NMOS Mock Paper 1

The sum of numbers A and B is 305.8. Number A is obtained when the decimal point in B is
moved to the right by one decimal place. Find the value of A.

The sum of the sum of 2 numbers and their difference is 120. The difference is 3 times as large
as the number subtracted. Find the difference.

The value of A is 36. The lowest common multiple of A and B is 288, while the greatest
common divisor of A and B is 4. Find the value of B.

After ⅕ of the fruits in a fruits shop were sold, another 66000 kg of fruits were delivered into
the shop. The mass of fruits is now ⅙ more than the original mass of fruits. Find the original
mass of fruits.

In a triangle, the first interior angle is 3 times as large as the second interior angle. The third
interior angle is half the size of the second interior angle. Find the size of the first interior
angle.

Find the sum of all the digits in the boxes in the figure below.

There are a few 4-digit numbers with 3 as the hundreds digit and 6 as the tens digit. Some of
these numbers can be divided by both 2 and 3. A is the largest possible such number, while
B is the smallest possible number. Find the total sum of the thousands and units digits of A
and B.

Two students are doing multiplication calculation. One student mistook the units digit of one of the numbers as 1 instead of 4. He obtained a result of 525. The other student mistook the units digit of that same number for 8 and obtained a result of 700. Find the correct product.

In a division, the quotient is 12 while the remainder is 26. The sum of the dividend, divisor,
quotient and remainder is 454. Find the divisor.

3 cows and 8 goats eat 93 kg of grass in total in a day. 5 cows and 15 goats eat 165 kg of grass
in total in a day. How many kilograms of grass do a cow and a goat eat in total in a day?

A walks 50 m per minute, B walks 60 m per minute, and C walks 70 m per minute. A and
B set off from East Village at the same time, while C sets off from West Village at the same
time as A and B. C meets A two minutes after meeting B. Find ¼ of the distance between East Village and West Village.

As seen in the figure below, side BA of triangle ABC is extended by its length until point D.
Side CB is extended by twice its length until point E, while side AC is extended by thrice its
length until point F. Given that the area of triangle ABC is 1 unit, find the area (in units) of
triangle DEF.

How many numbers between 1 and 10,000 give a remainder of 1 when divided by 5, 6 and 7?

Find the number of consecutive zeroes at the end of 1 × 2 × 3 × · · · × 100.

Pick 4 digits from the digits 0, 1, 4, 7, and 9 to form a 4-digit number. Arrange all such 4-digit numbers which are divisible by 3 in increasing order. Find the last digit of the 5th number in the sequence.

The sides of a triangle are consecutive 2-digit even numbers. The sum of the last digits of each
side is divisible by 7. Find the perimeter of the smallest such triangle.

The maximum amount of fuel an airplane can store lasts for 6 hours. When an airplane flies
to its destination, it flies in the wind’s direction at 1500 km per hour. When the airplane
returns, its speed will be 1200 km per hour. Find the maximum possible distance the airplane can travel to have enough fuel to reach its destination and return.

As seen in the figure below, 16 chairs are arranged in a circle, and numbered 1 to 16. A person sitting on chair 1 moves 328 seats in the clockwise direction, 485 seats in the anti-clockwise direction, another 328 seats in the clockwise direction, another 485 seats in the anti-clockwise direction, and finally 136 seats in the clockwise direction. Find the number of the chair he is sitting on at the end.