number system Model Questions & Answers, Practice Test for ssc cgl tier 1 2023
ssc cgl tier 1 2023 SYLLABUS WISE SUBJECTS MCQs
Number System
Ratio Proportion & Partnership
Averages
Percentages
Profit & Loss
Time & Work
Time & Distance
Simple Interest & Compound Interest
Mensuration: Area & Volumes
Algebraic Expressions
Linear Equations
Squareroots & Cuberoots
After distributing the sweets equally among 25 children, 8 sweets remain. Had the number of children been 28, 22 sweets would have been left after equally distributing. What was the total number of sweets ?
Answer: (a)
Let the total number of sweets be (25x + 8).
Then, (25x + 8) – 22 is divisible by 28
⇔ (25x – 14) is divisible by 28 ⇔ 28x – (3x + 14) is divisible by 28
⇔ (3x + 14) is divisible by 28 ⇔ x = 14.
∴ Total number of sweets = (25 × 14 + 8) = 358.
Taking $√2$ = 1.414, $√3$ = 1.732, $√5$ = 2.236 and $√6$ = 2.449, find the value of ${9 + √2}/{√5 + √3} + {6 - √2}/{√5 - √3}$ to the three places of decimal.
Answer: (a)
${9 + √2}/{√5 + √3} + {6 - √2}/{√5 - √3}$
= ${9(√5 - √3) + √2(√5 - √3) + 6(√5 + √3) - √2(√5 + √3)}/{(√5 + √3)(√5 - √3)}$
= $1/2(9√5 - 9√3 + √{10} - √6 + 6√5 + 6√3 - √{10} - √6)$
= $1/2(15√5 - 3√3 - 2√6)$
$1/2[15 × 2.236 - 3 × 1.732 - 2 × 2.449]$
$1/2[33.540 - 5.196 - 4.898] = 11.723$
What is the remainder when $4^1000$ is divided by 7?
Answer: (b)
Remainder $4^1000 = {4^(333 × 3 + 1)}/7$
= ${(64)^333 × 4}/7$ = 1 × 4 = 4
If the 14th term of an arithmetic series is 6 and 6th term is 14, then what is the 95th term?
Answer: (c)
q $T_{14}$ = 6
⇒ a + 13d = 6
and $T_6$ = 14 ⇒ a + 5d = 14
On solving equations (i) and (ii), we get
a = 19, d = – 1
∴ $T_{95}$ = a + 94d = 19 – 94 = – 75
How many times must 79 be subtracted from 5 × $10^4$ so as to obtain 43759 ?
Answer: (b)
Let x be the number of times, then
79x + 43759 = 50,000
⇒ x = (50000 – 43759) ÷ 79 = 79
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