Revision Library

revisionlibrary.co.uk

11+ · Number and Calculation

EP.M113 Missing Digit and Calculation Puzzles

GL ASSESSMENT GL-11PLUS-MATHS · Calculators not allowed · about 55 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

In the addition below the blank stands for one digit. 4_6 + 289 = 715. What is the missing digit?

A) 1
B) 2
C) 3
D) 4
E) 5

(Total for Question 1 is 1 mark)

In this subtraction the blank is a single digit. 89_ - 457 = 433. Which digit replaces the blank?

A) 8
B) 1
C) 0
D) 9
E) 7

(Total for Question 2 is 1 mark)

Find the missing digit: 65 x _ = 455

A) 6
B) 5
C) 8
D) 7
E) 9

(Total for Question 3 is 1 mark)

The blank is a single digit: _8 ÷ 4 = 22. What is the blank?

A) 6
B) 4
C) 7
D) 8
E) 2

(Total for Question 4 is 1 mark)

In the addition below the blank is a single digit. 3_8 + 267 = 615. Find the blank.

A) 1
B) 3
C) 4
D) 2
E) 5

(Total for Question 5 is 1 mark)

Find the missing digit in the subtraction: 6_2 - 175 = 487

A) 5
B) 8
C) 6
D) 4
E) 7

(Total for Question 6 is 1 mark)

Each symbol # stands for the same single digit. #7 + 35 = 102. What digit does # represent?

A) 5
B) 6
C) 7
D) 4
E) 3

(Total for Question 7 is 1 mark)

Each symbol # stands for the same single digit. #5 + 48 = 123. What digit does # represent?

A) 6
B) 5
C) 7
D) 4
E) 8

(Total for Question 8 is 1 mark)

In the calculation below a blank is one digit. 4_ x 12 = 528. Find the missing digit.

A) 3
B) 4
C) 5
D) 2
E) 6

(Total for Question 9 is 1 mark)

Which digit replaces the blank? 11_ + 289 = 400

A) 0
B) 1
C) 2
D) 3
E) 4

(Total for Question 10 is 1 mark)

Find the digit in the blank: 7_9 - 341 = 438

A) 5
B) 6
C) 7
D) 8
E) 9

(Total for Question 11 is 1 mark)

In the addition below the blank is a digit. _56 + 237 = 893. What is the blank?

A) 4
B) 6
C) 7
D) 5
E) 8

(Total for Question 12 is 1 mark)

In the multiplication below a blank stands for a digit. 2_3 x 4 = 892. Find the missing digit and show the method.

(Total for Question 13 is 2 marks)

A three-digit number written as _52 minus 379 equals 173. Find the missing digit and show your working.

(Total for Question 14 is 2 marks)

Each digit d is the same in both places. d5 + 5d = 121. Find d. Show the steps.

(Total for Question 15 is 3 marks)

Find the missing digit in the subtraction 9_5 - 218 = 777. Show your working.

(Total for Question 16 is 3 marks)

A two-digit number less than 70, multiplied by 3, gives 2_1. Find the blank and show your method.

(Total for Question 17 is 3 marks)

A three-digit number 1_2 when divided by 24 leaves remainder 6. Find the missing digit. Show how you decided.

(Total for Question 18 is 3 marks)

In the addition below a digit is blank: _47 + 538 = 985. Find the missing digit and show your steps.

(Total for Question 19 is 4 marks)

Multi-part column puzzle. Use exact arithmetic and show steps in each part.

(a)Write the missing digit in the three-digit number _23 so that _23 + 479 = 802.(2)

(b)Multiply the three-digit number you found in part (a) by 4. Write the product.(3)

(c)In the product from part (b) the tens-hundreds place is shown as 1_92. Write the missing digit.(3)

(Total for Question 20 is 8 marks)

Mark scheme · EP.M113 Missing Digit and Calculation Puzzles

Question 1

B1 correct option B (2) cao
Answer: B) 2 (because 426 + 289 = 715).

Question 2

B1 correct option C (0) cao
Answer: C) 0 (because 890 - 457 = 433).

Question 3

B1 correct option D (7) cao
Answer: D) 7 (since 65 x 7 = 455).

Question 4

B1 correct option D (8) cao
Answer: D) 8 (88 ÷ 4 = 22).

Question 5

B1 correct option C (4) cao
Answer: C) 4 (348 + 267 = 615).

Question 6

B1 correct option C (6) cao
Answer: C) 6 (662 - 175 = 487).

Question 7

B1 correct option B (6) cao
Answer: B) 6 (67 + 35 = 102).

Question 8

B1 correct option C (7) cao
Answer: C) 7 (75 + 48 = 123).

Question 9

B1 correct option B (4) cao
Answer: B) 4 (44 x 12 = 528).

Question 10

B1 correct option B (1) cao
Answer: B) 1 (111 + 289 = 400).

Question 11

B1 correct option C (7) cao
Answer: C) 7 (779 - 341 = 438).

Question 12

B1 correct option B (6) cao
Answer: B) 6 (656 + 237 = 893).

Question 13

M1 division or equivalent method: 892 ÷ 4 (= 223) seen
A1 missing digit 2 in 2_3 (223) cao
Answer: Missing digit = 2 (223 x 4 = 892).

Question 14

M1 add 379 + 173 (= 552) or equivalent method seen
A1 hundreds digit 5 (552) cao
Answer: 5 (the number is 552).

Question 15

M1 form equation: (10d + 5) + (50 + d) = 121 seen
M1 simplify to 11d + 55 = 121 and 11d = 66 seen
A1 d = 6 cao
Answer: d = 6 (since 65 + 56 = 121).

Question 16

M1 add 218 + 777 (= 995) or equivalent method seen
M1 write result 995 or show hundreds, tens and units correctly
A1 missing digit 9 cao
Answer: 9 (because 995 - 218 = 777).

Question 17

M1 divide 2_1 by 3 or show 3 x ? = 201 seen
M1 correct quotient 67 or equivalent calculation seen
A1 blank = 0 cao
Answer: 0 (because 67 x 3 = 201).

Question 18

M1 recognise equation 1_2 = 6 (mod 24) or show trial with possible digits
M1 show candidate 102 and compute 102 ÷ 24 remainder (= 6) or equivalent
A1 blank = 0 cao
Answer: 0 (102 ÷ 24 leaves remainder 6).

Question 19

M1 set up subtraction 985 - 538 or equivalent method seen
M1 compute subtraction (= 447) seen
M1 identify hundreds digit 4 or show the filled number 447
A1 blank = 4 cao
Answer: 4 (447 + 538 = 985).

Question 20

(a) M1 set up subtraction 802 - 479 (= 323) or equivalent
(a) A1 hundreds digit 3 cao
(a) Answer: 3
(b) M1 correct method for multiplication seen (323 x 4)
(b) M1 intermediate partial product correct or 323 x 2 = 646 seen
(b) A1 final product 1292 cao
(b) Answer: 1292
(c) M1 recognise product 1292 from part (b) or recalc 1292
(c) M1 identify the blank (the hundreds digit) correctly
(c) A1 blank = 2 cao
(c) Answer: 2

Missing Digit and Calculation Puzzles - Worksheets, Questions and Revision