List of top Quantitative Aptitude Questions on Linear Equations asked in CAT

In a school with 1500 students, each student chooses any one of the streams out of science, arts, and commerce, by paying a fee of Rs 1100, Rs 1000, and Rs 800, respectively. The total fee paid by all the students is Rs 15,50,000. If the number of science students is not more than the number of arts students, then the maximum possible number of science students in the school is

In a casino, there are three coloured tokens — Red (₹20), Green (₹50), Blue (₹100). Total worth ₹18,500. On a busy day, all Red tokens were upgraded to ₹200 (no change in Green/Blue). New worth: ₹27,500. Average number of tokens per colour equals the number of Green tokens. Find the total number of tokens.

What is the sum of the series $1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \ldots$?

If 5x = 25, what is x?

If 3x + 2y = 12 and x - y = 1, what is x?

A confused bank teller transposed the rupees and paise when he cashed a cheque for Shailaja, giving her rupees instead of paise and paise instead of rupees. After buying a toffee for 50 paise, Shailaja noticed that she was left with exactly three times as much as the amount on the cheque. Which of the following is a valid statement about the cheque amount?

The price of Darjeeling tea (in rupees per kilogram) is $ 100 + 0.10n $ on the $ n^{\text{th}} $ day of 2007 ($ n = 1, 2, \ldots, 100 $), and then remains constant. The price of Ooty tea (in rupees per kilogram) is $ 89 + 0.15n $ on the $ n^{\text{th}} $ day of 2007 ($ n = 1, 2, \ldots, 365 $). On which date in 2007 will the prices of these two varieties of tea be equal?

An airline has a certain free luggage allowance and charges for excess luggage at a fixed rate per kg. Two passengers, Raja and Praja have 60 kg of luggage between them, and are charged Rs 1200 and Rs 2400 respectively for excess luggage. Had the entire luggage belonged to one of them, the excess luggage charge would have been Rs 5400.

The number of solutions of the equation $2x + y = 40$ where both $x$ and $y$ are positive integers and $x \leq y$ is:

A change-making machine contains 1-rupee, 2-rupee, and 5-rupee coins. Total coins = 300, total value = Rs. 960. If 1-rupee and 2-rupee coin counts are interchanged, value decreases by Rs. 40. Find the total number of 5-rupee coins.

At a certain fast food restaurant, Brian can buy 3 burgers, 7 shakes, and one order of fries for Rs. 120 exactly. At the same place it would cost Rs. 164.5 for 4 burgers, 10 shakes, and one order of fries. How much would it cost for an ordinary meal of one burger, one shake, and one order of fries?

What is the value of $k$ for which the following system of equations has no solution: $2x - 8y = 3$ and $kx + 4y = 10$

In the questions two columns are given. You are required to solve the equations given in the "equations" column and match them with the correct statement given about the desired equation in the "conditions" column.

	Equations		Conditions
(a)	2x2 – 11x + 12 = 0	(d)	Product of roots is negative
(b)	5x2 21x – 20 = 0	(e)	Product of roots is completely divisible by 6
( c)	x2 – 17x + 72 = 0	(f)	Sum of both roots is positive

The digit at the unit place of P would be: Given, P=(6+1) (6²+1) (6³+1) ......... (6100+1)