TIMO 2018 Grade 5 Heat Set 4

Find the 2-digit number CA, given that A and C are two non-zero digits and the 2-digit numbers formed by these two digits have the following properties: 1. CA is divisible by 13; 2. AC is a square number;

5 numbers, A, B, C, D and E, represent different numbers from 1 to 9. Given the following conditions: 1. The sum of A and E is less than the sum of C and 5. 2. The sum of A, C and E equals D. 3. The sum of A and D equals B. 4. D is divisible by C. 5. The sum of A and C is less than E. 6. D is greater than 6. Find the number to represent D.

A stationery store had a batch of ball pens. One half but 6 fewer pens were sold on the first day. One half of the remaining part and 8 more pens were sold on the second day. Finally, 20 ball pens are left. How many ball pen(s) did the stationery store have originally?

John wrote a four-digit number with all digits different. Guess 1703 has two correct digits in correct positions; guess 2745 has two correct digits in wrong positions; guess 3541 has all digits correct but all in wrong positions. Find the number.

Given that there are 12 signs of the zodiac, at least how many student(s) is / are there such that there exists at least 11 of them having the same sign of the zodiac?

Find the value of 13×$42+26$×$11+39$×12.

Find the value of 2017²−1017².

Find the value of $1+3+5+7$+...+$2015+2017$.

Find the value of $1+2$+...+$2016+2017+2016$+...+$2+1$.

Find the value of 123456787654321÷1234321.

If the 10-digit number 2017A1221B is divisible by 72, find $A+B$.

Find the unit digit of A: A is a product of 2017 copies of 2017 and 1221 copies of 1221.

Define a⊗b=b×b−2×a×b+a×a. Find (13⊗14)⊗15.

The sum of two positive numbers A and B is 96. Find the maximum value of the product of A and B.

How many 3-digit number(s) that can be divisible by 3 or 5 is / are there?

How many rectangle(s) is / are there in the figure below?

In rectangle ABCD, the areas of triangles BEG and CFG are 2017cm² and 1221cm² respectively. Find the shaded area in cm².

35 small cubes with side length 1cm are combined according to the pattern shown below, find the surface area in cm2.

A big rectangle is formed by 2017 small squares with side length 1cm. What is the perimeter of that rectangle in cm?

How many right-angled triangle(s) is / are there in the figure below?