A group of 5,000 investors responded to a survey asking whether they

Question

A group of 5,000 investors responded to a survey asking whether they owned stocks and whether they owned bonds. Of the group, 20 percent responded that they owned only one of the two types of investments. If r is the number of investors in the group who owned stocks but not bonds, which of the following represents the number of investors in the group who owned bonds but not stocks, in terms of r ?

A. 5000
B. 1000 - r
C. r - 1000
D. 1000r
E. (0.2)(5000 - r)

A. 5000
B. 1000 - r
C. r - 1000
D. 1000r
E. (0.2)(5000 - r)

u1983 · Answer

Total people =  5000 , People with bond no stock = a  & People with stock no bond =  r 
People with only bond or only stock =  20%  of  5000=1000 = a+r

Hence  a =People with bond no stock= 1000-r 
Hence I would go for  option B .

asfandabid · Answer

Bunuel   u1983   VeritasKarishma   chetan2u 
Hi im a little confused, why can't people have both bond and stocks in this group of 5000 people i.e the remaining 4000 people. The question does not explicitly say that there are none who don't? Please help, i think i'm missing something..

u1983 · Answer

Yes... they would. That's why we have not taken those 4000 people into account. Thus our group to concentrate upon is 1000 people, who responded they have either of them but not both.
Hope it helps!!

KarishmaB · Answer

Out of the 4000 people, there might be people who have both and there might be people who have neither. We have been given that exactly 1000 said that they have one of the two things. We need number of people who owned "bonds only". Hence we can ignore the other 4000. 
Out of 1000, r have stocks only and 1000-r have bonds only.

ScottTargetTestPrep · Answer

Let n = the number of investors who owned bonds but not stocks. We can create the equation:

5,000 x 0.2 = r + n

1000 - r = n

Answer: B

BrentGMATPrepNow · Answer

20% of 5,000 = 1,000
So, we know that 1,000 investors responded that they owned  only one  of the two types of investments

We can write: ( number of investors who owned STOCKS but NOT BONDS ) + ( number of investors who owned BONDS but NOT STOCKS ) = 1,000

Given:  r is the number of investors in the group who owned STOCKS but NOT BONDS

So, we can write: ( r ) + ( number of investors who owned BONDS but NOT STOCKS ) = 1,000

Which of the following represents the number of investors in the group who  owned BONDS but NOT STOCKS

Solve our equation to get: ( number of investors who owned BONDS but NOT STOCKS ) = 1,000 - ( r )

Answer: B

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A group of 5,000 investors responded to a survey asking whether they

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