7TH NUMBERS TALENT - POSITIVE AND NEGATIVE-WORD PROBLEMS - 2

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📝 Numbers & Operations Olympiad MCQ Quiz

1. [Integers] The product of three integers is negative. If two of them are −4 and +5, what could be the value of the third integer?

(a) −3 (b) 0 (c) 6 (d) −6

Correct Answer: (c) 6

Let the third integer be x.
Product = (−4) × (+5) × x = −20 × x.
Since the overall product must be negative, and −20 is negative, x must be a positive integer. Looking at the options, only 6 is positive.

2. [Positive and Negative Numbers] A submarine is situated 350 meters below sea level. If it rises 120 meters and then dives 85 meters, what is its final position relative to sea level?

(a) −315 meters (b) −230 meters (c) −455 meters (d) −145 meters

Correct Answer: (a) −315 meters

Initial position = −350.
Rises 120 meters: −350 + 120 = −230.
Dives 85 meters: −230 − 85 = −315 meters.

3. [Rational Numbers] Which of the following rational numbers lies exactly halfway between −3/4 and 1/4?

(a) −1/2 (b) −1/4 (c) 1/2 (d) −2/3

Correct Answer: (b) −1/4

Midpoint formula: (a + b) / 2.
(−3/4 + 1/4) / 2 = (−2/4) / 2 = (−1/2) / 2 = −1/4.

4. [Rational Numbers] If x = 2/3 and y = −4/5, what is the value of |x − y|?

(a) 2/15 (b) −22/15 (c) 22/15 (d) 1/3

Correct Answer: (c) 22/15

x − y = 2/3 − (−4/5) = 2/3 + 4/5.
Common denominator is 15: (10 + 12)/15 = 22/15.
Absolute value |22/15| = 22/15.

5. [Irrational Numbers] Which of the following numbers is an irrational number?

(a) √225 (b) 3.14159 (c) 0.121221222... (d) 4/7

Correct Answer: (c) 0.121221222...

√225 = 15 (rational).
3.14159 is a terminating decimal (rational).
4/7 is a fraction of integers (rational).
0.121221222... is non-terminating and non-recurring, hence irrational.

6. [Real Numbers] Which of the following statements is always true for any two distinct real numbers?

(a) Their sum is always positive. (b) There is at least one irrational number between them. (c) Their product is always greater than both numbers. (d) One of them must be an integer.

Correct Answer: (b) There is at least one irrational number between them.

The real number line is dense, meaning between any two distinct real numbers, there exists infinitely many rational and irrational numbers.

7. [Integers] If a − b = 15 and b is a negative integer, which of the following must be true about a?

(a) a must be negative (b) a must be greater than 15 (c) a must be less than 15 (d) a must be zero

Correct Answer: (b) a must be greater than 15

Given a − b = 15, we can write a = 15 + b.
Since b is negative (b < 0), adding a negative number to 15 means a will be less than 15? Wait! Let's check: a = 15 + (−b_val) = 15 − b_val. Thus a must be *less* than 15 (Option c). Let's verify: if b = −2, a = 15 + (−2) = 13, which is less than 15. Correct answer is (c) a must be less than 15.

8. [Rational Numbers] Express the repeating decimal 0.23 (with 23 recurring) as a rational number p/q. What is q − p?

(c) 76 (b) 65 (c) 76 (d) 53

Correct Answer: (a) 76 (Note: p = 23, q = 99, q − p = 99 − 23 = 76)

Let x = 0.2323...
100x = 23.2323...
99x = 23 => x = 23/99.
Here p = 23, q = 99. q − p = 99 − 23 = 76.

9. [Real Numbers] Which of the following numbers can be placed on a number line between 2.236 and 2.237?

(a) √5 (b) 2.2365 (c) Both (a) and (b) (d) Neither (a) nor (b)

Correct Answer: (c) Both (a) and (b)

√5 is approximately 2.236067... wait, √5 is roughly 2.236. Let's check √5 precisely: √5 = 2.2360679..., which is less than 2.236? No, 2.236 is smaller than 2.2360679. Let's re-evaluate: √5 = 2.23606..., which lies between 2.236 and 2.237. Also, 2.2365 clearly lies between 2.236 and 2.237. Thus both fit.

10. [Positive and Negative Numbers] If the temperature drops by 4 degrees every hour from an initial temperature of +6°C, what will be the temperature after 5 hours?

(a) −14°C (b) −20°C (c) −10°C (d) −26°C

Correct Answer: (a) −14°C

Total drop in temperature = 4°C × 5 hours = 20°C decrease.
Final temperature = Initial temperature − Total drop = +6 − 20 = −14°C.