# even

3,083 total views

3,083 total views Previous QuestionNext Question What is the digit in unit’s place of 251? [CAT, 1998]a. 2 b. 8 c. 1 d. 4 Solution: Although the problem of large exponents have been solved in many of the questions whose links can be found in this website, yet the exponent of 2 deserves a special attention. If the exponent […]

2,636 total views

2,636 total views Previous QuestionNext Question Let x and y be positive integers such that x is prime and y is composite. Then a. y – x can’t be an even integer b. yx can’t be an even integer c. can’t be even integer d. None of these [2003] Solution: Integers, Composite numbers, and Prime numbers: Integers are […]

911 total views

911 total views Previous QuestionNext Question The remainder obtained when a prime number greater than 6 is divided by 6 is [1995] a. 1 or 3b. 1 or 5c. 3 or 5d. 4 or 5 Solution: Remainder: Firstly, understand Euclid’s division algorithm. The algorithm says any positive integer ‘a’ divided by a positive integer ‘b’ always leaves a remainder ‘r’ […]

2,160 total views

2,160 total views Previous QuestionNext Question Two positive integers differ by 4 and sum of their reciprocals is . Then one of the numbers is [1995]a. 3b. 1c. 5d. 21 Solution: Integers are in the form of …-3, -2, -1, 0, 1, 2, 3…. But it is said in the question that we have to take only positive integers […]

4,051 total views

4,051 total views Previous QuestionNext Question Consider a sequence, where the nth term is tn =, , n=1, 2…The value of t3 * t4 * t5 * … t53 equalsa. b. c. d. e. Solution:sequence:This is a monotonically increasing sequence where each next term is greater than the previous one.That is pn+1-pn>0.If pn=3 then the next term […]

1,357 total views

1,357 total views Previous QuestionNext Question The remainder, when is divided by 19, is ? a.4 b.15 c.0 d.18 [CAT, 2004] Solution: The laws of exponents: According to the laws of exponents when the powers are the same, bases are added.am+bm = a+bmif the numbers are in multiplication with the same bases thenam×bm = […]

595 total views

595 total views Previous QuestionNext Question Which among , , , and is the largest ? a. b. c. d. e.[CAT, 2004] Solution:Fractional Power: When the power (exponent) is a fraction, its denominator indicates nth root. First, understand the following example: Let the number be “a” and its power be m/n. It is now a(m/n) which is in under root form […]

3,508 total views

3,508 total views Previous QuestionNext Question Let S be a set of positive integers such that every element n of S satisfies the conditionsa) 1000 ≤ n ≤ 1200b) Every digit in n is odd.Then how many elements of S are divisible by 3? [2005]a.9 b.10 c.11 […]

4,665 total views, 4 views today

4,665 total views, 4 views today Previous Question Next Question How many pairs of positive Integers m, n satisfy , where n is an odd integer less than 60? a. 4 b. 7 c. 5 d. 3 [CAT, 2007] Solution: […]

2,020 total views

2,020 total views Previous QuestionNext Question Consider four-digit numbers for which the first two digits are equal and the last two digits are also equal. How many are such numbers perfect squares?a. 2 b. 4 c. 0 d. 1 [CAT, 2007] Solution: Consider four digit-numbers Numerals and Digits: The First part of this question says: Consider four digits numbers whose first and […]