Data for Questions 1 to 5 :
If
M means greater than
N means equal to
O means not less than
P means less than
Q means not equal to
and R means not greater than
1. If yPz and zNa, then which of the following is true?
a) yMa
b) yPa
c) yOa
d) none of these
Explanation: yPz means that y is less than z and zNa means z = a. Thus, y is less than a
yPa. Option (b) is correct.
2. If 10aM6b and 12bM20c
a) 5aMc
b) aM5c
c) aNc
d) none of these
Explanation: 10a is greater than 6b. and 12b is greater than 20c
6n is greater than 10c. Thus 10a is greater than 10c or a is greater than c. Option (d) is correct.
3. If aP0 and b+2Pa, then which of the following is true?
a) bM – 2
b) bN – 2
c) bP – 2
d) none of these
Explanation: a is negative and b + 2 is less than a implies that b must be below –2. Hence, option (c) is correct.
4. If sOt, tRu and tRv then which of the following could be true about s and u/v or u and v?
a) sMu
b) sPv
c) sNv
d) can’t be determined
Explanation: Nothing can be said about the relationships between s, u or v or for that matter about u and v. Hence, cannot be determined. The correct answer is option (d).
5. If |t – u| M0, then which of the following is/are true
a) sMt
b) tMs
c) sNt
d) (a), (b) and (c) could be true
Explanation: Since the modulus value is always positive, all the three, i.e. the first, second and third relationships are possible. Hence, option (d) is correct
Data for Questions 6 to 8 :
If
aAb implies a + b
aMb implies a – b
aPb implies a ¥ b
aQb implies a ∏ b
6. Which of the following equations is correct?
a) 30Q10A4P2M2 = 15
b) 5P2A4Q2P2 = 14
c) 2Q3B5P6A7 = –5
d) none of these
Explanation: Option (b) is correct since we will get 10 + 4 = 14.
7. Calculate 5A6M3P4Q8
a) 10
b) 9
c) 9.5
d) 10.5
Explanation: 11 – 1.5 = 9.5. Option (c) is correct.
8. Calculate (2A3M4P5)P(5M6P8Q4)
a) –105
b) -120
c) 120
d) none of these
Explanation: (–15)(–7) = 105. Hence, option (d) is correct.