Raito Problem 05

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phoenix9801: Master | Next Rank: 500 Posts; Posts: 190; Joined: Thu Jan 14, 2010 8:29 pm; Thanked: 2 times

Raito Problem 05

by phoenix9801 » Sat Jun 02, 2012 8:43 pm

Can you plug in number to make my life easier??

A class contains only juniors and seniors in a ratio of p:q. How many seniors are there if there are only r juniors?
A) q(r+p)
B) pq/p
C) pr/q
D) qr/p
E) qp/r

For every x executives there are 2y directors. If there are z executives, how many total executives and directors are there?
A) 2yz/x
B) x+2y+z
C) z/1+2y
D) 2yz/2y+x
E) zx/x+2y

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Source: Beat The GMAT — Problem Solving | Sat Jun 02, 2012 8:43 pm

Birottam Dutta: Master | Next Rank: 500 Posts; Posts: 342; Joined: Wed Jul 08, 2009 8:50 am; Thanked: 214 times; Followed by:19 members; GMAT Score:740

by Birottam Dutta » Sat Jun 02, 2012 10:38 pm

Let number of juniors be J and seniors be S.

Therefore, J/S= p/q. Again, J=r.

So, r/S=p/q => S= qr/p.

Answer is D!

Problem 2.

For x executives there are 2y directory.

Therefore, for 1 executive, there are 2y/x executives (simple unitary method)

So, for z executives, there are 2yz/x executives.

Answer is A!

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https://www.youtube.com/watch?v=H7p56NzAVKc

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pm; Location: Milpitas, CA; Thanked: 1854 times; Followed by:523 members; GMAT Score:770

by Anurag@Gurome » Sat Jun 02, 2012 10:39 pm

phoenix9801 wrote:A class contains only juniors and seniors in a ratio of p:q. How many seniors are there if there are only r juniors?

p juniors --> q seniors
1 junior ---> q/p senior
r juniors --> (q/p)*r seniors

The correct answer is D.

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GMAT/MBA Expert

Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pm; Location: Milpitas, CA; Thanked: 1854 times; Followed by:523 members; GMAT Score:770

by Anurag@Gurome » Sat Jun 02, 2012 10:44 pm

phoenix9801 wrote:For every x executives there are 2y directors. If there are z executives, how many total executives and directors are there?

x executives --> 2y directors
1 executive ---> (2y/x) directors
z executives --> (2y/x)*z directors

Hence, total executives and directors = [z + z*(2y/x)] = [xz + 2yz]/x

Check your options.

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GMAT/MBA Expert

Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pm; Location: Milpitas, CA; Thanked: 1854 times; Followed by:523 members; GMAT Score:770

by Anurag@Gurome » Sat Jun 02, 2012 10:58 pm

phoenix9801 wrote:Can you plug in number to make my life easier??

To solve this by plugging numbers you have to determine the expression qr/p. Without determining that we cannot plug numbers. Hence, the approach I made is more easier and less time consuming than plugging numbers.

But this problem can be solved efficiently by plugging the options.
We know that, ratio of number of juniors to number of seniors is p:q.

Let's check each of the options for which r/(option) = p/q

A) r/[q(r+p)] â‰ p/q
B) r/[pq/p] â‰ p/q
C) r/[pr/q] â‰ p/q
D) r/[qr/p] = p/q ---> CORRECT OPTION
E) r/[qp/r] â‰ p/q

The correct answer is D.

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Birottam Dutta: Master | Next Rank: 500 Posts; Posts: 342; Joined: Wed Jul 08, 2009 8:50 am; Thanked: 214 times; Followed by:19 members; GMAT Score:740