Quant Boosters - Ravi Handa - Set 2
Consider the side as a and hypotenuse as (L - a)
Calculate third side and find out area.
You will find out that it depends on your ability to maximize a * a * (L-2a)
Its sum is constant at L.
=> Product will be maximum when all the three terms are equal.
=> Hypotenuse = Twice of side
=> Angle between them is 60 degrees
Q27) The positive integer N and N^2 both end in the same sequence of four digits 'abcd' when written in base 10 where digit 'a' is not zero. find three digit number abc.
N^2 - N will end in 000
=> N(N-1) will be divisible by 625
=> abc5 or abc0 is divisible by 625
=> From the options only 9375 is divisible by 625
=> So, 937 is the answer
Q28) If p, q and r are in A.P & x, y and z are in G.P, Then x^(q-r) * y^(r-p) * z^(p-q) = ?
Using options (if available) and assuming values works best in such cases.
Take, p = 1, q = 2, r = 3 and x = 1, y = 2, z = 4
=> x^(q-r) * y^(r-p) * z^(p-q) = 1^(-1) * 2^2 * 4^(-1) = 1
To solve it properly, take the AP values as (a-d), a, (a+d) and the GP values as b/r, b, br
=> x^(q-r) * y^(r-p) * z^(p-q)
= (b/r)^(-d) * b^(2d) * (br)^(-d)
= b^(-d + 2d - d) * r^(d + 0 - d)
= b^0 * r^0
Q29) LCM of 2 numbers is 315. Which of the following cannot be the sum of two numbers, given that their HCF is prime number > 3
First of all, find out the factors of 315
315 = 3^2 * 5 * 7
=> HCF can be 5 or 7
Case 1: HCF is 5
=> The two numbers are 5a and 5b, where a & b are coprime to each other
=> 5 * a * b = 315
=> a * b = 63
=> a & b are (1,63) or (7,9)
=> Sum of the numbers = 5a + 5b = 5 * 64 or 5 * 16 = 320 or 80.
=> This eliminates option C.
Case 2: HCF is 7
=> The two numbers are 7a and 7b, where a & b are coprime to each other
=> 7 * a * b = 315
=> a * b = 45
=> a & b are (1,45) or (5,9)
=> Sum of the numbers = 7a + 7b = 7 * 46 or 7 * 14 = 322 or 98
=> This eliminates options A & B
=> Answer is Option D
Q30) Find Remainder [47^17/19]
Remainder [47^17 / 19]
= Remainder [9^17/19]
= Remainder [9 * 81^8/19]
= Remainder [9 * 5^8/19]
= Remainder [9 * 25^4/19]
= Remainder [9 * 6^4/19]
= Remainder [9 * 36^2/19]
= Remainder [9 * (-2)^2/19]
= Remainder [9 * 4/19]
= Remainder [36/19] = 17
Rakesh Achanta last edited by
@handakafunda Sir is answer 20c10-18c8 is correct for this question??