List of top Quantitative Aptitude Questions asked in CAT

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:
In the given figure, ‘O’ is the centre of the semi-circle and ∠MON =48°, Find ∠MRP.
The semi-circle
Find the value of: \( \frac{x^4-81}{ 2x2+13x+15 }\times\frac{2x+3}{x^3+27}\times\frac{[(x-3)^2+3x](x+5)}{(x+3)^2-6x}\)
A shopkeeper has two jars P and Q containing almond oil in the ratio 2 : 3 respectively. He mixes '3x' litres and '2x' litres of olive oil in P and Q, respectively, after which the percentage of olive oil in jar P becomes 80% more than that in jar Q. If mixtures from jar P and jar Q are then mixed in the ratio of 3 : 1, what will be the percentage of olive oil in the resultant mixture?
If (3x-\(\frac{1}{3x}\))=4, , then what is the value of (27x3-\(\frac{1}{27x^3}\)) ?
If x2-4x+3=0, then what is the value of (x3+4x2+7x+24)(x2+2x+3)-1?
If \(\frac{5(4x^2+1)-3x}{4x}=8\) and x ≠ 0, then what is the value of \((√2x-\frac{1}{√2x}) \)?
Is\( (\sqrt{x}-\frac{1}{\sqrt{x}})=\sqrt{-5}\) and x≠ 0, then what is the value of \(\frac{3(x^2+3)-6-3x}{4x}\) ?
Upstream speed of a motorboat is 70% of that downstream speed. The motorboat goes 220 km downstream but while returning the same distance in upstream, the rate of stream was double of itself. In this way, the motorboat takes the total time of 31 hours. What was the difference between time taken to go 220 km downstream and return the same distance in upstream?
The area of a circle is equal to the sum of the area of a rectangle and a square. The length of the rectangle is 1 cm more than the twice of the side of the square and breadth of the rectangle is 1.5 cm less than \(\frac{3}{2}\) times of the radius of the circle. What is the difference between the circumference of the circle and perimeter of the square if the side of the square is 6 cm less than the radius of the circle?
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=\(\frac{2x^2+x-6}{(x+2)^2-(x-2)^2}\), 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
Aman bought '3x' shares for Rs. 420 per share, '4x' shares for Rs. 450 per share and '3x' shares for Rs. 430 per share. He sold 40% of the shares at Rs. 480 per share and the rest at Rs. 'y' per share. If he made a total profit of 20% on the whole transaction, find the value of 'y'.
What is the minimum value of (a + b) such that 4a x 5b will be a multiple of 5000?
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?
How many odd factors of the number 456 x 565 x 776 are multiples of 63?
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.
How many numbers between 90 and 600 have exactly three factors?
How many factors of N=26 x 38 x 510 x 712 are perfect squares as well as perfect cubes?
Out of 40 members of team A only 60% are selected for the tour and out of 60 members of team B only 40% are selected for the tour. Ratio of male members to female members on the tour is 5:3. Ratio of male members who are selected from team A to female members who are selected from team A is 5:1. Find total number of female members who are selected for tour from team B.
If \(x=a^2+1\ \text{and} \ y=a^2-a+1\), then find the value of \(\frac{x^3-y^3-xy^2+x^2y}{(x+y)^2}\)
The radii of three concentric circles are in the ratio 2: 3: 4. What is the ratio of sum of areas of two inner circles to the area of the region between outermost circle and innermost circle?
In a ∆PQR, internal angle bisectors of ∠Q and ∠R meet at I while external angle bisectors of ∠Q and ∠R meet at X. If ∠P = 54°, then find the measures of ∠QIR and ∠QXR, respectively.
In a trinary base system, how many numbers from 0 to 100 end with digit 1?
What is the number of factors of the number formed by the last three digits of 10051001?