(^1 )
(^2 )
This indicates that 280 of the 400 numbers in
the list are less than the average of the 400
numbers. This means that both the 200th and
the 201st numbers, as well as the median, are
less than the average and, therefore, that the
average is greater than the median;
SUFFICIENT.
This indicates that (0.3)(400) = 120 of the
numbers are greater than or equal to the
average. This means that the other 400 - 120
= 280 numbers are less than the average,
which is the same as the information in (l);
SUFFICIENT.
1h e correct answer 1s D;
each statement alone is sufficient.
DS03678
- In a two-month survey of shoppers, each shopper bought
one of two brands of detergent, X or Y, in the first month
and again bought one of these brands in the second
month. In the survey, 90 percent of the shoppers who
bought Brand X in the first month bought Brand
X aga们in the second month, while 60 percent of the
shoppers who bought Brand Y in the first month bought
Brand Y aga们in the second month. What percent of the
shoppers bought Brand Y in the second month?
(1) In the first month, 50 percent of the shoppers
bought Brand X.
(2) The total number of shoppers surveyed was 5,000.
Arithmetic
This problem can be solved by using the following
contingency table where A and B represent,
respectively, the number of shoppers who bought
Brand X and the number of shoppers who bought
Brand Yin the first month; C and D represent,
respectively, the number of shoppers who bought
Brand X and the number of shoppers who bought
Brand Yin the second month; and Trepresents
the total number of shoppers in the survey. Also in
the table, 0. 9A represents the 90% of the shoppers
who bought Brand X in the first month and also
bought it in the second month, and O.lA
represents the (100 - 90)% = 10% of the shoppers
who bought Brand X in the first month and Brand
Yin the second month. Similarly, 0.6B represents
the 60% of the shoppers who bought Brand Y in
the first month and also bought it in the second
month, and 0.4B represents the (100- (^60) )% =
40% of the shoppers who bought Brand Yin the
first month and Brand X in the second month.
5.5 t,, Sutf Cl€ 1 Answer Explanations
/夕
Second Month \
X y Total
X 0.9A O.lA A
First Y 0.4B 0.6B B
Month
\ Total C D T
Determine the value of f2 as a percentage.
T
(1) This indicates that 50% of the shoppers
bought Brand X in the first month, so A=
0.5T It follows that the other 50% of
the shoppers bought Brand Yin the first
month, so B = 0.5T Then, D = 0.1A +
0.6B = 0.1(0.5T) + 0.6(0.5乃= 0.05T+
0.30T= 0.35T It follows that—D = 0.35T =
T T
0.35, which is 35%; SUFFICIENT.
(2) This indicates that T= 5,000, as shown in
the following table:
/
Second Month
\
X Y Total
X 0.9A 0.1A A
First Y
Month 0.4B 0.6B B
\ Total C D 5,000
But not enough information is given to be able to
determine Dor Das a percentage of 5,000; NOT
sufficient.
1h e correct answer 1s A·, (^)
statement 1 alone is sufficient.
DS15902
- If m and n are positive integers, ism+ n divisible by 4?
(1) m and n are each divisible by 2.
(2) Neither m nor n is divisible by 4.
Arithmetic
Determine whether the sum of the positive
integers m and n is divisible by 4.
(1) It is given that mis divisible by 2 and n is
divisible by 2. If, for example, m = 2 and n =
2, then each of m and n is divisible by 2 and
m + n = 2 + 2 = 4, which is divisible by 4.