Quant Boosters  Hemant Yadav  Set 2

Q16) A 1000 digit number has the property that every two consecutive digits form a number that is a product of four prime numbers. The digit in the 500th position is
(a) 2
(b) 4
(c) 5
(d) 6
(e) 8[OA : 8]

Q17) A standard die with sides labelled 1 through 6 is rolled three times. Find the probability that the product of the three numbers rolled is divisible by 8.

Q18) Smallest number to be added to 17 * 20 * 23 such that it becomes a perfect square is ?

Q19) How many positive integral solutions does the equation x^2 + y^2 = 50 have?
[OA : 3]

Q20) Sum of two positive numbers a and b is 1001, then how many different values HCF(a, b) can take ?

Q21) a + b + c + d = 24, number of solutions such that a, b, c, d are distinct natural numbers

Q22) Find the minimum value of x  1 + 2x  1 + 3x  1 + 4x  1
[OA : 4/3]

Q23) There are three sugar solutions A, B and C. A is four litres with 45% concentration, B is five litres with 48% solution, C is one litre with k% solution. Now m/n litre of solution C is added to A and the remaining part is added to B such that both the resultant solutions are now 50% concentrated solutions. m and n are coprime to each other. Find the value of k + m + n.

Q24) Number of ways in which 1050 can be written as sum of:
 consecutive integers
 consecutive positive integers
 consecutive even positive integers
 consecutive odd positive integers

Q25) A kite of area K is inscribed in a circle of radius R . The length of the shorter side of kite is 7 cm . A parallelogram with shorter side 8 and area P is inscribed in the same circle. Which of the following is definitely true?
a. K > P
b. K = P
c. K < P
d. Can not say

Q26) Pascal High School organized three different trips. Fifty percent of the students went on the first trip, 80% went on the second trip, and 90% went on the third trip. A total of 160 students went on all three trips, and all of the other students went on exactly two trips. How many students are at Pascal High School?
a) 1400
b) 600
c) 1200
d) 800
e) 1600

Q27) How many threedigit numbers are there such that no two adjacent digits of the number are consecutive?
a) 592
b) 516
c) 552
d) 600
e) 596

Q28) For all positive integers n, S(n) is number of positive integral ordered pairs (x, y) satisfying the equation 1/x + 1/y = 1/n. For how many n ≤ 400, S(n) = 5

Q29) Connie has a number of gold bars, all of different weights. She gives the 24 lightest bars, which weigh 45% of the total weight, to Brennan. She gives the 13 heaviest bars, which weigh 26% of the total weight, to Maya. She gives the rest of the bars to Blair. How many bars did Blair receive?
a) 14
b) 15
c) 16
d) 17
e) 18

Q30) How many 7 digit numbers abcdefg are there such that a > b ≥ c > d ≥ e > f ≥ g ?
[OA : 13C7]