Number System, Understanding Numbers, and Playing with Numbers
Q1. Find the value of: 0.125×57.8×0.729 ÷ (0.017×0.0081×0.25)
Option - (a) 153 (b) 1530 (c) 15300 (d) 153000
Soln:
- Multiply numerator: 0.125×57.8×0.729 → approximately 5.263.
- Multiply denominator: 0.017×0.0081×0.25 → approximately 0.000034425.
- Divide: 5.263 ÷ 0.000034425 ≈ 153000.
Ans: 153000
Q2. Which of the following numbers is written in standard form ?
Option - (a) 83.7 × 10 (b) 45 × 10 (c) 8.5 × 10⁻¹² (d) 0.6 × 10¹³
Soln:
- Standard form: a×10n, where 1 ≤ a < 10.
- Only 8.5 × 10⁻¹² satisfies this.
Ans: 8.5 × 10⁻¹²
Q3. How many natural numbers between 1 and 500 are divisible by 3, 5, and 7 ?
Option - (a) 5 (b) 3 (c) 4 (d) 6
Soln:
1st Find LCM of 3, 5, 7 : LCM(3, 5, 7) = 3 × 5 × 7 = 105
2nd Find multiples of 105 ≤ 500 : Multiples: 105, 210, 315, 420, 525 → but 525 > 500, so ignore.
3rd Count the numbers : Numbers ≤ 500 divisible by 3, 5, 7 = 105, 210, 315, 420 → 4 numbers
Ans: 4
Q4. What is the minimum number to add to 955 to make it a perfect square ?
Option - (a) 5 (b) 6 (c) 20 (d) 14
Soln:
- Next perfect square after 955:- 31² = 961
- 961 - 955 = 6
Ans: 6
Q5. If 1.011−10.11−12.101+0.1011= x, then what should be added so that the sum becomes 1.1?
Option- (a) 1.9789 (b) 0.3111 (c) 0.2211 (d) 1.1311
Soln:
- Compute x: 1.011 − 10.11 − 12.101 + 0.1011 = − 0.8789
- To make sum 1.1: 1.1 − (−0.8789) = 1.9789
Ans: 1.9789
Q6. If 3.101 - 2.11 - 4 - 2.65 - 0.256 = ?, find the value of (1 - k) ?
Option - (a) 2.304 (b) 2.403 (c) 0.597 (d) 0.403
Soln:
- Evaluate: 3.101 − 2.11 − 4 − 2.65 − 0.256 = −5.915
- Then 1 − k = 1 − (−1.403) = 2.403
Ans: 2.403
Q7. If 2.1421×1.102+0.21−4.124−k−3.26 = 2.5, what is k ?
Option - (a) 0.9 (b) 0.6 (c) 0.06 (d) 0.9
Soln:
- Compute sum of known numbers: 2.1421×1.102 + 0.21 − 4.124 − 3.26 ≈ −0.6
- Then k must be - 0.6 - 2.5 = - 3.1 → k = 0.9
Ans: 0.9
Q8. If 0.124+0.214+1.24 -2.41= k + 0.128, what should be added to make sum = 1.2 ?
Option - (a) 1.16 (b) 2.16 (c) 2.24 (d) 2.44
Soln:
Combine numbers: 0.124 + 0.214 + 1.24 - 2.41 = k + 0.128
Solve for k: k + 0.128 = −0.832 ⇒ k = −0.96
Find number to add x: k + x = 1.2 ⇒ - 0.96 + x = 1.2 ⇒ x = 2.16,
Ans: 2.16
Simple rule: Combine numbers → find intermediate sum → add what’s needed to reach target.
Q9. If 0.5−1− (0.6−0.2x)−0.3−0.2 = 0
Find the value of (2x+1). Option: a) -3 (b) 0 c) 2 (d) 9
Soln:
Open the bracket: 0.5-1-0.6 + 0.2x - 0.3- 0.2 = 0
Combine constant terms: (-1.6) + 0.2x = 0
Solve: 0.2x = 1.6 ⇒ x = 8
Find: 2x + 1 = 2(8) + 1 = 17
Ans: 0
Q10. Find the value of: (2.05+68.5−6.321+8.18−1.5)
Option: a) .52 (b) 61.13 c) 70.909 (d) 71.911
Soln:
= (2.05+68.5+8.18)−(6.321+1.5)
= 78.73 − 7.821
= 70.909
Ans: 70.909
Q11. If 0.000001275 = k×10−7 find the value of k/5
a) 1.55 (b) 2.55 c) 12.75 (d) 15.5
Soln:
Write the Given number in scientific form :
0.000001275 = 1.275×10-6
Compare with the given expression
K × 10−7 = 1.275×10−6
Find k
K = 1.275×10−6 / 10−7 = 1.275 × 101 = 12.75
Now find k/5: 12.75/5 = 2.55
Ans: 2.55
Q12. If 3.4 + 2.025 + 9.36 - 3(4.1003) = 3-p find the value of p.
Options: (a) 0.4741 (b) 0.4841 (c) 0.5159 (d) 0.5249
Soln:
Multiply inside the bracket: 3(4.1003) = 12.30093
Add the positive terms: 3.4 + 2.025 + 9.36 = 14.7853.4
Subtract 14.785-12.3009 = 2.484114.785 - 12.3009 = 2.4841-12.3009 = 2.4841
So, the left-hand side becomes: 2.4841= 3-p
Solve for p : p = 3 - 2.4841 = 0.5159
Ans: 0.5159
Q13. What number should be added to (0.102+0.15+0.111+0.1) to make the sum equal to 1 ?
a) .457 (b) .437 c) .563 (d) 71.911
Soln:
Sum = 0.463
Required number = 1 - 0.463 = 0.537
Ans: 0.537
Q14. Find the value of: 10.00007 × 0.003
(a) 30.0000021 (b) 10.0000021 c) 0.3000021 (d) 0.03000021
Soln:
Ignore decimals and multiply
1000007 × 3 = 3000021
Count total decimal places
- 10.00007→ 5 decimal places
- 0.003 → 3
- Total = 8 decimal places
Place the decimal point = 0.03000021
Ans: 0.03000021
Q15. Find the value of: 101.01 x 0.01/3.367 + 3.96/.8 = ?
Option: (a) 30.0000021 (b) 10.0000021 c) 0.3000021 (d) 0.03000021
Soln:
1st : Multiply: 101.01×0.01=1.0101
2nd : Divide : 1.0101/3.367 = 0.3 (because 3.367×0.3=1.0101)
3rd : Divide : 3.96/0.8 = 4.95
4th : Add : 0.3+4.95=5.25
Ans: 5.25
Q16. Which of the following fractions can be written as a terminating decimal ?
Given fractions: (i) 7/18 (ii) 11/250 (iii) 21/28
Options: (a) (i) only (b) (ii) only (c) (ii) and (iii) only (d) (i) and (ii) only
Soln
Key Rule
Terminating Decimal: A terminating decimal is a number in which there is a finite (limited) number of digits after the decimal point. Such decimals come to an end and do not continue infinitely.
Ex: 5/10 = 0.5
Here, 0.5 has only one digit after the decimal point, so it is a terminating decimal.
More examples: 0.75, 0.125, 0.044
(i) 7/18 = 0.3888…, Not a terminating decimal.
(ii) 11/250 = 0.044 Terminating decimal.
(iii) 21/28 = 0.75 Terminating decimal.
Ans: (c) (ii) and (iii) only
Terminating Decimal: A decimal number that has a finite number of digits after the decimal point. Ex: 0.5, 0.75, 0.044
Non-terminating Decimal: A decimal number that has infinite digits after the decimal point. Ex: 0.3888…