... expression given to us can be easily simplified.
5 .28 222 /1)14 (23 214 32
555555 525 55
XXXXXX
Compare the powers of both sides: 2X – 2 = 8X + 2. 5 6X = -4.5
X = -3/4 and therefore X ... consecutive numbers.
X
2
– Y
2
= 27
The best answer is B.
Simplify the expression: X
2
– Y
2
= (X – Y)(X + Y) = 1(X + X – 1) = 2X – 1.
2X – 1 = 27 2X = 28 ...
...
A: X
B: Y
AI: 25 6
2
4
25
3
YX
YX
The best answer is A.
Rewrite the expression:
822 526
25
26
25
3
22 2
2
2
2
4
YXYXYX
YX
YX
YX
YX
X-Y – 2
=8.
And therefore ... – 2 = 2.
The third term is 4 (2) – 2 = 6.
The fourth term is 4(6) – 2 = 22 .
The fifth term is 4 (22 ) – 2 = 86.
The fifth term is 4(86) – 2 = 3 42. Stop here s...
... diameter is
4
2
d
.
The area of the first circle is
4
2
1
d
.
The area of the second circle is
4
2
2
d
.
We know that
4
2
1
d
= 2 x
4
2
2
d
22
2
1
2
2
2
1
d
d
dd ... AC
2
> AB
2
+ BC
2
The best answer is A.
Draw a sketch of the triangle.
If the triangle was a right triangle (ABC = 90
0
), AC
2
= AB
2
+ BC
2
.
Since the AC...
... 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. ...
The best answer is B.
Column A = X
2
+ Y
2
Column B = X
2
+ Y
2
+ 2XY, subtract X
2
+ Y
2
from both sides.
Column A = 0 while column B = 2XY.
2XY is greater than...
... liters in 2 minute
The best answer is A.
Question
s
Wor
Time
Work
s
Wor
Time
Work
Data
2
ker
2
2
1
ker
1
1
Question
Liters
Data
7
60
6
2
3
Liters = 105
6
2
3760
... 10 meters per hour.
2. 5 Km = 25 00 meters.
The time it would take him to walk that distance is (25 00)/(10) = 25 0 hours.
Column A is ten times bigger than column B.
23 ....
... 16
3
x 32
2
x 8
B: 64
2
x 4
3
x 16
The best answer is A.
Translate all the numbers to a base of 2.
Column A = 2
12
x 2
10
x 2
3
= 2
25
.
Column B = 2
12
x 2
6
x 2
4
= 2
22
.
We ... number there is greater.
21 .
A:
3
2
22
YXXY
B:
2
3
1
YX
The best answer is C.
Simplify the expression in column A:
3
)(
3
2
3
2
222 22...
...
2.
A: (X + Y)(X – 2Y)
B: XY + 8
The best answer is D.
Open the parenthesis in column A: X
2
– 2XY +YX – 2Y
2
= X
2
– XY – 2Y
2
.
Subtract XY – 8 from both sides to get:
A = X
2
...
24 .
A: X
2
B: (X – Y)
2
AI: X > 0 > Y
The best answer is B.
Column B can be written as X
2
– 2XY + Y
2
.
Subtract X
2
from both columns to get 0 in column A and Y
2...
... = Z
12
21
.
Column A is equal to Z +
ZZ
12
33
12
21
and column B is equal to
Z
12
42
, which is
greater and so B is the answer.
16.
A: Q + 2W – P
B: 2P + 2Q
AI: 0.5Q = 1.5W = 2P
... and simplifications
36.
A: (Y – 2)
2
B: 2 – Y
AI: 0 < Y < 1
The best answer is A.
(Y – 2)
2
? 2 – Y
-(Y – 2) (2 – Y) ? 2 – Y
2 – Y ? 1
2 – Y is greater...
... = (20 1 + 20 2 + 20 3 + 20 4 + … + 25 0).
Y – X = (20 1 – 101) + (20 2 – 1 02) + … + (25 0 – 150) = 100 + 100 + … + 100 =
100 x 50 = 5,000. And therefore the answer is C.
3.
A:
2
R
B: ... square is
2
2
aa
.
The area of the shaded region is
22
aR
.
Since the areas are equal we can write the equation:
22 222
2 RaaRa
.
And therefore a =
2...