Forty per cent of a number is 56 more than twenty per cent of the same number. The number is:
Answer: A
The difference between 40% and 20% is 20% of the number, so \(0.2x = 56\) and \(x = 280\). Check: 40% of 280 is 112 and 20% is 56, differing by 56. Taking the difference of the percentages first avoids handling both terms separately.
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A number is increased by 10% and the result is then decreased by 10%. Compared with the original, the final value is:
Answer: B
The net multiplier is \(1.1 \times 0.9 = 0.99\), a 1% decrease. The rises and falls do not cancel because the 10% reduction is taken from the larger, increased amount. For any percentage \(p\), an increase then a decrease leaves a net loss of \(\dfrac{p^2}{100}\) per cent.
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If 15% of a number is 45, then 35% of the same number is:
Answer: C
From \(0.15x = 45\) we get \(x = 300\), and 35% of 300 is 105. Alternatively, scale directly: 35% is \(\dfrac{35}{15}\) times 15%, so the answer is \(45 \times \dfrac{7}{3} = 105\), which skips finding the number entirely.
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Two numbers are respectively 25% and 40% more than a third number. The ratio of the first to the second is:
Answer: D
Take the third number as 100.
\[ \text{first} = 125, \qquad \text{second} = 140 \]
\[ 125 : 140 = 25 : 28 \]
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The average of three numbers is 28. Two of them are 22 and 30. The third number is:
Answer: A
The three numbers total \(3 \times 28 = 84\). Two of them account for \(22 + 30 = 52\), so the third is \(84 - 52 = 32\). Converting an average into a total before doing anything else is the reliable first move in these questions.
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The average of five consecutive integers is 17. The largest of them is:
Answer: B
Five consecutive integers are symmetric about the middle one, so the average is the third.
\[ 15,\ 16,\ 17,\ 18,\ 19 \]
The largest is 19.
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The sum of five numbers is 290. Their average is:
Answer: C
\[ \frac{290}{5} = 58 \]
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The average of two numbers is 34 and one of them is 41. The other number is:
Answer: D
\[ \text{sum} = 2 \times 34 = 68 \]
\[ 68 - 41 = 27 \]
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When 15 is added to a number, the result equals four times the number decreased by 15. The number is:
Answer: A
The equation is \(x + 15 = 4x - 15\). Collecting terms gives \(3x = 30\), so \(x = 10\). Check: \(10 + 15 = 25\) and \(4 \times 10 - 15 = 25\). Reading the phrase as \(4(x - 15)\) instead changes the answer, so the wording must be parsed carefully.
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One-fifth of a number added to 8 gives 20. The number is:
Answer: B
\[ \frac{x}{5} + 8 = 20 \quad\Longrightarrow\quad \frac{x}{5} = 12 \]
\[ x = 60 \]
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