**UCAT** **Question Analysis - Quantitative Reasoning Question 19**

Printing costs

Digital printing (normal quality):

• Initial set-up cost: none

• 6p per page up to total 300,000 pages

• 5p per page between 300,001 pages and 600,000 pages

• 4p per page above 600,001 pages

• The total quantity printed determines the price per page. The same price is charged for all pages, e.g. for 500,000 pages, all pages will be charged at 5p.

Litho printing (higher quality):

• Initial set up cost: £1000

• 6p per page up to total 200,000 pages

• 4.5p per page between 200,001 and 550,000 pages

• 3.5p per page above 550,001 pages

• The total quantity printed determines the price per page. The same price is charged for all pages, e.g. for 300,000 pages, all pages will be charged at 4.5p.

Cover printing

• One colour only:

• £1.50 per book if ordering 1599 books or less

• £1.40 per book if ordering between 1600 and 1999 books

• £1.00 per book if ordering 2000 or more books

More than one colour: Add 20% to the cost of one colour only' printing regardless of the number of colours.

Lamination of the cover

• Matt laminate: 20p per book

• Gloss laminate: 12p per book

Retail data

• Bookshops purchase books directly from the publisher at 75% of the Recommended Retail Price (RRP)

**Mr Scribbler wants to print 1600 copies of his 126-page book. He wants the book printed using the litho technique, with a cover printed with one colour only and laminated in gloss. **

**Q19.1 How much will it cost?**

a. £10,547

b. £11,664

c. £12,504

d. £12,654

e. £14,678

**A customer needs 3,000 covers, and hesitates between 2 options: • Option A 1 colour, matt laminate • Option B: 2 colours, gloss laminate **

**Q19.2 How much cheaper is Option A compared to Option 8? **

a. £ 0

b. £ 80

c. £360

d. £960

e. £1,034

**A publisher had one of his titles printed at a cost of £34,500. He sold all copies of the book to a bookshop and made a profit of £9,672. The Recommended Retail Price for the book is £16. **

**Q19.3 How many copies of this book did he sell to the bookshop? **

a. 2156

b. 2761

c. 3681

d. 4256

e. 6783

**On 1 January, the publisher asked the printer for a quote based on 2000 copies of a book of 300 pages to be printed using digital tech-nology with a one-colour gloss-laminated cover. On 10 January, he realised the book had, in fact, 400 pages. **

**Q19.4 What is the difference between the actual price paid for the printing of the 400-page books, and the price originally quoted for 300 pages? **

a. £1,690

b. £2,000

c. £4,690

d. £8,000

e. £10,000

**A customer wants 50 copies of a 30-page book printed but cannot afford to pay the full price. The book is to be printed using digital technology and has a three-colour cover which is to be laminated gloss. As a gesture of goodwill, the printer charges him a lower printing cost per page and hands out a total invoice for £156. **

**Q19.5 What price did the printer charge per page? **

a. 2p

b. 3p

c. 4p

d. 5p

e. 5.5p

**Answer and Explanation**

**Q19.1 — c: £12,504 **

Litho printing: • Initial setup• cost = £1000 • Printing: 126 x 1600 = 201,600 pages at 4.5p each = £9,072 Cover

• 1600 at £1.40 each = £2,240 • Lamination (Gloss) = 1600 at £0.12 each = £192 Total= £12,504

**Q19.2 — c: £360 **

The cost of Option A is: 3000 x (£1.00 + £0.20) = £3,600 The cost of Option B is: 3000 x (£1.00 x 1.2 + £0.12) = £3,960 Cost difference = 3,960 — 3,600 = £360

**Q19.3 — c: 3681 **

If the printing cost was £34,500 and the profit was £9,672, then the income he received from the bookshop is £9,672 + £34,500 = £44,172.

We know that the bookshop buys books at 75% of the RRP (£16), i.e. at £12 per book. So the bookshop purchased 44,172112 = 3,681 copies.

**Q19.4 — b: £2,000 **

The quote was for 300 pages x 2000 books = 600,000 pages. This would have been quoted at 5p per page, i.e. £30,000. The actual number of pages printed was 400 pages x 2000 books = 800,000 pages, which should be priced at 4p per page, i.e. a total of £32,000. The difference on the printing of the pages is therefore £2,000. Note that the number of covers is the same (2000); therefore the difference is purely on the pages.

**Q19.5 — c: 4p **

The cost of printing the cover for 50 books (3 colours, laminated gloss) is: 50 x (1.5 x 1.2 + 0.12) = £96. Since the total cost was £156, then this leaves £60 for the actual printing of the pages.

He wants to print 50 x 30 = 1500 pages. Therefore the cost per page is: 60 / 1500 = 0.04 i.e. 4p.

Drafted by Juno Wong(UCAT Prep)