Number System
- Arrange the following fractions into ascending order.
4 ,− 2 ,− 7 , 5 3 9 8 12
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Decimal equivalents of fractions :
4 = 1.3 3 −2 = −0.2 9 −7 = −0.875 8 5 = 0.42 12
Correct Option: A
Decimal equivalents of fractions :
4 = 1.3 3 −2 = −0.2 9 −7 = −0.875 8 5 = 0.42 12
∴ – 0.875 < – 0.2 < 0.42 < 1.3i.e., −7 < − 2 < 5 < 4 8 9 12 3
- A certain number when successively divided by 3, 5 and 8 leaves remainder 1, 2, 3
respectively. Find the remainders when the same number is divided by reversing the divisors.
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This problem can be solved by determining true or complete remainder and dividing it by reversing the order of divisors.
True remainder = d1d2r3 + d1r2 + r1
Here, d1 = 3, d2 = 5, r1 = 1, r2= 2, r3 = 3
∴ True remainder = 3 × 5 × 3 + 3 × 2 + 1= 45 + 6 + 1 = 52
Now, we divide 52 by 8, 5 and 3
Hence, the remainders are 4, 1 and 1.Correct Option: B
This problem can be solved by determining true or complete remainder and dividing it by reversing the order of divisors.
True remainder = d1d2r3 + d1r2 + r1
Here, d1 = 3, d2 = 5, r1 = 1, r2= 2, r3 = 3
∴ True remainder = 3 × 5 × 3 + 3 × 2 + 1= 45 + 6 + 1 = 52
Now, we divide 52 by 8, 5 and 3
Hence, the remainders are 4, 1 and 1.
- What will be the unit’s digit in the product of (2467)153 × (341)72 ?
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The unit’s digit in (2467)153 = The unit’s digit in (7)153 = The
unit’s digit in (7)1 = 7
and the unit’s digit in (341)72 = 1
Because for any index to 1, the value of unit’s digit will be 1.
∴ The unit’s digit in the product of (2467)153 × (341)72 = 7 × 1 = 7Correct Option: C
The unit’s digit in (2467)153 = The unit’s digit in (7)153 = The
unit’s digit in (7)1 = 7
and the unit’s digit in (341)72 = 1
Because for any index to 1, the value of unit’s digit will be 1.
∴ The unit’s digit in the product of (2467)153 × (341)72 = 7 × 1 = 7
- A candidate in an examination was asked to find 5/14 of a certain number. By mistake he found 5/14 of it. Thus, his answer was 25 more than the correct answer. The number was :
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Let us assume the required number be n.
As per given question,⇒ n × 5 − n × 5 = 25 4 14
Solve this equation further to get the answer.Correct Option: A
Let us assume the required number be n.
As per given question,⇒ n × 5 − n × 5 = 25 4 14 ⇒ 5n 
1 − 1 
= 25 4 14 ⇒ 5n 7 − 2 = 25 ⇒ 5n × 5 = 25 28 28 ⇒ n = 25 × 28 = 28 5 × 5
- In an examination, a student was asked to find 3/14 of a certain number, By mistake, he found 3/4 of it. His answer was 150 more than the correct answer. The given number is :
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Let us assume the number is p.
According to given question,3 p − 3 p = 150 4 14 ⇒ 21p − 6p = 150 28
Solve this equation further to get the answer.
Correct Option: B
Let us assume the number is p.
According to given question,3 p − 3 p = 150 4 14 ⇒ 21p − 6p = 150 28
⇒ 15p = 28 × 150⇒ p = 28 × 150 = 280 15
