DS Percentages question

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pratyoosh: Senior | Next Rank: 100 Posts; Posts: 57; Joined: Sat Apr 10, 2010 6:20 am

by pratyoosh » Sat Nov 20, 2010 2:34 pm

Hello,

Can anyone explain the resolution to the below DS problem:

A manufacture produced x percent more video cameras in 1994 than in 1993 and y percent more video
cameras in 1995 than in 1994. If the manufacturer produced 1,000 video cameras in 1993, how many video
cameras did the manufacturer produce in 1995?
(1) xy=20
(2) x+y+xy/100 = 9.2

Thanks.

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Source: Beat The GMAT — Data Sufficiency | Sat Nov 20, 2010 2:34 pm

clock60: Legendary Member; Posts: 759; Joined: Mon Apr 26, 2010 10:15 amFollowed by: 3 members; Thanked: 85 times

by clock60 » Sat Nov 20, 2010 3:16 pm

you need to find what is
1000(1+x/100)(1+y/100)=1000((100+x)/100)((100+y)/100)=1/10(100+x)(100+y)=1/10(100^2+100x+100y+xy)
(1) does not provide any useful information, we have xy=20 but no separate values for x,y
(2)
x+y+xy/100 = 9.2
100x+100y+xy=920
from initial 1/10(100^2+100x+100y+xy)
we can insert and left with 1/10(100^2+920)=1092 that is our answer
so B

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fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members; Thanked: 59 times

by fskilnik@GMATH » Mon Nov 22, 2010 6:37 am

Hi there!

From the fact that V95 = 1,000*(1+y/100)*(1+x/100) (verify that), we will be able to DECIDE (or to BIFURCATE) if and only if we are able to DECIDE (or to BIFURCATE) on the expression (1+y/100)*(1+x/100) ...

(1) BIFURCATES:

> Take x = 20 and y = 1 , to realize that the value asked (in the simplified expression) is 1.01*1.20 (certainly rational)
> Take x = y = square root of 20 = sqrt(20), to realize that the same value above is (1+sqrt(20)/100)^2 , and it is easy to realize that this last expression is a positive fraction of integers (thefore rational) plus an irracional number (sqrt(5) over 25), check that, therefore an irrational result, different from the one we got before, for sure!

(2) Please note that (1+y/100)(1+x/100) = 1 + 1/100 * (x+y + xy/100) therefore this sttm DECIDES (and the value is 1+ 9.2/100).

Regards,
Fabio.

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

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rishab1988: Master | Next Rank: 500 Posts; Posts: 332; Joined: Tue Feb 09, 2010 3:50 pmFollowed by: 7 members; Thanked: 41 times; GMAT Score:720

by rishab1988 » Mon Nov 22, 2010 8:37 am

Read the problem carefully.It applies the concept of Compound Interest,in which the interest in second year and each subsequent year is calculated on the principle+interest in the previous year).

the c.i formula of p=1000 r=x for 2 years is

A(amount in 1995)= 1000(1+x/100)^2. Now if rate of interest in second year is different from rate of interest in first year,lets say y,then the formula becomes:

A= 1000(1+x/100)(1+y/100)
= 1000 [ 1+x/100+y/100+ xy/(100)^2]
= 1000 + 10x +10y +xy/10
= 1000 + 10 [x+y+xy/100]

In short the question asks : x+y+xy/100 =? or x+y=? and xy=?

1) it gives xy=20 but x+y could be anything; x=5 y=4 x+y=9 x=20 y=1 x+y=21.

Hence the amount in 1995 will be different.Not sufficient.Eliminate A and D

2) gives x+y+xy/100 =9.2

hence sufficient.

You can go ahead and solve 1000+10 [9.2]=1092

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pratyoosh: Senior | Next Rank: 100 Posts; Posts: 57; Joined: Sat Apr 10, 2010 6:20 am

by pratyoosh » Tue Nov 23, 2010 5:33 am

Thank you Clock60, Fabio and Rishab.

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