UKCAT Quantitative Reasoning Sample Questions

Try our tough Quantitative Reasoning questions and see if you can answer them correctly.

UKCAT Quantitative Reasoning

Subtest length: Nine sets of graphs/charts/tables, four questions each
Subtest timing: 24 minutes

Sample length: One set of charts, four questions
Sample timing: 2 minutes

Sample Question; Quantitative Reasoning

Linden Grove School is designated a Specialist Language College. All students at Linden Grove must study at least one language to GCSE level, and many students take GCSEs in two languages.

All students in Year 11 at Linden Grove take at least one of three languages:

61 students in Year 11 study French

35 students in Year 11 study German
47 students in Year 11 study Spanish

These numbers include students who take a single language, as shown in the first chart, as well as students taking more than one language, as shown in the second, third and fourth charts.

All students in Year 11 Who Study One Language Only
UKCAT Quant Graph 1
The second languages of students in Year 11 who also study French
UKCAT Quant Graph 2
The second languages of students in Year 11 who also study German
UKCAT Quant Graph 3
The second languages of students in Year 11 who also study Spanish
UKCAT Quant Graph 4

No student in Year 11 studies more than two languages.


1. What is the total number of students in Year 11?

A. 80

B. 101

C. 122

D. 143

E. Can’t tell


2. The number of students who study Spanish as their only language is equal to the total number of students that study which two languages?

A. Mandarin and Portuguese

B. Italian and Mandarin

C. Italian and Japanese

D. Italian and Portuguese

E. Japanese and Portuguese


3. What percentage of students who study German also study Mandarin?

A. 4%

B. 11%

C. 19%

D. 26%

E. 43%


4. At the start of the academic year, Linden Grove decides to allow Italian as a first-language choice. Three students switch from studying French and Italian to Italian only, and one switches from Spanish and Italian to Italian only. During the autumn term, four new students joining Year 11 opt for Italian only; one selects French and Italian; and three take Italian and Japanese. Half of all Portuguese students in Year 11 also decide to switch their first language to Italian in the autumn term. Which chart shows the second languages of students in Year 11 who are studying Italian at the end of the autumn term?

A
UKCAT Quant Chart A
B
UKCAT Quant Chart B
C
UKCAT Quant Chart C
D
UKCAT Quant Chart D
E
UKCAT Quant Chart E

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