taking (1) and ( 2 ) together allows for both沪-y三
(3)(6) =^18 and x^2 千= (-3)(6) = -18.
Th e correct answer 1s E·
both statements together are still not sufficient.
DS01267
284.For each landscaping job that takes more than
4 hours, a certain contractor charges a total of
r dollars for the first 4 hours plus 0.2r dollars for each
additional hour or fraction of an hour, where r > 100.
Did a particular landscaping job take more than
10 hours?(1) The contractor charged a total of $288 for the
job.
(2) The contractor charged a total of 2.4r dollars for
the job.Algebra
If y represents the total number of hours the
particular landscaping job took, determine
if y> 10.(1) This indicates that the total charge for
the job was $288, which means that
r+ 0.2r(y—4) = 288. From this it cannot be
determined if y > 10. For example, if r = 120
and y = 11, then 120 + 0.2(120)(7) = 288,
and the job took more than 10 hours.
However, if r = 160 and y = 8, then
160 + 0.2(160)(4) = 288, and the job took
less than 10 hours; NOT sufficient.
(2) This indicates that r + 0.2r(y- 4) = 2.4r,
from which it follows that
r + 0.2ry - 0.8r = 2.4r use distributive
property
0.2ry = 2.2r subtract (r -0.8r)
from both sides
y = 11 divide both sides
by 0.2r
Therefore, the job took more than 10
hours; SUFFICIENT.Th e correct answer 1s B·，
statement 2 alone is sufficient.
DS17600- If x^2 = 2 x, what is the value of x?
(1) 2x= (1J
3
(2) X =^2 x-^25.5 Answer ExplanationsAlgebra
Given x^2 = 2 x, determine the value of x. Note
that x ct- 0 because 02 = 0 and 2°= 1.
3
(1) This indicates that 2x=尸），so2x=立and
2 8
l6x=正.Since x ct-0, then 16 =正，
so x = -4 or x = 4. However, (-4)^2 = 16 and尸＝一^1 ，sox ct--4. Therefore, x = 4;
16
SUFFICIENT.( 2 ) This indicates that x = 2 x -^2 , so x = 2^2 x and
2
4x = Y Since it is given that x^2 = 2飞then
4 x = x 2 and, because x ct- 0, it follows that
x = 4; SUFFICIENT.Th e correct answer 1s D·，
each statement alone is sufficient.
0S01169- The sequence s1, s 2 , s3, ... , Sn, ... is such that
Sn=—^1 -^1 for all integers n�l. If k is a positive
n n+l
integer, is the sum of the first k terms of the sequence
greater than—?^9
10
(1) k>lO
(2) k< 19Arithmetic
The sum of the first k terms can be written as(½ 勹忖-½)+... +(卢-1飞－上）
=1+(上片(_1.+1.)+... +(_1.+勹__1__
2 2 3 3 k k妇 1=1—-^1 —.
妇1
Therefore, the sum of the first k terms is
greater than—^9 if and only if 1-—^1 —>—^9 , or
10 k+l 10
1-—^9 >—^1 , or->-—.^1 1 Multiplying both
10 k+l 10妇1
sides of the last inequality by lO(k + 1) gives theequivalent condition女+1 > 10, or女>9.(^1 ) Given that k > 10, then it follows that左> 9;
SUFFICIENT