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The game of QUIET is played between two teams. Six teams, numbered 1, 2, 3, 4, 5, and 6, play in a QUIET tournament. These teams are divided equally into two groups. In the tournament, each team plays every other team in the same group only once, and each team in the other group exactly … Read more
The number of distinct integer solutions (x, y) of the equation |x + y| + |x – y| = 2, is If 10^68 is divided by 13, the remainder is1) 8 2) 9 3) 4 4) 5 Find the number of all positive integers up to 500 with non-repeating digits. Show/Hide Solution Type of Number … Read more
After two successive increments, Gopal’s salary became 187.5% of his initial salary. If the percentage of salary increase in the second increment was twice of that in the first increment, then the percentage of salary increase in the first increment was ?1) 252) 203) 27.54) 30 A regular octagon ABCDEFGH has sides of length 6 cm each. Then the … Read more
Surd Algebra Question Q1 \( a \) and \( b \) are natural numbers, then the value of \( a + b \) is: \[ (a + b\sqrt{3})^2 = 52 + 30\sqrt{3} \] Sequence Sum Solution Q2 Consider the sequence: \[ t_1 = 1, \quad t_2 = -1, \quad t_n = \left( \frac{n – 3}{n … Read more
Question 1 Roots and Expression Value The roots \( \alpha, \beta \) of the equation \( 3x^2 + \lambda x – 1 = 0 \) satisfy \[ \frac{1}{\alpha^2} + \frac{1}{\beta^2} = 15. \] The value of \( (\alpha^3 + \beta^3)^2 \) is: Question 2 Trapezium + Triangles ABCD is a trapezium in which AB is … Read more
Ques 1 When 3^333 is divided by 11, the remainder is Ques 2 A function f maps the set of natural numbers to whole numbers, such that f(xy) = f(x)f(y) + f(x) + f(y) for all x, y and f(p) = 1 for every prime number p. Then, the value of f(160000) is 1) 4095 2) 1023 … Read more
Inequality Question All the values of \( x \) satisfying the inequality \( \frac{1}{x + 5} \leq \frac{1}{2x – 3} \) are: 1) \( -5 < x < \frac{3}{2} \) or \( x > \frac{3}{2} \) 2) \( -5 < x < \frac{3}{2} \) or \( \frac{3}{2} < x \leq 8 \) 3) \( x ... Read more
Ages + RatiosWhen Rajesh’s age was same as the present age of Garima, the ratio of their ages was 3 : 2. When Garima’s age becomes the same as the present age of Rajesh, the ratio of the ages of Rajesh and Garima will become 1) 2 : 12) 3 : 23) 4 : 34) 5 : 4 Mixtures … Read more
MathJax Inequality Region Area In the XY-plane, the area, in sq. units, of the region defined by the inequalities \( y \geq x + 4 \) and \( -4 \leq x^2 + y^2 + 4(x – y) \leq 0 \) is: 1. \( 3\pi \) 2. \( 2\pi \) 3. \( 4\pi \) 4. \( … Read more
MathJax Question Let \( x, y, \) and \( z \) be real numbers satisfying: \( 4(x^2 + y^2 + z^2) = a \), \( 4(x – y – z) = 3 + a \). Then \( a \) equals: 1. \( 1 \) 2. \( 4 \) 3. \( 3 \) 4. \( 1 … Read more
MathJax Question For any natural number \( n \), let \( a_n \) be the largest integer not exceeding \( \sqrt{n} \). Then the value of \( a_1 + a_2 + \cdots + a_{50} \) is When 10^100 is divided by 7, find the remainder. a. 1 b. 6 c. 3 d. 4
Ratios + Simple Equations A fruit seller has a total of 187 fruits consisting of apples, mangoes and oranges. The number of apples and mangoes are in the ratio 5 : 2. After she sells 75 apples, 26 mangoes and half of the oranges, the ratio of number of unsold apples to number of unsold … Read more
CAT 2023 QA Slot 3 – Questions and Solutions Question 1 Let \( a \) and \( b \) be two sequences such that \( a_n = 13 + 6(n-1) \) and \( b_n = 15 + 7(n-1) \) for all natural numbers \( n \). Then, the largest three-digit integer that is common to … Read more
CAT 2023 QA Slot 3 Quiz CAT 2023 QA Slot 3 Quiz 7. Algebra – Surds & Indices Let \( n \) be any natural number such that \( 5^{n-1} < 3^{n+1} \). The least integer value of \( m \) that satisfies \( 3^{n+1} < 2^{n+m} \) for all such \( n \) is? ... Read more
CAT 2023 QA Slot 3 – Questions and Solutions CAT 2023 QA Slot 3 Questions and Solutions Question 1 The number of positive integers less than 1000, having exactly two distinct prime factors, is: A. 10 B. 12 C. 15 D. 18 Show Solution Answer: C. 15 Detailed Solution: We count numbers of the form … Read more
CAT 2023 QA Slot 3 – Questions and Solutions CAT 2023 QA Slot 3 Questions and Solutions Question 1 Let \( n \) and \( m \) be two positive integers such that there are exactly 41 integers greater than \( 8^m \) and less than \( 8^n \), which can be expressed as powers … Read more
CAT 2023 QA Slot 2 – Questions and Solutions CAT 2023 QA Slot 2 Questions and Solutions Question 1 For some positive real number \( x \), if \( \log_{\sqrt{3}}(x) + \log_x(25) = \log_x(0.008) \), then the value of \( x \) is: A. 7 B. 6 C. 8 D. 9 Show Solution Answer: A. … Read more
CAT 2023 QA Slot 2 Questions Question 1: For any natural numbers m, n and k, such that k divides both m + 2n and 3m + 4n, k must be a common divisor of A. m and n B. m and 2n C. 2m and 3n D. 2m and n Show/Hide Solution Solution: Let … Read more
CAT 2023 QA Slot 2 – Questions and Solutions CAT 2023 QA Slot 2 Questions and Solutions Question 1 The number of positive integers less than 50, having exactly two distinct factors other than 1 and itself, is: A. 13 B. 15 C. 16 D. 17 Show Solution Answer: B. 15 Detailed Solution: Positive integers … Read more
CAT 2023 QA Questions and Solutions CAT 2023 QA Questions and Solutions Question 17: Geometry – Triangles A triangle is drawn with its vertices on the circle \( C \) such that one of its sides is a diameter of \( C \) and the other two sides have their lengths in the ratio \( … Read more