REMT 2016
MATHEMATICAL
REASONING
ANSWERS
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LAST NAME
FIRST NAME
GRADE
2016G2
1.
A drawer contains two white socks, two red socks, and two blue socks. If I grab two
socks at random from this drawer, what is the probability that I get a matching pair?
2.
How many ten-digit integers can be made using, as digits, one one, two twos, three
threes, and four fours?
3.
Jack sets out on a bike ride at 18 miles per hour. Jill sets out 10 minutes later and
follows the same route at 22 miles per hour. How many minutes after she starts will
Jill catch up to Jack?
4.
If
5.
In a poll of 100 people, 60 of them claimed to be good at math; a follow-up test showed
that only 50 are actually good at math. If 32 people correctly denied that they are good at
math, how many people are good at math but didn't admit it?
3𝑎
4
=
5𝑏
6
, what is
𝑎−𝑏
𝑎
?
2016G3
6.
If 4 cards are chosen from a standard deck of 52 cards without replacement, what is the
probability that all 4 of the cards are of the same suit?
7.
Eight people are posing together in a straight line for a photo. Alice and Bob must stand
next to each other, and Claire and Derek must stand next to each other. How many
different ways can the eight people pose for their photo?
8.
If 𝑓 (
9.
If 𝑥 + 𝑦 = 10 and 𝑥 2 + 𝑦 2 = 60, what is 𝑥 3 + 𝑦 3 ?
10.
Find the number of different routes from point A
to point B always heading north or east.
𝑥+3
𝑥
) = 𝑥 2 + 6𝑥 + 2, what is 𝑓(5) ?
B
A
2016G4
11.
Let 𝑥 = √16 + √16 + √16 + ⋯ . What is the value of x ?
12.
An infinite geometric sequence has a first term of 12, and all terms in the sequence sum
to 9. Compute the common ratio between consecutive terms of the geometric sequence.
13.
An ant begins at a vertex of a cube. On each move, it travels along an edge to a randomly
selected adjacent vertex. Find the probability that it is back at its starting position after 4
moves.
14.
Find the remainder when 220 + 330 + 440 + 550 + 660 is divided by 9.
15.
It takes three lumberjacks three minutes to saw three logs into three pieces each. How
many minutes does it take six lumberjacks to saw six logs into six pieces each?