16. The sum and the product of the roots of the quadratic equation [latex]x^{2}[/latex]+ 20x + 3 = 0 are?
A. 10, 3
B. -10, 3
C. 20, -3
D. None of these
Answer: Option D
Explanation:
Sum of the roots and the product of the roots are -20 and 3 respectively
17. Let N be the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case. Then sum of the digits in N is:
Answer: Option C
Explanation:
N = H.C.F. of (4665 - 1305), (6905 - 4665) and (6905 - 1305)
= H.C.F. of 3360, 2240 and 5600 = 1120.
Sum of digits in N = ( 1 + 1 + 2 + 0 ) = 4
18. The sum of three numbers is 98. If the ratio of the first to second is 2 :3 and that of the second to the third is 5 : 8, then the second number is:
Answer: Option B
Explanation:
Let the three parts be A, B, C. Then,
A : B = 2 : 3 and B : C = 5 : 8 = (5 *[latex]\frac{3}{5}[/latex]) : (8 * [latex]\frac{3}{5}[/latex]) = 3 : [latex]\frac{24}{5}[/latex]
A : B : C = 2 : 3 :[latex]\frac{24}{5}[/latex]
= 10 : 15 : 24
B = 98 * [latex]\frac{15}{49}[/latex] = 30
19. In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit?
A. 30%
B. 70%
C. 100%
D. 250%
Answer: Option B
Explanation:
Let C.P.= Rs. 100. Then, Profit = Rs. 320, S.P. = Rs. 420.
New C.P. = 125% of Rs. 100 = Rs. 125
New S.P. = Rs. 420.
Profit = Rs. (420 - 125) = Rs. 295.
Required percentage =([latex]\frac{295}{420}[/latex] * 100)% = 70%
20. What percentage of numbers from 1 to 70 have 1 or 9 in the unit's digit?
Answer: Option C
Explanation:
Clearly, the numbers which have 1 or 9 in the unit's digit, have squares that end in the digit 1. Such numbers from 1 to 70 are 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69.
Number of such numbers =14
Required percentage = ([latex]\frac{14}{70}[/latex] * 100)% = 20%