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

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**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

Answer: Option C

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**Text Explanation** :

(2 ⊕ 0) ⊕ (–5 ⊕ –6)

= (2 ⊕ 0) ⊕ 1

From statement A

(0 ⊕ 2) = 0 but we don’t know the value of (2 ⊕ 0).

∴ Statement A alone is not sufficient to answer the question.

From statement B

(2 ⊕ 0) = (0 ⊕ 2)

∴ Statement B alone is not sufficient to answer the question.

After combining both the statements, we get,

(2 ⊕ 0) = (0 ⊕ 2) = 0

∴ (2 ⊕ 0) ⊕ (–5 ⊕ –6)

= (2 ⊕ 0) ⊕ 1

= 0 ⊕ 1

= 0

∴ Both the statements are required to answer the question.

Hence, option (c).

Workspace:

**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.

**CAT 1998 LRDI | LR - Operator Based Questions CAT Question**

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

- (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 $\frac{3}{8}.$

Workspace:

**CAT 1998 LRDI | LR - Operator Based Questions CAT Question**

$\frac{\left\{\left(\left(1\#1\right)\#2\right)-({10}^{1.3}\nabla {\mathrm{log}}_{10}0.1)\right\}}{(1\nabla 2)}=$

- (a)
3/8

- (b)
$\frac{4\times {\mathrm{log}}_{10}0.1}{8}$

- (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 log_{10} 0.1

= log_{10} 10^{–1} = –1

Then 10^{1.3 }log_{10} 0.1= 10^{1.3 }× (–1) is negative.

So 10^{1.3} ∇ log_{10} 0.1 = 1

Hence, the numerator is equal to 4 –1 = 3

Since 1 × 2 = 2 is positive, (1∇2) = (1× 2)^{1+2} = 2^{3} = 8.

So the denominator = 8. Hence, the answer is $\frac{3}{8}.$

Workspace:

**CAT 1998 LRDI | LR - Operator Based Questions CAT Question**

$\left(\frac{\left(X\#-Y\right)}{\left(-X\nabla Y\right)}\right)=\frac{3}{8},$ 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

Answer: Option B

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**Text Explanation** :

The best possible way to solve this is to check each of the given answer choices. In options (a), (c) and (d), either both X and Y are positive or both X and Y are negative.

Since we have (–Y) in the numerator of our expression and (–X) in the denominator, X and Y will never be both positive and neither will XY be positive.

Hence, both the numerator and the denominator of our expression will be 1 and the value will always be 1.

Hence, the only possible answer choice is (b).

Workspace:

**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

Answer: Option A

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**Text Explanation** :

Here logic is : A + B = (A + B) – 18

Hence, 10 + 18 = {(10 + 18) – 18} = 10.

Hence, option (a).

Workspace:

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