# Quant Boosters - Hemant Malhotra - Set 3

• Q26) A function f is even if f(t) = f(–t), and it is odd if f(t) = –f(–t). Let f(x) = g(x) + h(x) and f(–x) = g(x) – h(–x). Which of the following is definitely correct?
a) f is an even function and g is an odd function.
b) Both f and g are even functions.
c) f is an even function and h is an odd function.
d) g is an even function and h is an odd function.

• g(x) is an even function et f(x)=g(x)+h(x) (1)
f(-x)=g(x)-h(-x) (2)
f(x)+f(-x)=2(g(x)
means g(x)=(f(x)+f(-x))/2
g(-x)=f(-x)+f(x)/2
so g(x)=g(-x) so even

• Q27) For how many positive integer values of ‘x’ is ||||x – 1| – 2| – 3| – 4| < 5

• ||||x – 1| – 2| – 3| – 4| < 5
so |x-1| < 5 + 4 + 3 + 2
so |x-1| < 14
so -14 < x-1 < 14
so -13 < x < 15
so max 14 and min = -12

• Q28) Let f be a function such that
f(a,b) = f(a-b , b) if a> = b
= a if a < b
Now, if f(n,5)= 3 and f(n,6)= 5, then n = ?

• f(a,b)=f(a-b,b) if a>=b
=a if a < b
f(n,5) =3
now f(n,6)=5
If f(n,5)=3 and we need 3
so n will be in form of 5k+3 for 3
and n should be also in form of 6k+5
now 5k+3=6k+5
so first number will be 23 and So on so OA=CBD

• Q29) f(x, y) is a polynomial function such that f(2, 3) = 30, f(3, 4) = 84 and f(4, 5) = 180. Find f(5, 6).
a) 310
b) 330
c) 340
d) 350

• (3+2) * 3 * 2 = 30
(3+4) * 4 * 3 = 84
(4+5) * 4 * 5 = 180
f(5,6) = (5 + 6) * 5 * 6 = 330

• Q30) To measure the weight between 1 to 300 how many minimum weighs are required so that all weight can be measured?

• for any weight we have 3 possibilities:-

1. Place it on the weight pan
2. Place it on other pan, along with something whose weight we need to find
3. We don't use it

So, it is similar to base 3, hence by taking weight of form 3^n, we can ensure that we are using least number of weights and when we just have two possibilities. so 3^n >=300 so n=6

67

61

63

64

71

33

51