 30√q.



But what if is p = 18?

Bunuel
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thank you!
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Re: If p and q are positive integers, each of the following can be the val [#permalink] New post   24 May 2023, 14:37
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raissacr wrote:
ScottTargetTestPrep wrote:
If p and q are positive integers, each of the following can be the value of \(\sqrt{200pq}\) except.

A. \(20\sqrt{q}\)

B. \(20\sqrt{p}\)

C. \(20\sqrt{2p}\)

D. \(30\sqrt{q}\)

E. \(300\sqrt{q}\)

We see that, in order for 200pq to become 900q, p must be 4.5. However, since p is a positive integer, we see that 200pq can’t be 900q, i.e., √(200pq) can’t be 30√q.



But what if is p = 18?

Bunuel
chetan2u
ScottTargetTestPrep

thank you!


If p = 18, then \(\sqrt{200pq}=\sqrt{200*18*q}=60\sqrt{q}\), which is not the same as \(30\sqrt{q}\).
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Re: If p and q are positive integers, each of the following can be the val [#permalink] New post   26 May 2023, 08:07
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raissacr wrote:
ScottTargetTestPrep wrote:
We see that, in order for 200pq to become 900q, p must be 4.5. However, since p is a positive integer, we see that 200pq can’t be 900q, i.e., √(200pq) can’t be 30√q.



But what if is p = 18?

Bunuel
chetan2u
ScottTargetTestPrep

thank you!


If p = 18, then √(200pq) = √(200 * 18 * q) = √(3600q) = 60√q. This only shows that √(200pq) can be equal to 60√q, which I don't object. The expression cannot equal 30√q though, as long as p is an integer.
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If p and q are positive integers, each of the following can be the val [#permalink] New post   01 Nov 2023, 20:31
Sajjad1994 wrote:
If p and q are positive integers, each of the following can be the value of \(\sqrt{200pq}\) except.

A. \(20\sqrt{q}\)

B. \(20\sqrt{p}\)

C. \(20\sqrt{2p}\)

D. \(30\sqrt{q}\)

E. \(300\sqrt{q}\)



Solution by Experts Global:

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If p and q are positive integers, each of the following can be the val [#permalink]
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