# Free DI and LR - 22 Practice Test - CAT

### Question 1

**If R is 6 years old and the absolute difference between the number of candies with S and T is 10, find the number of candies with P.**

#### SOLUTION

Solution :D

Based on the question we can complete the grid as follows

456810PXXX√XQXXXX√RXX√XXS√XXXXTX√XXX

It is given that |S-T|=10

P=13[4+R]

T=R2

T= P+S

Let us go from answer options

1) If P=6, R=14

T=, S= T-P=1

|S−T|≠10

2) If P=12, R=32

T=16, S=4

|S−T|≠10

3) If P=20, R= 56,

T= 28, S=8

|S−T|≠10

4) If P=8, R=20,

T=10, S=2

|S−T|≠10

Hence, the answer is none of these

### Question 2

**Which of the following statement(s) is/are FALSE?
A: The difference of ages of Q and S is 6 years.
B: The difference of ages of T and Q is 3 years.
C: The ratio of ages of P and S is 2.
D: The ratio of the ages of R and T is 1.6.**

#### SOLUTION

Solution :D

We will get the answer based on the previous question itself since the question is about what is definitely false. Using the previous grid, the statements B and D are false.

### Question 3

What can be the absolute difference between the ages of Q and T?

#### SOLUTION

Solution :E

Based on the conditions given in question 4 and question 1,we can arrive at an answer for question 1.

Based on the data in question 4, the grid can be drawn up as follows

456810PXXX√XQ√XXXXRXXXX√SXX√XXTX√XXX

the difference between the ages of Q and T can be both 1 and 5 years. Answer is option (e)

### Question 4

If S is 6 years old and has 40 candies and R is not the youngest, find the difference between the number of candies with Q and P.

#### SOLUTION

Solution :From the given data in the question

S=40 ⇒ T=20

⇒R=25x|S−T|=8

P=13(Q+R)3P-Q=8

Q+P=T=20

Solving (1) & (2), we get P= 7 and Q=13. Q-P=6.

### Question 5

**If P is younger than S and elder than Q, find the ratio of number of candies with Q and S?**

#### SOLUTION

Solution :B

Given that Q<P<S. This is possible only when the ages of Q,P & S are 4, 6 ,8 respectively.

From the conditions given initially

T=Q+S

Since

⇒R=25x|S−T|

⇒R=25×|S−Q−S|

⇒R=25×Q......(1)

S=13[Q+R]

S=13[Q+25Q]=13×[75Q]⇒S=715×QFrom this the ratio Q:S= 15:7.

### Question 6

If the overall profit was Rs.6 per share, then the profit earned per share by selling Reliance share is:

#### SOLUTION

Solution :A

Let the total number of shares for the month of August 2007 be x and the total profit earned in that month be Rs. Y.

The Overall profit =y/x = Rs. 6 per share.

We need to find the profit earned by selling one share of Reliance

i.e. profit share earned by selling reliance shares/Number of shares of reliance

= = Rs.5.46 Hence (a).

Alternately:

Let the number of shares be 100, hence the total profit is Rs. 600

From the chart, the number of shares of Reliance= 35

profit % from Relaince=32% of 600

Profit /Share= (32% of 600)/35 = 5.5

### Question 7

How much more profit can be earned by selling one share of NTPC over one share of Tata?

#### SOLUTION

Solution :D

Let the total number of shares for the month of August 2007 be x and the total profit earned in that month be Rs. Y.

The profit earned by selling one share of NTPC = 15y/10x = Rs. 3y/2x

The profit earned by selling one share of Tata = 4y/8x = Rs. y/2x

The required percentage =

Hence option (d).

Alternately:

NTPC:profit/Share=15/10Tata: Profit/Share=4/8

% increase in profit= (1.5 - 0.5)/0.5 = 200%

### Question 8

If the number of shares of Tata sold is 12 more than that of GMR at the end of August 2007, then the selling prices of shares of Tata and GMR could have been:

#### SOLUTION

Solution :E

The selling price of the Shares is asked, as information about number of shares and profit% is given, we cannot determine the selling price of the shares.

### Question 9

If Ramesh wants to earn equal profit by selling shares of NTPC and Unitech, how much more shares of NTPC than Unitech should be sold?

#### SOLUTION

Solution :C

Let the total number of shares for the month of August 2007 be x and the total profit earned in that month be Rs. Y.

the difference in profit is = Rs.

Selling 20x/100 shares of Unitech earned a profit of Rs.

Selling 10x/100 shares of NTPC earned a profit of Rs.

To earned a profit of Rs. , he should have sold more NTPC shares.

So required percentage = = 66.67%. hence (C)

Alternately:we can take numbers to calculate: taking data from the first question of this caselet. we have a total of 100 shares and a total profit of Rs. 600.

For NTPC: number of shares=10, profit earned=90

For Unitech: Number of shares=20 , Profit earned=150.

By selling NTPC shares we have to earn Rs.150, then No. of shares sold should be16.66. i.e an increase of 66.66% over 10 shares initially.

### Question 10

If the maximum profit earned by selling one share of any company was Rs.3, then the minimum profit earned by selling one share of any company was:

#### SOLUTION

Solution :D

We can observe that the maximum and the minimum profit per share is obtained by selling NTPC share and Tata share respectively.

For NTPC share/profit = 15/10=3/2=1.5 this carries a value of Rs.3, which is the maximum.

For Tata the Share/Profit is 4/8=0.5 this should carry a value of Rs.1

Hence (d).