Arithmetic Operations Questions and Answers

Answer: A

The mass of 2 dozen eggs is 1.56 kg.

Two dozen is 24 eggs:

\[ 24 \times 65 = 1560\ \text{g} = 1.56\ \text{kg} \]

1 kg 56 g is 1.056 kg, a place-value slip. 1.304 kg and 1 kg 544 g do not match \(24 \times 65\).

Answer: C

The duration of service was 31 years 2 months and 19 days.

From 13 January 1992 to 13 January 2023 is 31 years, and on to 13 March 2023 is 2 more months. From 13 March to 31 March is 18 days, and counting both the joining day and the retirement day as days of service adds one more, giving 19 days.

The options with 30 years miscount the years. 31 years 2 months and 18 days is the difference between the dates without counting the joining day, while the key counts both ends of the service.

Answer: C

22 hm 8 dam is equal to 2280 m.

One hectometre is 100 m and one decametre is 10 m:

\[ 22 \times 100 + 8 \times 10 = 2200 + 80 = 2280\ \text{m} \]

2208 m treats dam as metres, and 22800 m and 22080 m multiply by the wrong powers of ten.

Answer: C

The value is 13320.

\[ 12000 + 1300 + 20 = 13320 \]

13 hundred is 1300, which carries into the thousands place. 12132 writes the numbers side by side as digits, and 130132 and 121320 come from similar place-value errors.

Answer: B

The number of 1 L cans is 30.

\[ \begin{aligned} \text{Total} &= 5 \times 20 = 100\ \text{L} \\ \text{Used} &= 10 \times 5 + 10 \times 2 = 70\ \text{L} \\ \text{Left} &= 100 - 70 = 30\ \text{L} \end{aligned} \]

30 L fills thirty 1 L cans. The other options come from miscounting the oil already poured into the 5 L or 2 L cans.

Answer: D

The value of * is 5.

\[ 92496 \div 123 = 752 \]

So the three-digit number 7*2 is 752, and the missing digit is 5. Check: \(752 \times 123 = 92496\). With 2, 1 or 4 the products 722, 712 or 742 times 123 do not give 92496.

Answer: D

The sum cannot be determined.

Write the subtraction as an addition: the top number is 48a89 + 1111, where a is the missing digit in the subtrahend.

\[ 48a89 + 1111 = 49200 + 100a \]

The top number must begin with 5, so a = 8 or 9. With a = 8 the top is 50000 and the missing digits 0, 0, 0, 0 and 8 sum to 8. With a = 9 the top is 50100 and the missing digits 0, 1, 0, 0 and 9 sum to 10.

Both fit, giving two different sums, 8 and 10, so neither option alone can be the answer; 11 fits neither case.

Answer: B

The Earth rotates through 63°.

A full turn of 360° in 24 hours is 15° an hour, or 1° every 4 minutes. 4 hours 12 minutes is 4.2 hours:

\[ \begin{aligned} 4 \times 15^{\circ} &= 60^{\circ} \\ 12 \text{ min} \div 4 &= 3^{\circ} \\ \text{Total} &= 63^{\circ} \end{aligned} \]

60° ignores the 12 minutes, and 64° and 65° overcount them.

Answer: A

The clerk gave the information at 9:15 am.

Buses leave every 30 minutes, so the bus before the 9:35 one left at 9:05. The clerk said that bus had left ten minutes earlier:

\[ 9{:}05 + 10 \text{ min} = 9{:}15 \]

9:05 is the departure time of the previous bus, not the time of speaking, and 9:20 and 9:08 do not fit both facts.

Answer: C

The frog needs 75 jumps.

Each full jump-and-slide gains \(70 - 30 = 40\) cm. But on the final jump the frog leaves the well and does not slide back, so stop counting slides before the last jump.

\[ \begin{aligned} 40(k - 1) + 70 &\ge 3000 \\ k - 1 &\ge 73.25 \Rightarrow k = 75 \end{aligned} \]

After 74 jumps (and slides) the frog is at \(74 \times 40 = 2960\) cm, and the 75th jump of 70 cm takes it to 3030 cm, out of the well. Dividing 3000 by 40 gives exactly 75 here, but only by coincidence; 76 and 78 come from ignoring the last-jump rule in other ways, and 73 stops short.