Arithmetic Operations Questions and Answers

Answer: B

She needs ₹ 0.50 more.

Add up her money and subtract it from the price:

\[ \begin{aligned} \text{She has} &= 5 + 2(1) + 5(0.50) \\ &= 5 + 2 + 2.50 = 9.50 \\ \text{Needed} &= 10 - 9.50 = 0.50 \end{aligned} \]

The answer ₹ 2.50 is what you get by forgetting the fifty-paise coins, and ₹ 1.50 or ₹ 2.00 come from miscounting the coins.

Answer: A

The ascending order is \(\frac{1}{4} \lt \frac{1}{3} \lt \frac{1}{2}\).

All three fractions have numerator 1, so the larger the denominator, the smaller each part: a whole cut into four parts gives smaller pieces than one cut into three or two. So one quarter is the smallest and one half the largest.

Checking with a common denominator of 12: \(\frac{1}{4} = \frac{3}{12}\), \(\frac{1}{3} = \frac{4}{12}\) and \(\frac{1}{2} = \frac{6}{12}\). The other options put a larger fraction before a smaller one; option C is the descending order, the common error of ranking by the size of the denominator.

Answer: C

The journey took 4 hours 25 minutes.

Count on from the start time:

\[ \begin{aligned} 16{:}50 \to 17{:}00 &= 10\ \text{min} \\ 17{:}00 \to 21{:}00 &= 4\ \text{h} \\ 21{:}00 \to 21{:}15 &= 15\ \text{min} \end{aligned} \]

Total: 4 hours and 10 + 15 = 25 minutes. As a check, 16:50 plus 4 hours is 20:50, and 25 more minutes reaches 21:15. The other options miscount either the minutes or the hours.

Answer: A

The sum is 200.

Let the whole number be n. Then:

\[ (100 + n) + (100 - n) = 200 \]

The n added and the n subtracted cancel, so the sum is always 200, whatever whole number is chosen. For example, with n = 30: 130 + 70 = 200. The answers 0 and 100 come from treating the operations as cancelling the 100s rather than the n.

Answer: D

The sum is 5.

Group the terms in pairs: each pair 5 - 5 gives 0. With an odd number of terms, all but the last term pair off, and the last term is a +5:

\[ \begin{aligned} 5 &= 5 \ (1\ \text{term}) \\ 5 - 5 + 5 &= 5 \ (3\ \text{terms}) \\ 5 - 5 + 5 - 5 + 5 &= 5 \ (5\ \text{terms}) \end{aligned} \]

The answer 0 holds for an even number of terms, and -5 would need the series to end on a minus term; 15 is the sum of the positive terms only for five terms, ignoring the subtractions.

Answer: D

9 kg minus 7 kg 7 g is 1.993 kg.

Convert everything to grams or to kilograms with three decimal places, since 1 kg = 1000 g. Then 7 kg 7 g = 7.007 kg, not 7.7 kg or 7.07 kg.

\[ \begin{aligned} 9.000 - 7.007 &= 1.993\ \text{kg} \\ \text{or } 9000 - 7007 &= 1993\ \text{g} \end{aligned} \]

The distractors come from place-value slips with the 7 g. Writing it as 7.07 kg gives 1.93 kg; 1.093 kg and 1.3 kg come from similar misplacements of the grams. Remembering that grams occupy three decimal places of a kilogram avoids all of them.

Answer: B

The balance at the start of the month was ₹ 5,118.

Work backwards from the closing balance: undo the deposit by subtracting it, and undo the withdrawal by adding it back.

\[ \begin{aligned} \text{Start} - 4560 + 2567 &= 3125 \\ \text{Start} &= 3125 + 4560 - 2567 \\ &= 7685 - 2567 = 5118 \end{aligned} \]

Check: 5118 − 4560 = 558, and 558 + 2567 = 3125, the stated closing balance.

The other values do not survive this check: 5,128 is ten more than the correct balance, and 4,998 and 5,213 come from adding or subtracting the wrong amounts.

Answer: D

The product is 956400.

The predecessor of a number is the number just before it, and the successor the number just after it. So the predecessor of 201 is 200 and the successor of 4781 is 4782.

\[ 200 \times 4782 = 956400 \]

Option C, 956200, is 200 × 4781, from forgetting to take the successor. 965560 and 965650 come from mixing up the digits. A quick check is that any multiple of 200 must end in 00, which rules both of those out at once.

Answer: B

The total distance is 15.193 km.

Write each distance in kilometres with three decimal places (1 km = 1000 m): 3 km 725 m = 3.725 km and 2 km 9 m = 2.009 km. She walks the first on three days and the second on two:

\[ \begin{aligned} 3 \times 3.725 &= 11.175 \\ 2 \times 2.009 &= 4.018 \\ 11.175 + 4.018 &= 15.193\ \text{km} \end{aligned} \]

The usual slip is writing 9 m as 0.9 km or 0.09 km instead of 0.009 km, which inflates the total and leads to the larger options.

Answer: C

The number in standard form is \(8.5 \times 10^{-12}\).

Standard form writes a number as \(k \times 10^{n}\), where \(1 \le k \lt 10\) and n is an integer. In \(8.5 \times 10^{-12}\), k = 8.5 lies between 1 and 10.

The others break the rule for k: 83.7 and 45 are 10 or more, and 0.6 is less than 1. In standard form they would be \(8.37 \times 10^{-8}\), \(4.5 \times 10^{4}\) and \(6 \times 10^{14}\).