A: The quantity in Column
A is greater.
B: The quantity in Column B is greater.
C: The two quantities are equal.
D: The relationship cannot be determined from the information given.
B: The quantity in Column B is greater.
C: The two quantities are equal.
D: The relationship cannot be determined from the information given.
1.
Column A
x<0 Column
B
x2-x5
0
Sol: If x=-1 then x2-x5
=(-1)2- (-1)5 = 1- -1=1+1 =2 and column A is
larger. If x=-2 , then x2-x5
=(-2)2
–(-2)5=4—32 =4+32 =36 and column A is larger. Finally, if
x=-1/2 then x2- x5
= (-1/2)2- (-1/2)5 = ¼
- -1/32 = 9/32 and column A is still
larger.
This covers the three types of negative numbers, so we can
confidently conclude the answer is A.
2. Column A
Column B
ab2
a2b
Sol: If a=0 both columns are equal
zero. If a=1 and b=2 the two columns are unequal.
This is a double case and answer is D.
3. Column
A A
precious stone was accidentally Column B
dropped and broke into 3 pieces of
equal
weight. The value of this
type of
stone is always
proportional
to the square of its weight.
The
value of the 3 broken
The value of the original stone
pieces
together
Let x
be the weight of the full stone. Then the weight of each of the three
broken pieces is x/3.
Since
we are given that the value of the stone is proportional to the square of its
weight, we have that if kx2 is the value of the full stone,
then the value of each small stone should be k(x/3)2, where k
is the proportionality constant. Hence, the value of the three
pieces together is
k(x/3)2 + k(x/3)2+ k(x/3)2=3 kx2/9
=
3kx2/9
=kx2/3
Hence,
Column A equals kx2/3 and Column B equals kx2.
Hence, Column A is one third of Column B. The answer is (B).
4.
Column A a
and b are positive.
Column B
(a + 6) : (b + 6) = 5 : 6
a +10/b +10 1
Since a and b are positive, a
+ 6 and b + 6 are positive. From the ratio (a + 6) : (b +
6) = 5 : 6, we get a + 6/b + 6 =5/6 . Since 5/6 < 1, a +
6 < b + 6. Adding 4 to both sides yields a + 10 < b +
10. Since b is positive, b + 10 is positive. Dividing the
inequality by b + 10 yields
a +10/b +10 < 1.
Hence, Column A < Column B, and
the
answer is (B).
5.
Column A 12
students from section A and 15
Column B
students from section B failed an
Anthropology exam.
Thus, equal
percentage of attendees failed the
exam from either section.
Number
of attendees for the Number
of attendees for the
exam
from section A
exam from section B
Given
that an equal percent of attendees failed the exam in sections A and B. Let x
be the percent. If a students took the exam from section A and b students
took the exam from section B, then number of students who failed from
the sections would be a(x/100) and b(x/100),
respectively. Given that the two equal 12 and 15, respectively, we have a(x/100)
= 12 and b(x/100) = 15. Since 12 < 15, a(x/100)
< b(x/100). Canceling x/100 from both sides yields a
< b. Hence, Column B > Column A, and the answer is (B).
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