DSJ6470
266.After winning 50 percent of the first 20 games it played,
Team A won all of the rema皿ng games it played. What
was the total number of games that Team A won?
(1) Team A played 25 games altogether.
(2) Team A won 60 percent of all the games it played.Arithmetic
Let r be the number of如remaining games
played, all of which the team won. Since the teamwon (50%)( (^20) ) = 10 of the first 20 games and the r
remaining games, the total number of games the
team won is 10 + r. Also, the total number of games
the team played is 20 + r. Determine如value of r.
(1) Given that the total number of games
played is 25, it follows that 20 + r = 25, or
r= 5; SUFFICIENT.
(2) It is given that the total number of
games won is (60%)(20 + r), which can
be expanded as 12 + 0.6r. Since it is also
known that the number of games won is 10
- r, it follows that 12 + 0.6r = 10 + r.
Solving this equation gives 12 - 10 = r - 0.6r,
or 2 = 0.4r, or r = 5; SUFFICIENT.
Th e correct answer 1s D;
each statement alone is sufficient.
DSl 7181
267.Is x between O and 1?
(1) x^2 is less than x.
(2) 3. x 1s pos1t1ve.
Arithmetic
(1) Since x2 is always nonnegative, it follows
that here x must also be nonnegative, that is,
greater than or equal to 0. If x = 0 or 1, then
x2 = x. Furthermore, if xis greater than 1,
then x2 is greater than x. Therefore, x must
be between O and 1; SUFFICIENT.
(2) If x^3 is positive, then xis positive, but x can
be any positive number; NOT sufficient.
1h e correct answer 1s A;
statement 1 alone is sufficient.
DS04083
268.If m and n are nonzero integers, is mn an integer?
(1) nm is positive.
(2) nm is an integer.
5.5 k, S:iff,� e- Answer Explanations
Arithmetic
It is useful to note that if m > 1 and n < 0, then
0<旷<1, and therefore mn will not be an
integer. For example, if m =^3 and n = -2, then
旷=3-^2 =-^1 =^1 -.
(^32 9)
(^1 ) Although it is given that n气s positive, mn
can be an integer or mn can fail to be an
integer. For example, if m = 2 and n = 2,
then nm = 2^2 = 4 is positive and mn = 2^2 = 4
is an integer. However, if m = 2 and n = -2,
then nm= (-2)^2 = 4 is positive and
m" = 2 -^2 =—1 1 = -is not an integer; NOT
22 4
sufficient.
(^2 ) Although it is given that nm is an integer,
旷can be an integer or mn can fail to be
an integer. For example, if m = 2 and n = 2,
then nm = 2^2 = 4 is an integer and m" = 2^2 = 4
is an integer. However, if m = 2 and
n = - 2, then nm= (- (^2) )^2 = 4 is an integer
and m" = r^2 = -^1 = - is not^1 an integer;
22 4
NOT sufficient.
Taking ( (^1) ) and ( (^2) ) together, it is still not possible
to determine if mn is an integer, since the same
examples are used in both ( (^1) ) and ( 2 ) above.
Th e correct answer 1s E;
both statements together are still not sufficient.
DS16034
- What is the value of xy?
(1) x+y=lO
(2) X — Y=6Algebra (r(1) Given x + y = 10, or y = 10 - x, it follows
that xy = x(lO - x), which does not have a
unique value. For example, 正x = 0, then xy= ( (^0) )( (^10) ) = (^0) , but if x = 1, then
xy = ( (^1) )(9) = 9 ; NOT sufficient.
(2) Given x - y = 6, or y = x - 6, it follows that
xy = x(x - (^6) ), which does not have a unique
value. For example, if x = 0, then xy = ( (^0) )
(-6) = 0, but if x = 1, then
xy = ( (^1) )(- (^5) ) = -5; NOT (^) sufficient.