LR - Operator Based Questions - Previous Year CAT/MBA Questions

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1. CAT 2000 LRDI | LR - Operator Based Questions CAT Question

Choose 1; if the question can be answered by using one of the statements alone, but cannot be answered using the other statement alone.
Choose 2; if the question can be answered by using either statement alone.
Choose 3; if the question can be answered by using both statements together, but cannot be answered using either statement alone.
Choose 4; if the question cannot be answered even by using both statements together.

For any two real numbers

a ⊕ b = 1 if both a and b are positive or both a and b are negative.
= –1 if one of the two numbers a and b is positive and the other negative.

What is (2 ⊕ 0) ⊕ (–5 ⊕ –6)?

a ⊕ b is zero if a is zero.
a ⊕ b = b ⊕ a

(a)
1
(b)
2
(c)
3
(d)
4

Direction: Answer the question based on the following information.

The following operations are defined for real numbers.
a # b = a + b, if a and b both are positive else a # b = 1
a ∇ b = (a × b)^{a + b} if a × b is positive else a ∇ b = 1.

2. CAT 1998 LRDI | LR - Operator Based Questions CAT Question

$\frac{(2 \neq 1)}{(1 \nabla 2)} =$

(a)
1/8
(b)
1
(c)
3/8
(d)
3

Answer: Option C

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Text Explanation :

Since both 2 and 1 are positive, (2 # 1) = 2 + 1 = 3.
(1∇2)= (1× 2)¹⁺² = 23 = 8.
Thus, the given expression is equal to $\frac{3}{8} .$

3. CAT 1998 LRDI | LR - Operator Based Questions CAT Question

$\frac{\{((1 # 1) # 2) - (10^{1.3} \nabla \log_{10} 0.1)\}}{(1 \nabla 2)} =$

(a)
3/8
(b)
$\frac{4 \times \log_{10} 0.1}{8}$
(c)
$\frac{(4 + 10^{13})}{8}$
(d)
None of these

Answer: Option A

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Text Explanation :

Let us first simplify the numerator. Since 1 is positive,
(1 # 1) is 1 + 1 = 2 which again is positive. Then
(1 # 1) # 2 = 2 # 2 = 2 + 2 = 4
Now note that log₁₀ 0.1
= log₁₀ 10^–1 = –1
Then 10^1.3log₁₀ 0.1= 10^1.3× (–1) is negative.
So 10^1.3 ∇ log₁₀ 0.1 = 1
Hence, the numerator is equal to 4 –1 = 3
Since 1 × 2 = 2 is positive, (1∇2) = (1× 2)¹⁺² = 2³ = 8.
So the denominator = 8. Hence, the answer is $\frac{3}{8} .$

4. CAT 1998 LRDI | LR - Operator Based Questions CAT Question

$(\frac{(X # - Y)}{(- X \nabla Y)}) = \frac{3}{8},$ then which of the following must be true?

(a)
X = 2, Y = 1
(b)
X > 0, Y < 0
(c)
X, Y both positive
(d)
X, Y both negative

5. CAT 1991 LRDI | LR - Operator Based Questions CAT Question

If 8 + 12 = 2, 7 + 14 = 3 then 10 + 18 = ?

(a)
10
(b)
4
(c)
6
(d)
18

LR - Operator Based Questions - Previous Year CAT/MBA Questions

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