1. ## Percentages change

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  Reply With Quote

2. 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.  Reply With Quote

3. 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  Reply With Quote

4. Thank you very much!  Reply With Quote

5. Answer = 50. Please let me know if that is correct and I can provide the explanation.  Reply With Quote

6. 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%)  Reply With Quote

7. 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  Reply With Quote

8. Let the total percentage of credit card users be c%
Since 40% of credit card users do not use cheque book, so the equation will be
.4c/100 = (c/100) - (.3)

Solving we get c = 50  Reply With Quote

9. I don't understand how to use the double matrix for it? can anyone explain?  Reply With Quote

10. I agree with answer as 50. You can use Venn diagram to determine the same.  Reply With Quote