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Solving Problems 2 (Difficult)

This is the second quiz in our Difficult group of quizzes on Solving Problems. If you have played the previous ones then you should be quite good at these sorts of questions by now. Every question is different, and you will have to work out which operators you need to use, and in which order.

For example, if it takes 2 men 12 hours to dig a hole, how long will it take 3 men to do the same job?

First we need to multiply: if it takes 2 men 12 hours to dig a hole then it would take one man 24 hours because 12 x 2 = 24.

Next we must divide: if it takes one man 24 hours to dig a hole, then 3 men could do it in 8 hours because 24 ÷ 3 = 8.

These questions aren’t so hard, once you know how to do them. Play all these quizzes until you can get every answer right first time. Then you’ll be a master of problem solving!

1 .

Annabelle can run 3 times faster than Brenda. If it takes Brenda 48 minutes to run 4 miles, how long will it take Annabelle to run the same distance?

16 minutes

20 minutes

24 minutes

28 minutes

First calculate Brenda’s speed: 48 (number of minutes) ÷ 4 (distance travelled) = 12. This means that it takes Brenda 12 minutes to run one mile. From this we can calculate that Brenda is running at a speed of 5 mph because 60 (number of minutes in one hour) ÷ 12 (the time it takes Brenda to run one mile) = 5
If Brenda is running at 5 mph, then Annabelle is running at 15 mph because 5 x 3 = 15
At 15 mph, it takes Annabelle 4 minutes to run one mile (60 ÷ 15 = 4).
If she can run one mile in 4 minutes, it will take Annabelle 16 minutes to run 4 miles (4 x 4 = 16).
Of course, a quicker way to work this out would be to divide 48 by 3!

2 .

It takes two pumps 32 hours to empty a pond. How many pumps would be needed to empty it in one hour?

32 pumps

64 pumps

96 pumps

128 pumps

If it takes two pumps 32 hours to empty a pond, then it would take one pump 64 hours to do the job (32 x 2 = 64).
If it takes 64 hours for one pump to empty a pond, then it would take 64 pumps to empty it in one hour

3 .

Aurora wants 17 DVDs of the film she has acted in, so that she can give a copy to her closest friends, but that would cost her £221. She can only afford to buy 6 DVDs. How much will 6 DVDs cost?

£68

£73

£78

£83

First we need to find the price of one DVD: 221 ÷ 17 = 13
If one DVD costs £13, then 6 will cost £78 (13 x 6 = 78)

4 .

The temperature in an oven is increasing by 13^o every minute. If the temperature is already 18^o when the oven is turned on, how hot will it be after 17 minutes?

185^o

203^o

221^o

239^o

If the temperature is increasing by 13^o every minute, then after 17 minutes it will have risen by 221^o (13 x 17 = 221)
The initial temperature was 18^o so we need to add this to the final answer:
221 + 18 = 239^o

5 .

If a turntable rotates (turns) at a speed of 4,680 revolutions (complete turns) in one hour, how many revolutions does it make in 5 minutes?

390

There are 12 lots of 5 minutes in one hour (60 ÷ 5 = 12) so, to find the answer all we have to do is divide 4,680 by 12:
4,680 ÷ 12 = 390

6 .

A water tank is leaking 125 ml of water every 7 minutes. If the tank contains 500 litres of water, how long will it take before the tank is empty?

28,000 minutes

20,000 minutes

12,000 minutes

4,000 minutes

First of all, we need to convert 500 litres into ml by multiplying by 1,000:
500 x 1,000 = 500,000
Next, we divide 500,000 (the water in the tank in ml) by 125 (the amount leaked in 7 minutes):
500,000 ÷ 125 = 4,000.
Next we need to multiply 4,000 (the groups of 7 minutes) by 7 to find the total number of minutes:
4,000 x 7 = 28,000 minutes - that’s about 19 and a half days!

7 .

The planet Mars is 4 times further from the Sun than the planet Mercury. If Mars is 142 million miles from the Sun, how far is Mercury?

568 million miles

355 million miles

35.5 million miles

3.55 million miles

Don’t let the large number put you off – in fact, you can ignore the millions in your calculations, as long as you remember to put them back in at the end!
142 ÷ 4 = 35.5

8 .

One flu injection contains 10 ml of the vaccine. Doctor Do-a lot has 3,780 patients he has to inject. How much vaccine will he need?

3.78 litres

37.8 litres

378 litres

3,780 litres

10 ml x 3,780 = 37,800 ml.
Next we convert 37,800 ml to litres by dividing by 1,000 (the number of ml in one litre):
37,800 ÷ 1,000 = 37.8 litres

9 .

The antiques shop is having a sale and all items are being sold for 60% of their original price. A gramophone now costs £522 so, how much was it before the sale?

£844

£870

£970

£1,044

If £522 is 60% of the original price then, to find the original price we:
Divide 522 by 60 to find 1% of the original price: 522 ÷ 60 = 8.7
Next we multiply 8.7 by 100 to find the original price: 8.7 x 100 = £870

10 .

Ben Nevis, the highest mountain in Britain, is 4,411 feet tall. If 1 metre = 3.28 feet, how high is Ben Nevis in metres to the nearest metre?

14,468 metres

9,335 metres

4,450 metres

1,345 metres

Convert feet to metres by dividing by 3.28:
4,411 ÷ 3.28 = 1,344.817 which we round up to 1,345 metres.
Of course, conversions are only ever approximate. The actual height of Ben Nevis is 1,344.527 metres

Author: Frank Evans (Specialist 11 Plus Teacher and Tutor)