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10 Apr 2023, 04:31
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
67% (03:01) correct
33%
(03:03)
wrong
based on 206
sessions
History
Date
Time
Result
Not Attempted Yet
An investment manager is considering 3 stocks, P, Q, and R for her portfolio. For the cost of 1 share of P, she could buy 3 shares of Q or 5 shares of R. If she invested an amount equal to the cost of 4500 shares of Q but purchased equal numbers of shares of P and R and no shares of Q, how many shares of R did she buy?
(A) 250
(B) 625
(C) 1250
(D) 3,650
(E) 3,750
(A) 250
(B) 625
(C) 1250
(D) 3,650
(E) 3,750
10 Apr 2023, 05:44
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Bunuel
Solution:
- According to the question, \(P=3Q=5R\)
- Investment manager is investing 4500Q amount in 2 parts. Lets say x in stock P and 4500Q - x in stock R
- According to the question, \(\frac{x}{P}=\frac{4500Q-x}{R}\)
\(⇒\frac{x}{3Q}=\frac{4500Q-x}{\frac{3Q}{5}}\)
\(⇒x=22500Q-5x\)
\(⇒6x=22500Q\)
\(⇒x=3750Q\)
- No. of shares of R \(=\frac{4500Q-x}{R}=\frac{4500Q-3750Q}{\frac{3Q}{5}}=1250\)
Hence the right answer is Option C
10 Apr 2023, 06:38
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Bunuel
There are no style points awarded for HOW you get the correct answer, only WHETHER you get the correct answer. You can do the algebra if that's your strength. If it's not, you can use other techniques (and even if your algebra is pretty good, the other techniques are often faster and easier).
Algebra:
P=3Q=5R
Let's put the everything in terms of one variable (I've chosen R): P=5R and Q=5R/3.
4500Q = x(P+R)
Substitute in for P and Q from above.
4500(5R/3) = x(5R+R)
7500R = x(6R)
x = 1250
Answer choice C.
Hidden Plug In Technique:
Is there some piece of information that would make our lives a lot easier? Sure: what's the price of a share of any of the stocks! If there's a piece of information that you REALLY wish you knew, see if you can just make it up without violating the rules of the question; that makes it a "Hidden Plug In" question.
Let's make P=$15, which makes Q=$5 and R=$3.
4500 shares of Q = $22,500.
If we have the same number (x) of P and R, then we spend $15x+$3x = $18x and that equals $22,500.
22500/18 = 1250.
ThatDudeKnowsHiddenPlugIn
