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<b>AMO MOCK TEST #1</b>

<b>Grade 7</b>

<b>INSTRUCTIONS</b>

1. Please DO NOT OPEN the contest booklet until the Proctor has given
per-mission to start.

2. TIME: 1 hour 30 minutes.

3. Attempt all 25 questions. Each question scores 1 point. No points are
de-ducted for incorrect answers.

4. Write your answers neatly on the answer sheet.

5. PROCTORING : No one may help any student in any way during the contest.
6. No calculators are allowed.

7. All students must fill in your Name and School.

8. MINIMUM TIME: Students must stay in the exam hall at least 1h 15 min.
9. Students must show detailed working and put answers on the answer sheet.
10. No spare papers can be used in writing this contest. Enough space is provided

for your working of each question.

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<b>Question 1.</b> Find the sum of the counting numbers from 1 to 35
inclu-sive. In other words, if

S = 1 + 2 + 3 +· · ·+ 34 + 35,

find the value of S.

<b>Question 2.</b> In three bowling games, Alice scores 139,143, and 144.

What score will Alice need in the fourth game in order to have an
av-erage score of 145for all four games?

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<b>Question 3.</b> For all integers P and Q, P ⊗ Q is defined as P ⊗ Q =

P ×Q

2 . What is the value of 8⊗(1⊗6)?

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<b>Question 5.</b> Each of the smallest boxes in the below figure is a square.
How many different squares can be formed by using the lines in the
below figure?

<b>Question 6.</b> The product of some whole numbers is 120. Find their
least possible sum.

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<b>Question 7.</b> Soshana looks in a mirror and sees the reflection of a
clock behind her as shown in the figure on the left. How many minutes
later will the reflection in the mirror of the same clock next show the
image shown in the figure on the right?

<b>Question 8.</b> LetA and B be the following sets:

A = {21,22,23,24,25,26,27,28,29}
B = {9,10,11,12,13,14,15,16}

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<b>Question 9.</b> A number has a remainder of 1 when divided by 4, a
re-mainder of 2 when divided by 5, and a remainder of 3 when divided by

6. What is the smallest number that has the above properties?

<b>Question 10.</b> The perimeter of a rectangle is 20cm and the number of
centimetres in each of its length and width is a whole number. How
many rectangles with different shapes satisfy these conditions?

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<b>Question 11.</b> In a maths contest of 20 problems, 5 points were given
for each problem with correct answer and 2 points were deducted for
each problem with incorrect answer or no answer. If Nancy answered
all 20 problems and scored 72 points, how many correct answers did
she have?

<b>Question 12.</b> In the "magic square" at the right, the four numbers in
each column, in each row, and in each of the two diagonals, have the
same sum. What is the value of N?

10 13

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<b>Question 13.</b> Thirteen dots are arranged on a square grid in the
pat-tern below. How many different squares can be formed by connecting
at least four of these dots?

<b>Question 14.</b> A landscaper is designing a rectangular garden. The
length of the garden is to be 5 yards longer than the width. If the area
of the garden will be 104 square yards, what will be the length, in yards,
of the garden?

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<b>Question 15.</b> The complete outside including the bottom of a wooden 4
-cm cube is painted red. The painted cube is then cut into 1cm cubes as
in the below figure. How many of the 1-cm cubes do not have red paint
on any face?

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<b>Question 17.</b>A train can hold 78 passengers. The train starts out empty
and picks up 1 passenger at the first stop, 2 passengers at the second
stop, 3passengers at the third stop, and so forth. Given that no one
leaves the train during the trip, after how many stops will the train be
full?

<b>Question 18.</b> Find the least value of whole number N, with N > 10, so
that the expression 2N −7 is both a perfect square and a perfect cube.

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<b>Question 19.</b> In a deck of 54 playing cards, there are four different
suits of 13 cards each and two Joker cards. What is the minimum
num-ber of cards that must be drawn from the deck to ensure that there are
at least 5 cards of the same suit?

<b>Question 20.</b> If a kindergarten teacher places her children 4 on each
bench, there will be 3 children who will not have a place. However, if

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<b>Question 21.</b> How many numbers in the set {1,2,3, ...,28,29,30}
can-not be represented by adding two or more different numbers in the set

{0,2,3,5,8,13}? (Note that 4cannot be represented as the sum of
num-bers from the above list.)

<b>Question 22.</b> The ten-digit number 3872649A0B is divisible by 72. The
letters A and B each represent single digit even numbers. Find the

prod-uct (A×B).

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<b>Question 23.</b> Twelve identical machines, running continuously at the
same constant rate, take 8 days to complete a shipment. How many
additional machines, each running at the same constant rate, would be
needed to reduce the time required to complete a shipment by 2 days?

<b>Question 24.</b> In the addition problem below, each letter represents
a digit and different letters represent different digits. What three-digit
number does RID represent?

I N

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<b>Question 25.</b> Ms. Simon drives her car from her home to her workplace
every workday morning. The table below shows the distance, in miles,
and her average driving speed, in miles per hour (mph), when there is
no traffic delay, for each segment of her drive.

<b>Ms. Simon’s Workday Morning Drive</b>

Segment of drive Distance Average driving speed with
(miles) no traffic delay (mph)
From home to freeway entrance 0.6 25

From freeway entrance to freeway exit 15.4 50

From freeway exit to workplace 1.4 35

If Ms. Simon starts her drive at 6 : 30a.m., she can drive at her average
driving speed with no traffic delay for each segment of the drive. If she

starts her drive at 7 : 00 a.m., the travel time from the freeway entrance
to the freeway exit increases by 33% due to slower traffic, but the travel
time for each of the other two segments of her drive does not change.
Based on the table, how many more minutes does Ms. Simon take to
arrive at her workplace if she starts her drive at 7 : 00 a.m. than if
she starts her drive at 6 : 30 a.m.? (Round your answer to the nearest
minute.)

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