A: The average arithmetic mean of the rest of the grasshoppers B: 5 Centimeters AI: The average arithmetic mean of 15 grasshoppers is 8 centimeters.. Let’s say that the average of the re
Trang 1The best answer is A
Cindy’s initial weight was 50 Kg The question is how much is 15 out of
50 in percent terms: 100 % 30 %
50
15
and therefore column A is greater than column B
13
A: X
B: 15
AI: X percent of X are X/8
X 0
The best answer is B
Rewrite the extra data in percent terms:
8 100
X X
X Multiply both sides
by 100 to get: 12.5 X = X2 X = 12.5 and therefore column B is greater than column A
14
A: The total decrease in the car’s value
B: 60%
AI: The value of a car decreased by 20% and then it decreased by 40% more
The best answer is B
Let’s say the car cost $100
At first its price decreased to $80, then it decreased by 40%:
(0.6 x $80 = $48) The total decrease is (100 – 48 = 52%)
The car decreased by 52% and not by 60% and so column B is greater
15
A: The total increase in the stock’s value
B: 40%
AI: The value of a certain stock increased by 20% on January and by 20% more on February
The best answer is A
Let’s say that the value of the stock was $100
In January it increased to $120
In February it increased to (1.2 x 120 = $144)
All together, the stock’s value increased by 44%, which is greater than 40%
Trang 216
A: By how much percent are rollerblades more expansive than ice-skates B: 80%
AI: Rollerblades cost 40% more than skateboards and skateboards cost 40% more than ice-skates
The best answer is A
Let’s say that ice-skates cost $100 since there are no numbers in the question Skateboards cost 40% more, thus $140
Rollerblades cost 40% more than $140, which is $196
And therefore rollerblades cost 96% more than ice-skates, which is greater than 80%
17
A: The average (arithmetic mean) of the rest of the grasshoppers
B: 5 Centimeters
AI: The average (arithmetic mean) of 15 grasshoppers is 8 centimeters The average of 5 of the grasshoppers is 10 Centimeters
The best answer B
Let’s say that the average of the rest of the grasshoppers in column A is
X
8
3 5 10
X X
3X = 14
3
2 4
X , which is a little under 5 and therefore column B is greater
18
A: The original number of bells that Helen had
B: 700
AI: After Helen lost 30% of her bells, she had 500 bells
The best answer is A
500 bells are 70% of the number we are looking for
We can write the following equation:
?
500 100
70
The original number
of bells is (50,000)/(70) = A little over 700 and therefore column A is greater
19
Trang 3A: The amount of sugar (in liters) in a mix containing 3 liters of
strawberry juice and 2 liters of cola
B: 1.5
AI: The concentration of sugar in strawberry juice is 20% and in cola it’s 40%
The best answer is B
Calculate the amount of sugar in the mix:
20% of 3 liters is 3/5 liters plus 40% of 2 liters, which is 4/5 liters
The total is (3/5 + 4/5 = 7/5 = 1 and 2/5 = 1.4 liters)
Column B is greater than column A
20
A: The probability of guessing the code the safe
B: 1/(100,000)
AI: The code of a safe has 5 digits
The last digit is 0
The best answer is A
Since we already know the last digit, we need to guess only 4 digits Each digit can be between 0 and 9
The probability of guessing each digit is 1/10 and therefore the
probability of guessing the whole 4 is (1/10)4 = 1/(10,000), which is greater than the expression in column B
21
A: 82
B: 28
The best answer is B
Take the expression in column B and write it as followed:
28 = 162, which is greater than column A
22
A: X
B: Y
AI: X2 = 25 and Y 5
The best answer is D
X can be either 5 or -5, Y can either be 5 or -5 also and since there can be more than one answers to the problem, the right answer is D
23
Trang 4A: X
B: 10
AI: X2 = 81
The best answer is B
X can either be -9 or 9
10 is larger than both choices and therefore column B is greater than column A
24
A: Y
B: 0.25X
AI: X and Y are both negative integers
X/Y > 4
The best answer is B
X/Y > 4 X > 4Y divide both sides by 4: 0.25X > Y and therefore column B is greater than column A
25
A: X – 5
B: Y + 5
AI: -5 < -X < 5
-20 < -Y < -15
The best answer is B
Simplify the ranges and make them compatible with the question: -5 < -X < 5 5 > X > -5 0 > X – 5 > -10
-20 < -Y < -15 20 > Y > 15 25 > Y + 5 > 20
We can see that the expression in column A is negative while the expression in column B is positive and therefore greater
26
A: (1/16)0.5 + (1/25)0.5
B: (1/16 + 1/25)0.5
The best answer is A
Column A = (1/16)0.5 + (1/25)0.5 = ¼ + 1/5 = 9/20
Column B = (1/16 + 1/25)0.5 = (41/400)0.5 =
20
41
Now, 41 is smaller than 9 and therefore column A is greater
27
Trang 5A: (9/144)0.5 – (1/25)0.5
B: (9/144 – 1/25)0.5
The best answer is B
Column A = (9/144)0.5 – (1/25)0.5 = 3/12 – 1/5 = 1/20
Column B = (9/144 – 1/25)0.5 =
20
3 60
9 3600
81 25
144
144 25
9 0.5 0.5
We can see that column B is greater than column A
28
A: 7/1000
B: 0.049/7
The best answer is C
7/1000 = 0.007
0.049/7 = 0.007
The columns are equal to one another and so the answer is C
29
A: 0.63
B: 0.61/3
The best answer is B
0.6 is also 3/5
Column A = (3/5)3 = 9/125
Column B = (3/5)1/3 we know that a power that is not a fraction makes
a fraction smaller, its also good to remember that a power that is a
fraction makes a fraction larger and therefore the expression in column B
is greater than 3/5 and obviously from 9/125
30
A: The average of (X + 9Y + 191) and (9X + Y + 347)
B: The average of (5X + 4Y + 457) and (5X + 6Y + 87)
The best answer is B
Find the average in both columns:
Column A = (X + 9Y + 191 + 9X + Y + 347)/2 = (10X + 10Y + 538)/2 = (5X + 5Y + 269)
Column B = (5X + 4Y + 457 + 5X + 6Y + 87)/2 = (10X + 10Y + 544)/2
=
(5X + 5Y + 272)
Trang 6The best answer is B
31
A: 3.88
B: 17
The best answer is B
We know that 16 4 and that 25 5 and therefore 17, which is found between 16 and 25 will give a result between 4 and 5
Column B is greater than column A
32
A: Percent increase from 63 to 65
B: Percent increase from 65 to 67
The best answer is A
A = 2/63 and B = 2/65
The denominator is bigger in B and therefore column A is greater
33
A: X + Y
B: X + Z
AI: The product of three numbers is 1000
The best answer is D
All we know is that XYZ = 1000, this information is not sufficient to know whether Y is bigger than Z or not The right answer here is D
34
A: 0.1
B:
1
25
250
The best answer is C
10
1 250
25 25
250 1
and therefore column A and B are equal
35
A: 65% of 135
Trang 7B: 135% of 65
The best answer is C
Remember, don’t calculate- compare
A = 135
100
65
100
135
According to the multiplication law, these expressions are equal and thus the answer is C
36
A: 30% of 25
B: 65% of 15
The best answer is B
A = 25 7 5
100
30
100
975 15
100
65
Column B is greater than column A
37
A: A B
B: A B
AI: A > 0
B < 0
The best answer is B
If A = -B for example, column A = 0 while column B = 2A or 2B
The expression in column B is always positive as opposed to the
expression in column A, which can equal zero
38
A: (X + Y + Z)/3
B: Z
AI: X < Y < Z
The best answer is B
The expression in column A is actually the average (arithmetic mean), which means that its value is between X and Z, thus smaller than Z Since the average must be smaller than Z, column B is greater than A
39
Trang 8A: The sum of the numbers
B: 2188
AI: The average of 12 numbers is 182
The best answer is B
The average (arithmetic mean) of n numbers is their sum divided by n
If the average of 12 numbers is 182, their sum will be 12 x 182 = 2184 Column B is greater than column A
40
A: (23)-1
B: (24)-1
The best answer is A
A = 1/23 and B = 1/24, in column A 1 is divide into less parts and therefore the result is greater
41
A: A + B
B: 140
AI: A = 20 + 16 + 13 + 11 + 6 + 2
B = 22 + 18 + 13 + 11 + 8 + 4
The best answer is A
Rewrite A and B like this: A = 20 + 16 + 13 + 11 + 6 + 2
B = 4 + 8 + 11+ 13 + 18 + 22
Add them up: A + B = 24 + 24+ 24 + 24 + 24 + 24
A + B = 24 x 6 = 144
Column A is greater than column B
42
A: 2 x (0.2)
B: (0.2)2
The best answer is A
2 x (0.2) = 0.4
(0.2)2 = 0.04
Since 0.4 > 0.04, column A is greater than B
43
A: Y
B: 2X + 3.5
AI: 4Y – 8X = 14
Trang 9The best answer is C
4Y – 8X = 14, divide both sides by 4: Y – 2X = 3.5 Y = 2X + 3.5
We can see that the columns are equal to one another
44
A: 1.5 – 3X
B: Y
AI: 8Y – 24X = 12
The best answer is D
Take 8Y – 24X = 12 and divide it by 8: Y – 3X = 1.5
Y = 3X + 1.5
We don’t know if 3X + 1.5 are bigger or smaller than 1.5 – 3X since X can be positive, negative or even zero The right answer is D
45
A: 11 out of 12 in percent terms
B: 91%
The best answer is A
Column A =
12
100 , 1
% 100 12
11
Go to the other column and check if 12 x 91 is greater than 1100:
12 x 91 = 1,092 and therefore it’s more than 91%
Column A is greater than column B
46
A: X – Y + Z
B: 15
AI: Y – X – Z > 15
The best answer is B
Take Y – X – Z > 15 and divide both sides by -1:
X – Y + Z < -15 (don’t forget to flip the inequality)
We can see that the expression in column A is smaller than that in column
B
47
A: 4/9 + 5/12
B: 4/7 + 5/11
The best answer is B
Trang 10A = 4/9 + 5/12 =
108
93 108
45 48
< 1
B = 4/7 + 5/11 =
77
79 77
35 44
> 1 and therefore column B is greater
48
A: 07
B: 70
The best answer is B
Zero raised to any positive power is zero, so Quantity A = 0
Any number raised to 0 is unity, so Quantity B = 1
49
A: 1
B: X
AI: 1 2
X
The best answer is A
Since
X
1
is negative X must the negative
If X is negative, column A is greater
50
A: 66
B: The average of the six numbers
AI: The sum of 6 even consecutive numbers is 396
The best answer is C
The average is the sum divided by the amount of numbers
The average of the 6 numbers is 396/6 = 66 and therefore the columns are equal to one another
51
A: X2Y3
B: X3Y2
AI: X < 0 and Y > 0
The best answer is A
Pick up numbers: For example, X= -1 and Y= 2
Column A = 1 x 8 = 8
Column B = -1 x 4 = -4
Trang 11We can see that column A is positive while B is negative and so A is the right answer
52
A: The smallest prime number smaller than 4
B: 3
The best answer is B
The smallest prime number smaller than 4 is 1 and not 3 and therefore column B is greater than column A
53
A: 1 – 4/17
B: 27/68 + 17/34
The best answer is B
Column A = 1 – 4/17 = 13/17 = 52/68
Column B = 27/68 + 34/68 = 61/68
Column B is greater than column A
54
A: (0.99)3(0.99)4
B: (0.99)8
The best answer is A
When dealing with fractions, the smaller the power, the largest the result
A = (0.99)7 while B = (0.99)8 and therefore column A is greater since the power of the fraction there is smaller
55
A: X
B: 7
AI: 7 X
The best answer is B
If 7 X, then –X = 7 and so X = -7
7 > -7 and so column B is greater than column A
56
A: X2.25 X 8 1.5 16
B: X1.5 4
Trang 12The best answer is C
Take a power of two on both sides to get:
A = X2.25 X 8 1.5 16
B = X1.5 42 X2.25 X 8 1.5 16
And so column A is equal to column B
57
A: 115
B: 100,000
The best answer is A
100,000 can be written as 105
Now, 115 > 105 and therefore column A is greater than column B
58
A:
2
2Y
B: Y
The best answer is D
For a positive Y, column A is equal to column B
Now, for a negative Y, column A is greater than column B
Since there is more than one answer, the right answer is D
59
A: X
B: 13
AI: XY = 156
Y < 11
The best answer is A
156 is a multiplication of 12 and 13
Since Y is smaller than 11, X must be larger than 13 in order for the multiplication XY to be equal to 156
Since X > 13, column A is greater than column B
60
A: 1/X – 1/Y
B: (X – Y)/(XY)
The best answer is D
Trang 13Simplify column B into the following: (X – Y)/(XY) = 1/Y – 1/X
Since we have no further information on X and Y, the answer cannot be obtained and the right answer is D
61
A: (X – Y)/(XY)
B: 0
AI: Y > X > 0
The best answer is B
The easiest way is to plug in numbers
Replace X with 1 and Y with 2
Column A = (1 – 2)/(1 x 2) = -1/2
Column B = 0
Therefore, column B is greater than column A
62
A: 2
3
7
B: 2
4
6
The best answer is B
Simplify both columns
Column A = 7 32 7 2 21 3 10 2 21
Column B = 6 42 6 2 24 4 10 2 24
We can see that the expression in column B is greater than that in column
A
63
A:
99
999
,
999
B: 1111
The best answer is A
Since its hard calculating the expression in column A, do the following: Multiply 99 with 1111, the result is far less than 999,999 and therefore column A is much bigger than column B
64
A: One half of 40% of 65
B: One fourth of 35% of 140
Trang 14The best answer is A
10
260 2
1 65 100
40 2
1
4
49 10
490 4
1 10
14 35 4
1 140 100
35 4
1
We can see that column A is greater than column B
65
A: One seventh of 25% of 336
B: One sixth of 20% of 360
The best answer is C
7
84 100
8400 7
1 336 100
25 7
1
6
72 36 2 6
1 360 100
20 6
1
We can see that column A = column B and so the answer is C
66
A:
5 9 25 0
5 0 10
5 0 1
5
B: 6.5
The best answer is B
Simplify the expression in column A:
6 5 0
5 0 5 5 9 5 0
5 0 10
5 0 5
5 9 25
.
0
5
.
0
10
5
0
1
Column B is greater than column A by 0.5 and so the answer is B
67
A:
36
.
0
64
.
0
96
45
B:
36
.
0
63
.
0
36
177
The best answer is B
1
141 36 0 64 0
96 45
Trang 15
Column B =
99 0
141 36 0 63 0
36 177
, which is a little bigger than 141 and so column B is greater
68
A: (X2 + Y2)
B: (X + Y)2
AI: 0 > X > 1 > Y
The best answer is B
Column A = X2 + Y2
Column B = X2 + Y2 + 2XY, subtract X2 + Y2 from both sides
Column A = 0 while column B = 2XY
2XY is greater than zero since X and Y are positive and therefore column
B is greater than column A
69
A: 7/5
B: Y/X
AI:
7
2
X
Y
X
The best answer is A
Take
7
2
X
Y
X
and simplify it: 1 – Y/X = 2/7 Y/X = 1-2/7 = 5/7 Column A is greater than 1 where column B is smaller than 1 and so the answer is A
70
A:
0005
.
0
006
.
0
B:
0005
.
0
0008
.
0
The best answer is A
Move the decimals to the right, keep track of how many you moved
5 0
6 0005 0
006 0
Column B =
5
8 0005 0
0008 0
, which is smaller than 12 and so column A is the greatest
Trang 1671
A: X + X2 – X3 + X4
B: X4 – X2 + X3 – X
AI: X = -3
The best answer is B
The best way is to replace X with -3
Column A = -3 + 9 – 27 + 81 = 60
Column B = 81 – 9 + 27 – 2 = 97, which is greater than column A
72
A: Y – X
B: Y
AI: X and Y are positive prime numbers
X + Y = 8, Y > X
The best answer is B
There are two choices: 1 and 7 or 3 and 5
In the first option: X=1, Y=7; Column A = 6 and B = 7
In the second option: X=3, Y=5; Column A = 2 and B = 5
In both cases column B is greater than A and therefore B is the right answer
73
A: Y – X
B: 7
AI: X and Y are positive prime numbers
X + Y = 12, Y > X
The best answer is D
There are two choices: 1 and 11 or 5 and 7
In the first option: X=1, Y=11; Column A = 10 and B = 7
In the second option: X=5, Y=7; Column A = 2 and B = 7
The answer is different each time and so the right answer is D
74
A: A + B
B: 18
AI: A x B = 17