Number System - Study Mode

[#246] While writing all the numbers from 700 to 1000, how many numbers occur in which the first digits greater than the second digit, and the second digit is greater than the third digit ?
Correct Answer

(D) 85

Explanation

Solution: When the second digit is 1, third digit can be 0, i.e., there is one such number. When the second digit is 2, third digit can be 0 or 1, i.e., there are 2 such numbers. When the second digit is 3, third digit can be 0, 1 or 2, i.e., there are 3 such numbers, and so on. When the first digit is 7, second digit can be 1, 2, 3, 4, 5 or 6 So, there are (1 + 2 + 3 + 4 + 5 + 6) = 21 such numbers between 700 and 799 When the first digit is 8, second digit can be 1, 2, 3, 4, 5, 6 or 7 So, there are (1 + 2 + 3 + 4 + 5 + 6 + 7) = 28 such numbers between 800 and 899 When the digit is 9, second digit can be 1, 2, 3, 4, 5, 6, 7 or 8 So, there are (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8) = 36 such numbers between 900 and 999 Hence, the required number = (21 + 28 + 36) = 85

[#247] 98th term of the infinite series 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, .... is :
Correct Answer

(B) 2

Explanation

Solution: Given series is 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, ..... ∴ 96 th term is 4 So, $${T_{97}}$$ = 1 and $${T_{98}}$$ = 2 Hence, the 98 th term is 2

[#248] If x and y are two digits of the number 653xy such that the number is divisible by 80, then x + y is equal to :
Correct Answer

(D) 6

Explanation

Solution: Since, 653xy is divisible by 80, we must have y = 0 Now, 653x0 must be divisible by both 5 and 16 Clearly, it is divisible by 5 for all values of x Now, the number 53x0 must be divisible by 16 The least value of x is clearly 6 So, x + y = 6 + 0 = 6

[#249] P and Q are two positive integers such that PQ = 64. Which of the following cannot be the value of P + Q = ?
Correct Answer

(C) 35

Explanation

Solution: We may have (64 and 1), (32 and 2), (16 and 4) and (8 and 8) In any case, the sum is not 35

[#250] How many numbers less than 1000 are multiple of both 10 and 13 ?
Correct Answer

(B) 7

Explanation

Solution: Required numbers are multiples of (10 × 13), i.e., 130 These numbers are 130, 260, 390, 520, 650, 780 and 910 They are 7 in number.