Quantitative Reasoning

Number System

Medium

If x and y are negative integers, then which of the following statements is/are always true?

(A) x + y is positive integer.

(B) xy is positive integer.

(C) x-y is positive integer.

Choose the correct answer from the options given below:

(A) only

(B) only

(A) and (C)

(B) and (C) only

✅ Correct Option: 2

Given that $x$ and $y$ are negative integers, testing which statements are always true.

Using $x = -2$ and $y = -3$ as test values.

For Statement (A): $x + y$ is positive integer

$x + y = (-2) + (-3)$

$x + y = -5$

The result is negative, not positive. When two negative numbers are added, the result is negative.

Statement (A) is false.

For Statement (B): $xy$ is positive integer

$xy = (-2) \times (-3)$

$xy = 6$

The result is positive. The product of two negative numbers is always positive.

Testing with other values:

$(-5) \times (-4) = 20$

$(-1) \times (-10) = 10$

Statement (B) is always true.

For Statement (C): $x - y$ is positive integer

$x - y = (-2) - (-3)$

$x - y = -2 + 3$

$x - y = 1$

This is positive. However, testing with different values where $x = -5$ and $y = -2$ :

$x - y = (-5) - (-2)$

$x - y = -5 + 2$

$x - y = -3$

This is negative. The result depends on which number has a larger absolute value.

Statement (C) is not always true.

Only statement (B) is always true.

The correct answer is (B only).

2025: 24 May Shift 2

Given below are two statements:

Statement (I): 2469385422 is divisible by 18.

Statement (II): 3475824638 is divisible by 11.

In light of the above statements, choose the most appropriate answer from the options given below.

2023: 1 June Shift 1

Which of the following is correct for divisibility?

(1) A number is divisible by 6 if it is divisible by 3 or 2.

(2) A number is divisible by 5 if its unit digit is 0 or 5.

(3) A number is divisible by 3 if its unit digit is divisible by 3.

(4) A number is divisible by 4 if the number formed by its last two digits is divisible by 4.

Choose the correct answer from the options given below:

2022: 23 Aug Shift 1

If $\sqrt[3]{x} = 2y$ . Then, the value of $\frac{y^3}{x}$ is ______

2025: 14 May Shift 1

Consider the following statements

(A) The difference between the place values of 9 and 5 in the number 639457 is 4.

(B) The number π is an irrational number.

(D) The difference between the face values of 5 and 3 in number 475839 is 2.

Choose the correct answer from the options given below:

2026: 18 May Shift 1

Which of the following numbers is both a perfect square and a perfect cube?

2022: 26 Aug Shift 1

The value of $\left(\frac{8}{125}\right)^{\frac{-4}{3}}$ is __________

If x and y are negative integers, then which of the following statements is/are always true? (A) x + y is positive integer. (B) xy is positive integer. (C) x-y is positive integer. Choose the correct answer from the options given below:

Solution

Related questions:

Keyboard Shortcuts

CUET General Test Past Year Questions (Topic-Wise)

If x and y are negative integers, then which of the following statements is/are always true?

(A) x + y is positive integer.

(B) xy is positive integer.

(C) x-y is positive integer.

Choose the correct answer from the options given below: