Grade 6
MathGenius National Contest
March 2016
Critical Thinking Math
1. Of the following, which is the largest?
A. 0.03
B.
C.
2
25
1
20
D. 2.5%
E. Six hundredths
2. If yesterday was Thursday, what day will be 100 days from tomorrow?
A.
B.
C.
D.
E.
Monday
Wednesday
Friday
Saturday
Sunday
3. A container has capacity of
2
3
liter. It is filled three-fourths with water. How many
liters of water will be left in the container after
A.
B.
C.
D.
E.
1
6
liter is poured out?
5
6
1
6
1
12
1
2
1
3
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Grade 6
MathGenius National Contest
March 2016
Critical Thinking Math
4. What is the sum of all factors of 28 that are less than 28?
A.
B.
C.
D.
E.
7
14
27
28
56
5. The area of triangle PQR is 96 sq. inches. Point S lies on the side PQ. The length
of ̅̅̅̅
𝑃𝑆 is 9 in, and ̅̅̅̅
𝑃𝑄 is 32 in. What is the area of the triangle QRS in sq. in?
A.
B.
C.
D.
E.
48
56
69
72
81
R
P
9
S
32
Q
Note: Figure not drawn to scale
6. The average of seven positive integers is 42. The average of the first three integers
is 50. What is the average of the last four integers?
A.
B.
C.
D.
E.
32
34
35
36
38
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Grade 6
MathGenius National Contest
March 2016
1
1
1
7. (1- 2 ) x (1- 3 ) x (1- 4 ) …x(1A.
B.
C.
D.
E.
1
100
Critical Thinking Math
)?
1
2
1
100
99
100
1
50
1
1 𝑥 2 𝑥 3 𝑥 4…100
8. How many factors does 90 have?
A.
B.
C.
D.
E.
12
8
15
10
9
9. Eight people randomly picked eight different positive integers. If the average of
these eight numbers is 14, what could be the greatest possible integer that one
of them could have picked?
A.
B.
C.
D.
E.
15
84
99
105
112
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Grade 6
10.
A.
B.
C.
D.
E.
MathGenius National Contest
March 2016
Critical Thinking Math
If three fair coins are tossed, what is the probability all of them will be heads?
1
3
2
3
1
6
1
8
1
9
11. Ansley, Betty and Cathy have a total of 6 identical dolls. Each girl has at least
one doll. In how many different ways can this happen?
A.
B.
C.
D.
E.
1
3
6
9
10
2
On a line segment ̅̅̅̅̅̅̅̅̅̅
𝐴𝐵𝐶𝐷𝐸 , D is the midpoint of ̅̅̅̅
𝐴𝐸 . The length of ̅̅̅̅
𝐵𝐷 is the
3
̅̅̅̅ , and 𝐵𝐶
̅̅̅̅ = ̅̅̅̅
̅̅̅̅ ?
length of 𝐴𝐵
𝐶𝐷. What percent of ̅̅̅̅
𝐴𝐸 is 𝐴𝐶
12.
A.
B.
C.
D.
E.
33.3%
10%
40%
25%
20%
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Grade 6
13.
A.
B.
C.
D.
E.
MathGenius National Contest
March 2016
Critical Thinking Math
How many times does the digit 3 occur in all the numbers from 100 to 373?
132
99
132
65
119
14. If all the multiples of 3 and all multiples of 5 are removed from the set of
integers from 1 through 200, how many integers remain?
A.
B.
C.
D.
E.
40
66
93
99
106
15. If x and y both are integers and x + y is an even integer, which of the following
must be also be an even integer?
A.
B.
C.
D.
E.
xy
x + 2y
x – 2y
1 – (x2 - y2)
xy – y2
16.
What is the square root of 0.000049? Express the answer as a decimal number.
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Grade 6
MathGenius National Contest
March 2016
Critical Thinking Math
17. If each of the digits 2, 4, 5, 6, 8, and 9 are placed exactly in one of the boxes
in the below subtraction problem, what is the least possible positive difference?
________________
18. A palindrome is a number that reads same forward or backward, such as 323.
What is the greatest common factor of all two digit palindromes?
19. The base of an isosceles triangle is 12 and its area is 48. What is the length of
one of the congruent sides?
20.
Find the integer value of n that satisfies below inequalities:
4
101
>
1
𝑛
>
3
80
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