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23. If 1.4 is halfway between two points x & y what are the possible values of x & y ?A) -1.4 AND 2.4 B) -1 & 2 C) -0.3 & 3.1 D) 0.15 AND 1.55
Ans: 1.4 is halfway between x and y means that in the number line we have a situation like
So, 1.4-x=y-1.4 has to hold. This equation holds only for option (C) Ans: C
24. If x, w, z, correspond to four numbers -3, 1/2, -4,2 but necessarily in the same order, what is the largest possible value of the expression (wz/y)(z)2?
A) 96 B) 36 C) 24 D) 12 E) None of these
When we divide the number by a smaller value between 0 & 1 the result is larger. So, we choose y = 1/2. We have two negative numbers: -3 and -4. We must choose them for w & x (in any order); otherwise, the product will be negative, making the ultimate number 2.
:. (wx/y)(z)2 = ((-3x -4)/(1/2))(z)2 = 12x4x2= 96
Ans: (A)
25. what is the number of primes that are divisible by 3 ?
A) 1 B) 0 C) 2 D) Infinity
Ans: By definition, prime numbers are divisible by 1 & itself only. So, only 3 which is a prime can be divisible by itself. Hence the answer is A.
26. If x is an odd integer, for which of the following equations must y be an even integer?
A) xy= 5 B) x+y = 8 C) x + 2y= 6 D) x+2y= 6 E) None of these
Ans: we know, 5x1=5, So, in (A) y need not be an even integer.
(B): x+y = 8 or , odd+ y=even
or , y=even-odd=odd
:. (B) is not the answer.
(C) x+2y= 7 or, odd+2y=7
or, 2y=7-odd= even
:. y=(even/2) odd or even
Here, y may be odd or even. So, (C) is not the answer.
(D): 2x + y=6
2x is definitely even
:. even + y = even
or, y=even-even= even
:. (D) is the answer.
27. the difference between two hundred nine thousand fourteen and ninety three thousand seen hundred nine is ?
A) 116315 B) 115315 C) 116305 D) 115305 E) None
Ans: 209014 - 93709= 115305
Ans: (D)
28. Which of the following is not an integer?
A) -3 B) 0 C) 9.98 D) 2
Ans: Since 9.98 has a fractional part, it is not an integer. All the others are integers. Ans: (C)
Posted in: Number System
