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

Question

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}

ScottTargetTestPrep · Accepted Answer

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

chetan2u · Answer

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

Archit3110 · Answer

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..

pandeyashwin · Answer

For D , 900/200 = 4.5. Also incorrect

C & D are both incorrect

MahmoudFawzy · Answer

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

Bunuel · Answer

Edited. Thank you.

diljeetsingh · Answer

this is actually easy and 550 level Question

raissacr · Answer

But what if is p = 18?

Bunuel  
 chetan2u 
 ScottTargetTestPrep

thank you!

Bunuel · Answer

If p = 18, then  \sqrt{200pq}=\sqrt{200*18*q}=60\sqrt{q} , which is not the same as  30\sqrt{q} .

ScottTargetTestPrep · Answer

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.

RenB · Answer

Solution by Experts Global:

https://www.youtube.com/watch?v=OnotJ1e_JFY

shubhim20 · Answer

how did you get 450 for last option?

Krunaal · Answer

\sqrt{200pq}  =  300\sqrt{q}

Squaring both sides => 200pq = 90000q => 2p = 900 => p = 450

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

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

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