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"From a group of seven undergraduate students (A, B, C, D, E, F, and G),
four will
be selected to give a presentation to the students' union. The following
conditions
must be met:
- Either A or B must
be selected, but A and B cannot both be selected.
- Either E or F
must
be
selected, but E and F cannot both be selected.
- E cannot be
selected
unless C
is selected.
- G cannot be selected
unless B is selected.
If we know that F is not selected to present,
how
many
different groups of four can be made, following the above criteria?"
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"A university library budget committee must reduce exactly five of eight
areas of
expenditure—G, L, M, N, P, R, S, and W—in accordance with the following
conditions:
If both G and S are reduced, W is
also reduced.
If N is reduced, neither R nor S is reduced.
If
P is
reduced, L is not reduced.
Of the three areas L, M, and R, exactly
two
are
reduced. If both M and R are reduced, which one
of the following is a pair of areas neither of which could be reduced?"
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"Seven piano students—T, U, V, W, X, Y, and Z—are to give a recital, and
their
instructor is deciding the order in which they will perform. Each
student
will play
exactly one piece, a piano solo. In deciding the order of performance,
the
instructor must
observe the following restrictions:
X cannot play first or second.
W cannot play until X has
played.
Neither T nor Y can play seventh.
Either Y or Z must play
immediately
after W
plays.
V must play either immediately
after or immediately before U plays.
If V plays first, which one of the following must be true?"
-
"A charitable foundation awards grants in exactly four areas—medical
services,
theater arts, wildlife preservation, and youth services—each grant being
in
one of
these areas. One or more grants are awarded in each of the four quarters
of
a
calendar year.
Additionally, over the course of a calendar year, the following must
obtain:
Grants are awarded in all four areas.
No more than six
grants
are
awarded.
No grants in the same area are awarded in the same quarter
or
in
consecutive quarters.
Exactly two medical
services grants are awarded.
A wildlife preservation grant is
awarded
in the
second quarter.
If a wildlife preservation grant and a youth
services grant
are awarded in the same quarter of a
particular calendar year, then any of the following could be true that
year
EXCEPT:"
-
"On a particular Saturday, a student will perform six activities—grocery
shopping,
hedge trimming, jogging, kitchen cleaning, laundry, and motorbike
servicing.
Each
activity will be performed once, one at a time. The order in which the
activities
are
performed is subject to the following conditions:
Grocery shopping has to be immediately after hedge trimming.
Kitchen
cleaning has to be earlier than grocery shopping.
Motorbike
servicing
has to be
earlier than laundry.
Motorbike
servicing has to be either immediately before or immediately after
jogging.
Which one of the following, if substituted for the condition that
motorbike
servicing has to be earlier than laundry,
would have the same effect in determining the order of the student’s
activities?"
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"If all beaches were publicly owned, we would have to rely on government
funds to
maintain them. It is true that more people would have access to the
ocean
and
beaches, but at what cost? If the beaches are not cared for adequately,
soon
there
will be
nothing left worth having access to. We should consider carefully before
nationalising more coastal property. Which of the following, if true,
would
most
weaken the argument above?"
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The minimum number of straight lines required to make the given figure
are
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If white is called black, black is called red, red is called yellow,
yellow
is
called green, green is called blue, blue is called violet and violet is
called
orange, what would be the colour of human blood?
-
"A university library budget committee must reduce exactly five of eight
areas of
expenditure—I, J, K, L, M, N, O and P—in accordance with the following
conditions:
If both I and O are reduced, P is also reduced.
If L is
reduced,
neither N nor O is reduced.
If M is reduced, J is not reduced.
Of
the
three areas J, K, and N exactly two are reduced.
If both K and N are reduced, which one of the following is a
pair
of areas
neither of which could be reduced?"
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The number of triangles in the given figure are