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- Question 1 of 27
##### 1. Question

**Directions**(Qs. 1-4) : ‘∆’ means ‘is equal to’, ‘□’ means ‘is not equal to’, ‘+’ means ‘is greater than’, ‘–’ means ‘is less than’, ‘×’ means ‘is not greater than’, ‘÷’ means ‘is not less than’; a – b – c implies:##### Hint

a – b – c means a < b < c and this relation implies that b > a < c, i.e., b + a – c.

- Question 2 of 27
##### 2. Question

**Directions**(Qs. 1-4) : ‘∆’ means ‘is equal to’, ‘□’ means ‘is not equal to’, ‘+’ means ‘is greater than’, ‘–’ means ‘is less than’, ‘×’ means ‘is not greater than’, ‘÷’ means ‘is not less than’; a + b ÷ c implies:##### Hint

a + b ÷ c means that a > b ≥ c and this relation implies that c < b < a, i.e., c – b – a.

- Question 3 of 27
##### 3. Question

**Directions**(Qs. 1-4) : ‘∆’ means ‘is equal to’, ‘□’ means ‘is not equal to’, ‘+’ means ‘is greater than’, ‘–’ means ‘is less than’, ‘×’ means ‘is not greater than’, ‘÷’ means ‘is not less than’; a × b ÷ c implies that:##### Hint

a × b ÷ c means a ≤ b ≥ c and this relation implies that c ≤ b < a, i.e., c × b ÷ a.

- Question 4 of 27
##### 4. Question

**Directions**(Qs. 1-4) : ‘∆’ means ‘is equal to’, ‘□’ means ‘is not equal to’, ‘+’ means ‘is greater than’, ‘–’ means ‘is less than’, ‘×’ means ‘is not greater than’, ‘÷’ means ‘is not less than’; a + b + c does not imply:##### Hint

a + b + c means a > b > c and this relation does not imply that b < a < c, i.e., b – a – c.

- Question 5 of 27
##### 5. Question

**Directions**(Qs. 5-9) : ∆ = greater than, + = not greater than, θ = equal to, φ = not equal to, × = less than, □ = not less than; a × b θ c implies that:##### Hint

a × b θ c is equivalent to a < b = c. Hence between a and b , we have a < b or a ≠ b or a > b

Further b = c implies that b and c are interchangeable.

Hence (a), (b) and (c) are not possible.

[Observe that (b) states b < a which means a > b which is not possible. Similarly in (c) b > a which means a < b which contradicts the hypothesis.] (d) Is the correct answer which states that a ≠ b and b > c. Both statements are possible. - Question 6 of 27
##### 6. Question

**Directions**(Qs. 5-9) : ∆ = greater than, + = not greater than, θ = equal to, φ = not equal to, × = less than, □ = not less than; a □ b ∆ c implies that:##### Hint

Hypothesis (stem of the question) states a ≠ b & b > c. Only relation not possible between a and b is that of equality. Hence (a), (b), (c), (d) are all possible from the relation between a and b.

Coming to the second relation only (a) is possible . Hence (a) is the answer. - Question 7 of 27
##### 7. Question

**Directions**(Qs. 5-9) : ∆ = greater than, + = not greater than, θ = equal to, φ = not equal to, × = less than, □ = not less than; a ∆ b ∆ c does not imply:##### Hint

Note that in this question we have to determine which relation is not possible.

It is given that a > b > c.

Both relation in (a), (c) and (d) are possible. It is only (b) in which b = c is not true. Hence (b) is the answer.

[It should be noted that in case of negation of implication it is enough to show that just one relation is not possible.] - Question 8 of 27
##### 8. Question

**Directions**(Qs. 5-9) : ∆ = greater than, + = not greater than, θ = equal to, φ = not equal to, × = less than, □ = not less than; a × b θ c does not mean:##### Hint

With the situations given, a × b θ c mean a < b = c From option (a), a ∆ b φ c means a > b ≠ c, this is not true.

From option (b), a + b θ c means a ≤ b = c, this is true.

From option (c) ,a φ b θ c means a ≠ b = c, this is true From option (4), b θ c □ a means b = c ≥ a, this is true. So, the answer is (a). - Question 9 of 27
##### 9. Question

**Directions**(Qs. 5-9) : ∆ = greater than, + = not greater than, θ = equal to, φ = not equal to, × = less than, □ = not less than; c + b × a means:##### Hint

With the notations given, c + b × a means c ≤ b < a From option (a), a × b θ c means a < b = c, this is not true. From option (b), c ∆ b ∆ a means a > b > c, this is true.

From option (c), c × b × a means a < b < c, this is not true. From option (d), b θ c ∆ a means b = c > a, this is not true. - Question 10 of 27
##### 10. Question

**Directions**(Qs. 10-11) : Different alphabets stand for various symbols as indicated below:Addition : O, Subtraction : M, Multiplication : A, Division : Q, Equal to : X, Greater than : Y, Less than : Z. Which one of the following alternatives is correct ?

##### Hint

Using the proper notations in (b), we get the statement as 2÷1 + 20 × 1 < 6 × 4 or 22 < 24, which is true.

- Question 11 of 27
##### 11. Question

**Directions**(Qs. 10-11) : Different alphabets stand for various symbols as indicated below:Addition : O, Subtraction : M, Multiplication : A, Division : Q, Equal to : X, Greater than : Y, Less than : Z. Which one of the following alternatives is correct ?

##### Hint

Using the proper notations in (b), we get the statement as 10 = 2 × 3 × 2 – 2 ÷ 1 or 10 = 10, which is true.

- Question 12 of 27
##### 12. Question

**Directions**(Q.12-16): ‘A @ B’ means ‘A is added to S’. ‘A * B’ means ‘A is multiplied by B’. ‘M # B’ means ‘A is divided By B’. ‘A $ B’ means ‘B is subtracted from A’. Find out which expression correctly represents the statement.Total age of 12 boys is ‘X’ and the total age of 13 girls is ‘Y’. What is the average age (A) of all the boys and girls together?

##### Hint

Average age of all boys and girls

⇒ A1 = (x @ y) # 25 - Question 13 of 27
##### 13. Question

**Directions**(Q.12-16): ‘A @ B’ means ‘A is added to S’. ‘A * B’ means ‘A is multiplied by B’. ‘M # B’ means ‘A is divided By B’. ‘A $ B’ means ‘B is subtracted from A’. Find out which expression correctly represents the statement.Population of state M (P1) is less than half of population of state N (P2) by 1,50,000.

##### Hint

–1,50,000

⇒ P1 = (P2 # 2) $ 150000 - Question 14 of 27
##### 14. Question

**Directions**(Q.12-16): ‘A @ B’ means ‘A is added to S’. ‘A * B’ means ‘A is multiplied by B’. ‘M # B’ means ‘A is divided By B’. ‘A $ B’ means ‘B is subtracted from A’. Find out which expression correctly represents the statement.Number of boys (B) in a class is equal to one-fourth of three times the number of girls (G) in the class.

##### Hint

⇒ B = (3 * G) # 4 - Question 15 of 27
##### 15. Question

**Directions**(Q.12-16): ‘A @ B’ means ‘A is added to S’. ‘A * B’ means ‘A is multiplied by B’. ‘M # B’ means ‘A is divided By B’. ‘A $ B’ means ‘B is subtracted from A’. Find out which expression correctly represents the statement.Salary of Mr. X (S1) is more than 40% of Mr. Y’s salary (S1) by Rs 8,000

##### Hint

⇒ S1 = [S2 *(40 # 100)] @ 8,000 - Question 16 of 27
##### 16. Question

**Directions**(Q.12-16): ‘A @ B’ means ‘A is added to S’. ‘A * B’ means ‘A is multiplied by B’. ‘M # B’ means ‘A is divided By B’. ‘A $ B’ means ‘B is subtracted from A’. Find out which expression correctly represents the statement.Marks obtained by Sujit in History (H) are 85% of his marks obtained in Science (M).

##### Hint

s

⇒ H = (85 # 100) * M - Question 17 of 27
##### 17. Question

If ‘L’ denotes ‘÷’, ‘M’ denotes ‘×’, ‘P’ denotes ‘+’ and ‘Q’ denotes ‘–’, then which of the following statements is true?

##### Hint

Using the proper notations in (d), we get

9 + 9 ÷ 9 – 9 × 9

= 9 + 1 – 9 × 9 = 9 + 1 – 81 = –71.

∴ option (d) is true. - Question 18 of 27
##### 18. Question

If ‘P’ denotes ‘+’, ‘Q’ denotes ‘–’, ‘R’ denotes ‘×’ and ‘S’ denotes ‘÷’, which of the following statements is correct?

##### Hint

Using the proper notations in (d), we get

8 × 8 + 8 ÷ 8 – 8

= 8 × 8 + 1 – 8 = 64 + 1 – 8 = 57 - Question 19 of 27
##### 19. Question

Which one of the four interchanges in signs and numbers would make the given equation correct ?3 + 5 – 2= 0

##### Hint

By making the interchanges given in (a), we get the equation as

2 – 5 + 3 = 0 or 0 = 0 which is true.

By making the interchanges given in (b), we get the equation as

3 – 2 + 5 = 0 or 6 = 0, which is false.

By making the interchanges given in (c), we get the equation as

5 – 2 + 2 = 4 or 4 = 0 which is not true.

So, the answer is (a). - Question 20 of 27
##### 20. Question

If the given interchanges namely : signs ‘+’ and ‘÷’ and numbers ‘2’ and ‘4’ are made in signs and numbers, which one of the following four equations would be correct ?

##### Hint

Interchanging (+ and ÷) and (2 and 4), we get :

(a) 4 ÷ 2 + 3 = 3 or 5 = 3, which is false

(b) 2 ÷ 4 + 6 = 1.5 or 6.5 = 1.5, which is false.

(c) 2 + 4 ÷ 3 = 4 or ¹⁰⁄₃ = 4, which is false.

(d) 4 ÷ 2 + 6 = 8 or 8 = 8, which is true. - Question 21 of 27
##### 21. Question

It being given that : ‘>’ denotes ‘+’, ‘<’ denotes ‘–’, ‘+’ denotes ‘÷’, ‘–’ denotes ‘=’, ‘=’ denotes ‘less than’ and ‘×’ denotes ‘greater than’; find which of the following is a correct statement:

##### Hint

Using proper notations, we have:

(a) given statement is 3 ÷ 2 + 4 < 9 ÷3 – 1 or ¹¹⁄₂ < 2, which is not true. (b) given statement is 3 + 2 + 4 < 18 ÷ 3 – 2 or 9 < 4, which is not true. (c) given statement is 3 + 2 – 4 > 8 ÷ 4 – 2 or 1 > 0, which is true.

(d) given statement is 3 ÷ 2 – 4 > 9 ÷ 3 – 3 or – ⁵⁄₂ > 0, which is not true . So, the statement (c) is true. - Question 22 of 27
##### 22. Question

If ‘×’ stands for ‘addition’, ‘< ’ for ‘subtraction’, ‘+’ stands for ‘division’, ‘>’ for ‘multiplication’, ‘–’ stands for ‘equal to’, ‘÷’ for ‘greater than’ and ‘=’ stands for ‘less than’; state which of the following is true ?

##### Hint

Using the proper notations in (2), we get the statement as 5 × 2 ÷ 2 < 10 – 4 + 2 or 5 < 8 , which is true.

- Question 23 of 27
##### 23. Question

If ‘→’ stands for ‘addition’, ‘←’ stands for ‘subtraction’, ‘↑’ stands for ‘division’, ‘↓’ stands for ‘multiplication’, ‘↗’ stands for ‘equal to’; then which of the following alternatives is correct?

##### Hint

Using the proper notations in (d) we get the statement as

2 × 5 – 6 + 2 = 6

or 10 – 6 + 2 = 6 or 6 = 6, which is true. - Question 24 of 27
##### 24. Question

Of ‘x’ Stands for ‘addition’, ‘z’ for ‘subtraction’, ‘+’ for ‘division’, ‘>’ for ‘multiplication’, ‘–’ for ‘equal to’, ‘+’ for ‘greater than’ and ‘=’ for ‘less than’; state which of the following is true. ?

##### Hint

Using the proper notations in (c), we get the statement as

5 × 2 ÷ 2 < 10 – 4 + 8 or 5 × 1 < 18 – 4 or 5 < 14, which is true. - Question 25 of 27
##### 25. Question

It being given that ‘x’ denotes ‘greater than’, ‘φ’ denote ‘equal to’, ‘<’ denotes ‘not less than’, ‘⊥’ denotes ‘not equal to’, ‘∆’ denotes ‘less than’ and ‘+’ denotes ‘not greater than’; then choose the correct statement from the following if a x b ∆ c, it follows that:

##### Hint

Using the usual notations, we have

(a) The statement is a > b < c ⇒ a = c < b , which is false [since c > b]

(b) The statement is a > b < c ⇒ b < a > c, which is false. [since b < a] (c) The statement is a > b < c ⇒ a < b > c , which is true

(d) The statement is a > b < c ⇒ c < b < a , which is false. [since b < a] - Question 26 of 27
##### 26. Question

If A + D > C + E, C + D = 2B and B + E > C + D, it necessarily follows that

##### Hint

A + D > C + E

⇒ A + D > (2B – D) + E (since C + D = 2B)

⇒ A + D > (B + E) + (B – D)

⇒ A + D > (C + D) + (B – D)

⇒ A + D > B + C. - Question 27 of 27
##### 27. Question

If A + D = B + C, A + E = C + D, 2C < A + E and 2A > B + D, then

##### Hint

2 C < A + E, A + E = C + D ⇒ 2C < C + D ⇒ C < D ...(1) A + D = B + C, C < D ⇒ A < B ...(2) 2A > B + D, A < B ⇒ A > D …(3)

A + E = C + D , A > D ⇒ E < C ...(4)

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