5.5 :c1 S·1ff1C'c n Answer Explanations
Coffee
25 - y
(1) Given that xis equal to 6 0 percent of 75, or
4 5, the value of x + y cannot be determined;
NOT sufficient.
(2) Given that 90 percent of x + y is equal to x, it
follows that 0.9(x + y) = x, or 9 (x + y) = lOx.
Therefore, 9x + 9y = lOx, or 9y = x. From this
the value of x + y cannot be determined. For
example, if x = 9 and y = l, then all
4 percentages in the Venn diagram are
between O and 100, 9y = x, and x + y = 10.
However, if x = 18 and y = 2, then all
4 percentages in the Venn diagram are
between O and 100 , 9 y = x, and x + y = 20 ;
NOT sufficient.
Given both (1) and (2), it follows that x = 45
and 9y = x. Therefore, 9y = 45, or y = 5, and hence
X + J = 4 5 + 5 = 50.
Th e correct answer 1s C·
both statements together are sufficient.
DS05302
- A tank containing water started to leak. Did the tank
contain more than 30 gallons of water when it started
to leak? (Note: 1 gallon= 128 ounces)
(1) The water leaked from the tank at a constant
rate of 6.4 ounces per minute.
(2) The tank became empty less than 12 hours after
it started to leak.
Arithmetic
(1) Given that the water leaked from the tank
at a constant rate of 6.4 ounces per minute,
it is not possible to determine if the tank
leaked more than 30 gallons of water. In
fact, any nonzero amount of water leaking
from the tank is consistent with a leakage
rate of 6. 4 ounces per minute, since nothing
can be determined about the amount of
time the water was leaking from the tank;
NOT sufficient.
(^2 ) Given that the tank became empty in
less than 12 hours, it is not possible to
determine if the tank leaked more than 30
gallons of water because the rate at which
water leaked from the tank is unknown. For
example, the tank could have originally
contained 1 gallon of water that emptied in
exactly 10 hours or the tank could have
originally contained 31 gallons of water
that emptied in exactly 10 hours; NOT
sufficient.
Given ( (^1) ) and ( (^2) ) together, the tank emptied
at a constant rate of
(^6.^4 二)(^60 气)(古�)=(6� 芒启
(64)(6) -=3gal —gal for less than 12 hours.
(64)(2) hr hr
If tis the total number of hours the water leaked
from the tank, then the total amount of water
emptied from the tank, in gallons, is 3t, which is
therefore less than (3)(12) = 3 6. From this it is
not possible to determine if the tank originally
contained more than 30 gallons of water. For
example, if the tank leaked water for a total of 11
hours, then the tank originally contained
(3)(11) gallons of water, which is more than
30 gallons of water. However, if the tank leaked
water for a total of 2 hours, then the tank
originally contained (3)(2) gallons of water, which
is not more than 30 gallons of water.
Th e correct answer 1s E·
both statements together are still not sufficient.
D$12752
- In the xy-plane, lines k and€ intersect at the point
(1, 1). Is the y-intercept of k greater than the y-intercept
of£?
(1) The slope of k is less than the slope of£.
(2) The slope of£is positive.
Algebra
Let m1 and m2 represent the slopes oflines k
and£ , respectively. Then, using the point-slope
form for the equation of a line, an equation of
line及can be determined: y - 1 = m 1 (x — (^1) ), or
y=m 1 x+(l — m 1 ). Similarly, an equation for
line£ is y = m2x + ( 1 — m2). Determine if
(^1 - m 1 ) > ( (^1) - m 2 ), or equivalently if^ m 1 < mz.
L',
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