How to Pass Numerical Reasoning (48 page)

Now arrange the fractions in size order.

Academia 2000 has the largest ratio of job offers per applicant. If you are in doubt as to the relative size of the fractions, use a proportion to work it out. For example, which is larger,
³⁄
₁₀or
⁶⁄
₁₈?

Now ask ‘is 54 > 60?’ The answer is no, so you know that 6⁄18 is the larger ratio.

Section 10 Consultancy rates

Q1
b) £3,200

Add all the relevant costs to the client per consultant.

Daily rate	Overtime	Travel
Clancy	£240 × 5 days	7.5 hours	5 hours × £30
(50% × £30)	= £1,462.50
Osborne	£350 × 5 days	n/a	n/a = £1,750

Total charged to client = £1,462.50 + £1,750 = £3,212.50.

Q2
c) £123.20

22 days × 70 miles round trip × 8p per mile = £123.20.

Q3
d) £60

Find 15% of Smith’s daily rate:

The client will have to pay an extra £60 per day.

Section 11 Revenues for Cookie’s Bakery

Q1
c) 22%

Recall the formula to find a percentage:

Choose the answer closest to 25%.

Q2
a) £400

Custard tart profit = 9.5%.

Revenues for custard tarts in the North = £4,000.

Profit = 9.5% × £4,000 ≈ 10% of £4,000 ≈ £400.

Q3
c) 11%

Total revenues on all cakes in 1996 = (80 + 60 + 50 + 50 + 30) = 270,000.

Total revenues on all cakes in 1997 = 300,000.

Recall the formula to find the percentage change:

Q4
d) £10,250

The question tells you that in 1997 lemon pie profits = 20% and that 1997 revenues showed a 2.5% increase on 1996 lemon pie revenues.

1997 lemon pie revenue = £50,000 × 1.025 = £51,250.

Therefore, 1997 lemon pie profit = £51,250 × 20%.

10% of £51,250 = £5,125 (divide £51,250 by 10) and therefore 20% = £5,125 × 2 = £10,250.

Section 12 Currency fluctuation

Q1
b) Dollar and yen

Look for currencies that increase in value relative to the GB £. (This means that you get less currency for one GB £). The US $ strengthens against the GB £ between July and August (1.61 increases to 1.53). The Japanese yen also strengthens against the GB £ between June and July (179.21 increases to 177.66).

Q2
c) 40 euros

If the euro fell by 6%, you will receive 6% more currency for every GB £. First calculate the value of the euro in September by multiplying the value of the euro by 6%: 1.5 × 1.06 = 1.59

So in September 1.59 euros can be exchanged for £1, so £25 will buy 1.59 euros × £25 = 39.75 euros, or approximately 40 euros.

Q3
c) Rouble

Look for the currency that showed the largest percentage change in the period. First eliminate the answer choices that show an obviously small percentage change (euro, dollar and yen). Now work out the percentage change of the remaining choices. Use the percentage change formula: