GMAT® Official Guide 2019 Quantitative Review
(2) Given that k < 19, it is possible to have
k > 9 (for example, k = 15) and it is possible
to not have k > 9 (for example, k = 5); NOT
sufficient.
The correct answer is A;
statement 1 alone is sufficient.
DS05518- In the sequence S of numbers, each term after the first
two terms is the sum of the two immediately preceding
terms. What is the 5th term of S?
(1) The 6th term of S minus the 4th term equals 5.
(2) The 6th term of S plus the 7th term equals 21.Arithmetic c;ec Jer r c;
If the first two terms of sequence S are a and b,
then the remaining terms of sequence S can be
expressed in terms of a and b as follows.
/
nth term of
n sequence S1 a2 b3 a+b
(^4) a +2b
5 2a+ 3b
6 3a+ 5b
.^7 5a+ 8b
For example, the 6th term of sequence S is
3a + 5b because (a+ 2b) + (2a + 3b) = 3a + 5b.
Determine the value of the 5th term of sequence
S, that is, the value of 2a + 3b.
(1) Given that the 6th term of S minus
the 4th term of Sis 5, it follows that
(3a + 5b) - (a+ 2b) = 5. Combining like
terms, this equation can be rewritten as
2a + 3b = 5, and thus the 5th term of
sequence Sis 5; SUFFICIENT.
(2) Given that the 6th term of S plus the
7th term of Sis 21, it follows that
(3a + 5b) + (5a + 8b) = 21. Combining like
terms, this equation can be rewritten as
8a + 13b = 21. Letting e represent the 5th
term of sequence S, this last equation is
equivalent to 4(2a + 3b) + b = 21, or 4e + b = 21,
which gives a direct correspondence
between the 5th term of sequence S and
the 2nd term of sequence S. Therefore, the
5th term of sequence Scan be determined
if and only if the 2nd term of sequence S
can be determined. Since the 2nd term of
sequence S cannot be determined, the 5th
term of sequence S cannot be determined.
For example, if a= 1 and b = 1, then
8a + 13b = 8(1) + 13(1) = 21 and the 5th
term of sequence Sis 2a + 3b = 2(1) + 3(1) = 5.
However, if a = 0 and b =^21 , then
13
8a+ 13b = 8(0)+ 13( :~) = 21
and the 5th term of sequence Sis
2a+ 3b = 2(0)+ 3(^21 ) =^63 - NOT
13 13'
sufficient.
The correct answer is A;
statement 1 alone is sufficient.
DS01121
- If 75 percent of the guests at a certain banquet
ordered dessert, what percent of the guests ordered
coffee?
(1) 60 percent of the guests who ordered dessert
also ordered coffee.
(2) 90 percent of the guests who ordered coffee
also ordered dessert.Arithmetic c n f ..
Consider the Venn diagram below that displays
the various percentages of 4 groups of the guests.
Thus, x percent of the guests ordered both dessert
and coffee and y percent of the guests ordered
coffee only. Since 75 percent of the guests
ordered dessert, (75 - x)o/o of the guests ordered
dessert only. Also, because the 4 percentages
represented in the Venn diagram have a total
sum of 100 percent, the percentage of guests
who did not order either dessert or coffee is
100 - [(75 - x) + x + y] = 25 - y. Determine
the percentage of guests who ordered coffee, or
equivalently, the value of x + y.