# Previous CAT Quant Questions and Answers

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Solving the previous quantitative aptitude questions will gives us better understanding of the questions that are being asked in the CAT exam. Here we have provided some Quant questions and answers from previous solved papers.

Previous CAT Quant Questions:

Question 1: If R is an integer between 1 & 9, P – R = 2370, what is the value of R?
I. P is divisible by 4.
II. P is divisible by 9.

a) The question can be answered with the help of statement I alone,
b) The question can be answered with the help of statement II alone,
c) Both, statement I and statement II are needed to answer the question, and
d) The statement cannot be answered even with the help of both the statements.

Question 2: x, y, and z are three positive odd integers, Is x+z divisible by 4?
I. y – x = 2
II. z – y = 2

a) The question can be answered with the help of statement I alone,
b) The question can be answered with the help of statement II alone,
c) Both, statement I and statement II are needed to answer the question, and
d) The statement cannot be answered even with the help of both the statements.

Question 3: The unit price of product P1 is non-increasing and that of product P2 is decreasing.
Which product will be costlier 5 years hence?
I. Current unit price of P1 is twice that of P2.
II. 5 years ago, unit price of P2 was twice that of P1.

a) The question can be answered with the help of statement I alone,
b) The question can be answered with the help of statement II alone,
c) Both, statement I and statement II are needed to answer the question, and
d) The statement cannot be answered even with the help of both the statements.

Question 4: There were ‘x’ pigeons and ‘y’ mynahs in a cage. One fine morning, ‘p’ birds escaped to freedom. The bird-keeper, knowing only that p = 7, was able to figure out without looking into the cage that at least one pigeon had escaped. Which of the following does not represent a possible (x,y) pair?

a) (10,8)
b) (7,2)
c) (25,6)
d) (12,4)

Question 5: There are six boxes numbered 1, 2, 3, 4, 5, 6. Each box is to be filled up either with a white ball or a black ball in such a manner that at least one box contains a black ball and all the boxes containing black balls are consecutively numbered. The total number of ways in which this can be done equals.

a) 15
b) 21
c) 63
d) 64

Question 6: Consider the following steps :
1. Put x = 1, y = 2
2. Replace x by xy
3. Replace y by y +1
4. If y = 5 then go to step 6 otherwise go to step 5.
5. Go to step 2
6. Stop Then the final value of x equals

a) 1
b) 24
c) 120
d) 720

Question 7: I brought 30 books on Mathematics, Physics, and Chemistry, priced at Rs.17, Rs.19, and Rs.23 per book respectively, for distribution among poor students of Standard X of a school. The physics books were more in number than the Mathematics books but less than the Chemistry books, the difference being more than one. The total cost amounted to Rs.620. How many books on Mathematics, Physics, and Chemistry could have been bought respectively?

a) 5, 8, 17
b) 5, 12, 13
c) 5, 10, 15
d) 5, 6, 19

Question 8: The last time Rahul bought Diwali cards, he found that the four types of cards that he liked were priced Rs.2.00, Rs.3.50, Rs.4.50 and Rs.5.00 each. As Rahul wanted 30 cards, he took five each of two kinds and ten each of the other two, putting down the exact number of 10 rupees notes on the counter payment. How many notes did Rahul give?

a) 8
b) 9
c) 10
d) 11

Question 9: If a number 774958A96B is to be divisible by 8 and 9, the respective values of A and B will be

a) 7 and 8
b) 8 and 0
c) 5 and 8
d) None of these

Question 10: Instead of a metre scale, a cloth merchant uses a 120 cm scale while buying, but uses an 80 cm scale while selling the same cloth. If he offers a discount of 20% on cash payment, what is his overall profit percentage?

a) 20%
b) 25%
c) 40%
d) 15%

Solutions for Previous CAT Quant Questions:

Solutions:

Given: P – R = 2370
or P = 2370 + R ;
So if we consider only 1st statement, R can be 2 or 6 as 2372 and 2376 both will be divisible by 4.
And if we consider only 2nd statement, R will be having an absolute value of 6 as 2376 will be divisible by 6.
Hence by taking only 2nd statement into consideration, we can find unique value of R.
Concept: Try to find a way with which we can find an absolute/unique answer.

If only first statement taken into consideration:
y-x = 2 where x, y and z are three odd integers.
Nothing absolute can be said about divisibility of x+z with 4.
Now if only second statement taken into consideration :
z-y=2 and nothing absolute can be said about divisibility of x+z with 4.
If we consider both statement simultaneously then
we get x+z = 2y
Now as we know y is an odd integer , so 2y will never get a factor of 4.
Hence x+z is not divisible by 4.
As we find an absolute answer by using both statements Hence answer will be C)

Considering first statement only,current unit price of P1 is twice that of P2 and, Rates of P1 and P2 are either decreasing or P1 has constant rate. Now we can’t say that which product will be costlier aftre 5 years as nothing certain information is there about rates of decreasing. Similarly if we consider only 2nd statement or consider both statements simultaneously, nothing certain can be said about rate of decreasing hence D will be answer

If the number of mynahs is 7 or more and if 7 birds escaped, there is a possibility that no pigeon escaped. But the bird-keeper was able to conclude that atleast one pigeon escaped. So, the number of mynahs is less than 7.
From the options, we can see that only option a) violates this condition.

Total ways when all 6 boxes have only black balls = 1
Total ways when 5 boxes have black balls = 2
Total ways when 4 boxes have black balls = 3
Total ways when 3 boxes have black balls = 4
Total ways when 2 boxes have black balls = 5
Total ways when only 1 box has black ball = 6
So total ways of putting a black ball such that all of them come consecutively = (1+2+3+4+5+6) = 21

1. x=1 ; y=2
2. x=2 ; y=3
3. x=6 ; y=4
4. x=24 ; y=5
Hence when y=5 , x will be 24

As it is mentioned that difference in number of books is more than one
Hence option B and D are cancelled.
Now total amount is = 620 = 17M + 19P + 23C
we can check by putting values from option A and C.
Option C satifies the above eq.,Hence our answer will be C

According to question Rahul put exact number of 10 rs. notes, hence total price will be a multiple of 10.
And Rahul wants 30 cards, where he took 5 each of two kind and 10 each of other two kind.
So summation of (price of one type card multiplied by number of that type of card) should be a multiple of 10.
By looking at the prices of cards and to make the sum a multiple of 10, we can say that two 5 cards were of rs. 3.5 and 4.5
and two 10 cards were of prices 2 rs.and 5 rs each respectively.
Hence total sum will be 5 $$\times$$ (3.5+4.5) + 10 $$\times$$ (2+5) = 110
So rahul gave 11 notes of 10 rs.

According to the divisible rule of 9, the sum of all digits should be divisible by 9.
i.e. 55+A+B = 9k
So sum can be either 63 or 72.
For 63, A+B should be 8.
In given options, option B has values of A and B whose sum is 8 and by putting them we are having a number which divisible by both 9 and 8.