List of top Questions asked in CAT

In a library, the ratio of fiction books to non-fiction books is 7:5. The ratio of English fiction books to Hindi fiction books is 2:3. If there are 420 English fiction books, find the total number of non-fiction books in the library.

For any natural number n, suppose the sum of the first n terms of an arithmetic progression is n(n+1). If the nth term of the progression is divisible by 7, then the smallest possible value of n is:

The average weight of a group of people increases by 2 kg when a person weighing 65 kg joins them. If the initial average weight of the group was 55 kg, find the ratio of the number of people initially in the group to the total number of people in the new group.

How many factors of N=2⁶ x 3⁸ x 5¹⁰ x 7¹² are perfect squares as well as perfect cubes?

How many numbers between 90 and 600 have exactly three factors?

How many odd factors of the number 45⁶ x 56⁵ x 77⁶ are multiples of 63?

If=\(\frac{2x^2+x-6}{(x+2)^2-(x-2)^2}\), Q=\(\frac{x^2+3x+9}{(2x-3)(x^2-4)}\) and \(R=\frac{x^2-27}{x^4-4}\), then find the value of PXQ÷R

If (3x-\(\frac{1}{3x}\))=4, , then what is the value of (27x³-\(\frac{1}{27x^3}\)) ?

If \(\frac{5(4x^2+1)-3x}{4x}=8\) and x ≠ 0, then what is the value of \((√2x-\frac{1}{√2x}) \)?

If \(A=\frac{x^2-y^2}{x^2-y^2}\), \(B=\frac{x+y}{x^2+y^2+xy}\) and \(C=\frac{ 3xy^2-3x^2y}{x^2-y^2}\), then find the value of AB (A+C)

If \(N = 2^5 \times 3^4 \times 5^5 \times 11^2\), then how many factors of N are multiples of 66 but not of 72?

What is the minimum value of (a + b) such that 4a x 5b will be a multiple of 5000?

If x²-4x+3=0, then what is the value of (x³+4x²+7x+24)(x²+2x+3)^-1?

In the given figure, ‘O’ is the centre of the semi-circle and ∠MON =48°, Find ∠MRP.

In triangle ABC, ‘D’ and ‘E’ are two points on sides AB and AC, respectively such that DE is parallel to BC. If AD=16 cm, BD=(5x-16) cm, AE=2x cm and EC=(25-2x) cm, then find the value of ‘x’.

Is\( (\sqrt{x}-\frac{1}{\sqrt{x}})=\sqrt{-5}\) and x≠ 0, then what is the value of \(\frac{3(x^2+3)-6-3x}{4x}\) ?

Find the value of: \( \frac{x^4-81}{ 2x2+13x+15 }\times\frac{2x+3}{x^3+27}\times\frac{[(x-3)^2+3x](x+5)}{(x+3)^2-6x}\)

P and Q start a business with initial investment Rs.5000 and Rs.4000 respectively. After ’t’ years Q adds 25% of what he invested initially and another person R joins the business with them with initial investment Rs.7000 and after 5years from the start of the business P adds Rs.1000 more to his capital. If at the end of 8 years total profit from the business is Rs.11900 while share of Q is Rs.3750, what is the share of R in the profit.

PQRS is a rhombus such that length of its each side is 30 cm. If PR=36 cm and QS=\(4\sqrt{x}\) cm then the length of each side of the rhombus (in terms of ‘x’) is:

Directions: Answer the questions based on the information given below.
Sonia deposited Rs. 20 and Rs. 50 notes in her piggy bank on different days of the month and used to count total number of Rs. 20 and Rs. 50 notes deposited by her in the piggy bank at the end of the month. The bar graph given below shows the percentage by which number of Rs. 50 notes in the piggy bank was more/less than number of Rs. 20 notes at the end of the given months. (Note: +ve value shows more while –ve value shows less)

Added Information:
1. Number of Rs. 20 notes deposited in February was 42(6/7)% of total notes deposited in the same month.
2. Number of Rs. 50 notes deposited in February and March together is 35(5/13)% less than number of Rs. 20 notes deposited in February and March together.
3. Number of Rs. 20 notes deposited in April and March together is 80 more than total number of Rs. 20 notes deposited at the end of February.
4. If number of Rs. 20 notes deposited in April would have been 160 more, then number of Rs. 50 notes deposited in April would have been 26% more than number of Rs. 20 notes deposited.
5. Number of Rs. 50 notes deposited in April was 6 times more than number of Rs. 50 notes deposited in May.
6. Number of Rs. 20 notes deposited in June was 50% more than that deposited in May.

Directions: Answer the questions based on the information given below.
A train ‘T’ starts from station ‘A’ for station ‘F’. In between stations ‘A’ and ‘F’, there are four intermediate stations ‘B’, ‘C’, ‘D’ and ‘E’, respectively, in the same order. Stations ‘A’, ‘B’, ‘C’, ‘D’ and ‘E’ has quota for seats booking. The line graph given below represents the percentage distribution of quota of seats given to the respective stations out of total number of seats in the train and percentage of seats booked out of them.

The table below represents the total vacant seats in the train after leaving the respective stations.

Stations	Total vacant seats
B	562
C	494
D	514
E	472

Note:
1. When train left station A, number of vacant seats was 688 and 30% of quota seats of station A were not booked.
2. A seat can be booked for only one person from the respective stations and the same person can board the train from that station.
3. All the persons who booked tickets boarded the train.

Directions: Study the given information and answer the following questions based on it.
There are three buildings X, Y and Z in a linear row from west to east respectively such that each building has different number of floors. The floors of buildings X and Z are numbered in such a way that the ground floor is numbered 0, first floor is numbered 1, second floor is numbered 2 and so on. The floors of building Y are numbered in such a way that the ground floor is numbered 1, first floor is numbered 2, second floor is numbered 3 and so on. The topmost floor in any building is painted red and the three consecutive floors below it are painted black, white and blue respectively. The floor immediately below the blue floor is painted red and the sequence continues till the ground floor.
NOTE: (i) If the number of floors in between two floors A and B are given, then A and B are in the same building. Also, if A is immediately above/below B then, A and B are in the same building.
(ii) If floor A is in building X and is to the west of floor B, then B can be in building Y or Z and is horizontally aligned with A. In other words, if A is floor no. 5 of building X and is to the west of floor B which is in building Z, then B is also floor no. 5 of building Z.
O's floor is not numbered 0 and has two blue floors above it. Ground floor of building Z is not painted red. W is in building Y and is painted black. W has more than one floor above it. Two floors are in between H and R such that H is below R. H and E are in building X. R is painted blue. T's floor is numbered 0 and is painted with neither blue nor red. Six floors are above E. Floor L is to the east of floor V. The total number of floors in building Y is equal to the floor number of the floor immediately below L. O is painted red and there is no floor below it. G is in floor no. 9. G is neither immediately below V nor is the topmost floor of its building. D is to the immediate east of E and is painted white. Four floors painted red in building Z. N is the topmost floor of its building. The number of floors below N is twice that below D. Q is painted the same colour as E but its floor number is lower than that of E. S is immediately above Q. Two floors are in between M and S. M is not painted the same colour as H. M's floor is not numbered 0. Neither T nor G is adjacent to M.

Directions: Study the given information and answer the following questions based on it.
Eight movies A, B, C, D, E, F, G and H were released in March, April, May and June on either 11th or 30th of a month but not necessarily in the same order. All movies were released on different dates. Each of the movies was released on different OTT platforms among Netflix, Voot, Amazon prime, Zee5, Hotstar, SonyLiv, MX Player and Jio Cinema but not necessarily in the same order.
Three movies were released between C and E. Movie H was released neither on Amazon prime nor on MX Player. Two movies were released between D and H, which was released on an even number date. Movie A was released on Zee5 in the same month in which movie B was released. D was released on Voot immediately after G, which was not released on Amazon Prime. Movie F was released immediately before the movie which was released on SonyLiv. The number of movies released before movie H is same as the number of movies released after movie B, which was released on Hotstar. Movie E was released on Netflix in the month having an even number of days.

If \(x=a^2+1\ \text{and} \ y=a^2-a+1\), then find the value of \(\frac{x^3-y^3-xy^2+x^2y}{(x+y)^2}\)

Study the given information and answer the following questions based on it.
Eight friends - Amrita, Akash, Amit, Abhay, Anisha, Akshay, Aliah and Amber are working in eight different banks - SBI, PNB, UCO, HDFC, ICICI, HSBC, IDBI and Axis bank on eight designations - Clerk, PO, Assistant Manager (AM), Manager, Chief Manager (CM), Assistant General Manager (AGM), Deputy General Manager (DGM) and General Manager (GM) but not in the same order.
Note: The designations are in ascending order such that Clerk is the junior most while the GM is the senior most in each bank.
Akash is senior to Amit but immediate Junior to the person working in PNB. Anisha works in UCO Bank but she is neither most senior nor most junior among them and she is not AGM. The number of persons senior to Amit is one more than the number of persons junior to Amrita who works in Axis Bank. More than four friends are senior to Abhay who is not a Clerk. The person working in Axis Bank is immediate senior to Abhay. Aliah is senior to Amber who is immediate junior to the person working in ICICI Bank but junior to Akash who works in SBI Bank. Neither Aliah nor Amber works in HDFC Bank. The person working in IDBI Bank is senior to Amber.