QR

Quantitative Reasoning Advice:

1. Do not aim to be accurate. Always check the answer options first and work backwards from these. Estimating & guessing tend to be good options. Aim to use the whiteboard & mental maths first & the calculator only when necessary. 

2. Work out which question types always waste your time and remember to skip these first time round. 

3. Probably a little subjective in terms of what questions you would consider hard/easy. Around 25% of questions will likely require 60-90s minimum & involve multiple steps, and so those would be the ones to skip. 

4. A question may be long but easy - that one should also be skipped to return to at the end. 

5. Ones to skip you can identify from:

• long question with lots of words in

• multiple steps of calculation

• many pieces of data provided

• answer options close together

Estimating - few different ways to do this but usually when answer options are far apart. 

I) orders of magnitude

II) final digits (e.g. 2047 x 3994 is going to end in an 8 because 7x4=28)

III) divisibility tests (e.g. if you expect the answer to be a multiple of 3 then check that the digits sum to a multiple of 3) 

So something like 33 * 193 = 6369. This has to be a multiple of 3 as we have multiplied by a multiple of 3. So the sum of digits 6+3+6+9 = 24 is also a multiple. 

6. If you're rounding, always remember to round one number up and another down to try and cancel out errors.

7.  Remember some important decimal values like

• 1/6 - 0.1666....   (ends in 6)

• 1/7 - 0.143

• 1/8 - 0.125   (half a quarter)

• 1/9 - 0.11111...

• 1/5 = 0.2

• 1/4 = 0.25

• 1/2 = 0.5

• 1/3 = 0.333...   (third of a third)

Can be used in contexts like 100/7 = 14.3 (one seventh x 100)

These should also be applied to the context of time to go from minutes to hours:

•  20 mins = 0.333

• 12 mins = 0.2

• 15 mins = 0.25

• 10 mins = 0.167 (1/6)

• 6 mins = 0.1

These let you work directly using hours to work out speeds in things like mph. So say 100 miles in 2 h 39 mins, divide 100 by 2.6666 (39 mins is approximately 40 mins which is 0.66666)

8. On questions to do with prices, beware of sentences in small print at the end that change things (such as- "on Tuesdays the price is xyz times more" or "VAT applied" or "kids go free")

9. Break difficult calculations down into easier ones:

• 25 x 36 --> anything ending with a 5 you want to make easier by changing it into a zero

So you could do 25 x 4 x 9 = 100 x 9 (much easier)

• 231 / 7 --> break down 242 into a number that you know is in the 7 times table easily and then see what the difference is. For example, 231 = 210 + 21  and we know (7x30 = 210 & 7x3 = 21)

  • Use fractions as these can be easily simplified. For example, 450 items are bought at 60p

  • 450 x 60 is difficult. But if we make this 450 x £0.60, we know that it's 3/5 & that 1/5 is 90

  • So answer 90 x 3 = 270

Use of the calculator in QR:

What do the shortcuts do?

M+ = adds the value on the screen to the calculator memory

M- = takes away what’s on the screen from the calculator memory

MRC = brings what’s in the calculator memory back onto the screen

The reason for these shortcuts is to do multi step calculations.

Some examples of where you might want to use them:

1. 7/8 + 8/9 = ?

If we solved this by entering 7 ÷ 8 + 8 ÷ 9

Then the calculator would do ((7÷8)+8)÷9

One option would be to work out the first part, write it down and then work out the next part. But an easier way would be to do 7/8 first and then add this to the calculator memory by pressing M+. We could then work out 8/9, again using M+ to add to the calculator memory. If we then clear the screen and press MRC (which brings up whatever is saved in the memory), we will see the sum of 7/8 and 8/9

2. 73 - 11/9 = ?

We could do 73 then M+

Then work out 11 ÷ 9 and do M-

And so the memory would contain 73 - 11/9

The answer could be brought onto the screen by pressing MRC

3. 13,231 * 13,231 * 13,231 * 13,231 = ?

Instead of typing that three times, we could use M+ to add 13,231 to memory (after writing on screen) and then do

13,231 x MRC x MRC x MRC