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binskyba

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At a certain financial institution, 30% of the clients use both credit card and a cheque book, but 40% of the clients who use the credit card do not use the cheque book. What percentage of the members of the institution use the credit card?

 

A. 35

B. 40

C. 50

D. 65

E. 75

 

 

Pleas help me and give me a nice explanation, of course an explanation which takes less than 2 min. to do.

THNKS

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IMO C.

 

Let the total clients = 100

No. of clients using both credit card and cheque book = 30.

 

Let total no of clients using credit card = x

So, no. of clients using credit card but no cheque book = 0.4x

 

According to question,

0.4x+30 = x

x= 50 (which is the total number of clients using credit card)

Since we had assumed total no. of client to be 100, this value of x is the percentage answer.

 

You can aslo do it by making table as:

 

CC no CC Total

CB 30

 

no CB 0.4x

 

Total x 100

 

It took little less than a min to solve this. I hope this was helpful.

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MissionGMAT's solution is perfect. However, some students benefit from organizing the information in a more visual manner. This is where the Double Matrix Method comes in.

 

For questions involving a population of things (this time a population of clients) where each thing has two characteristics associated with it (here the 2 characteristics are: 1) having/not having credit card, and 2) having/not having cheque book), we can solve the question using the Double Matrix method.

 

For a free lesson on the Double Matrix Method, watch video #20 at GMAT Word Problems | GMAT Prep NowAfterwords you can tackle the practice questions #21 and #44 on the same page.

 

Cheers,

Brent

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  • 4 weeks later...

I think, for question with 2 yes/no options (like credit card y/n and cheque y/n) double matrix is the best option (given that the question is long!). for short question (but tricky) like this one, we can (also) go for calculation as follows -

 

30% uses both credit card and cheque.

40% of the credit card users (the tricky part) does not use cheque. SO, (100-40)% or 60% of credit card user uses cheque.

SO, 60% of credit card user is equal to 30% of total member of the institute.

SO, 100% of credit card user is 50% of the total member of the institute.

It is C. (50%)

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  • 2 weeks later...

30% of Total use both credit card and cheque book

40% of those who use credit card do not use cheque book

so, 60% of those who use credit card use both credit card and cheque book

or, 60% of those who use credit card = 30% of Total

so, 40% of those who use credit card = 20% of Total

so, 100% of those who use credit card = 50% of Total

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  • 2 weeks later...
  • 3 weeks later...
  • 3 weeks later...
  • 8 months later...
MissionGMAT's solution is perfect. However, some students benefit from organizing the information in a more visual manner. This is where the Double Matrix Method comes in.

 

For questions involving a population of things (this time a population of clients) where each thing has two characteristics associated with it (here the 2 characteristics are: 1) having/not having credit card, and 2) having/not having cheque book), we can solve the question using the Double Matrix method.

 

For a free lesson on the Double Matrix Method, watch video #20 at GMAT Word Problems | GMAT Prep NowAfterwords you can tackle the practice questions #21 and #44 on the same page.

 

Cheers,

Brent

 

The Double Matrix method is really helpful! Thanks!

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