Non Verbal Reasoning Questions and Answers

Parrot is captured in Cage in same way Man is captured in Prison.

Mango is Fruit in same way Potato is modified Stem.

Dog makes noise known as Bark and Goat makes noise known as Bleat.

This question concerns a committee's decision about which five of eight areas of expenditure to reduce. The question requires you to suppose that M and R are among the areas that are to be reduced, and then to determine which pair of areas could not also be among the five areas that are reduced.

The fourth condition given in the passage on which this question is based requires that exactly two of M, R, and L are reduced. Since the question asks us to suppose that both M and R are reduced, we know that L must not be reduced:

• Reduced: M, R
• Not reduced: L

The second condition requires that if N is reduced, neither R nor S is reduced. So N and R cannot both be reduced. Here, since R is reduced, we know that N cannot be. Thus, adding this to what we've determined so far, we know that L and N are a pair of areas that cannot both be reduced if both M and R are reduced:

• Reduced: M, R
• Not reduced: L, N

Answer choice (C) is therefore the correct answer, and you are done.

This question deals with an ordering relationship defined by a set of conditions concerning when seven piano students will perform. As an aid in visualizing this problem you can draw a simple diagram that shows the seven recital slots arranged in order from left to right. Student V is shown in the first slot, as specified by the supposition that "V plays first":

We can immediately fill in one of the empty slots in the diagram. The condition that "V must play either immediately after or immediately before U plays" tells us that U must occupy the second slot in the recital schedule. This is shown below:

Since the question asks us what must be true, we can eliminate incorrect responses by showing that they could be false. Response (A) is incorrect because the statement that "T plays sixth" is not necessarily true — we can place T in one of the slots other than sixth and still meet all the conditions of the problem. One such recital schedule, with T playing third, is shown in the diagram below:

This schedule can be derived as follows:

1. With V, U, and T in the first three positions, there are four positions left for W, X, Y, and Z.
2. W must come after X — because of the condition that "W cannot play until X has played" — so if X is fourth and W is fifth, this condition will be met.
3. This leaves two possible slots for Y and Z. Y cannot play seventh because of the condition that "Neither T nor Y can play seventh." Suppose, then, that Y is sixth and Z is seventh.

A check will verify that this schedule meets the conditions of the problem, including the one that "Either Y or Z must play immediately after W plays."

The schedule shown in the diagram also demonstrates that response (B)is incorrect. In it, X plays fourth, so it is not correct that the statement, "X plays third," must be true.

Response (C), "Z plays seventh," is the credited response. We can show Z must be seventh by demonstrating that:

• all the conditions can be met with Z in the seventh slot, and
• some of the conditions would be violated with Z in any slot other than seventh.

To demonstrate that Z can play seventh, you can refer to the schedule that was developed for the discussion of response (A), above. In it, Z plays seventh, and the supposition given in the question and all the conditions in the passage are met.

To demonstrate that Z cannot play in a slot other than seventh, we can attempt to find another student to play seventh. We already know that neither U nor V can play seventh. Hence, there are four remaining players: T, W, X, and Y. However, a review of the conditions shows that none of those players can play seventh:

• The third condition states that "Neither T nor Y can play seventh."
• W can't play seventh, because there must be a slot following W's in order to meet the condition, "Either Y or Z must play immediately after W plays." If W plays seventh, then there is no such slot left for Y or Z.
• For a similar reason X can't play seventh, because there must be a slot following X's in order to meet the condition, "W cannot play until X has played."

Since Z can play seventh and no other player can, then the statement that Z must play seventh is correct and (C) is the credited response.

Response (D) is incorrect because it is not necessarily true that "T plays immediately after Y." In our discussion of response (A), we developed a schedule in which T plays third and Y plays sixth, yet all conditions are satisfied.

This question involves the same original conditions as the previous problem, but it begins with an additional supposition: "U plays third." You must determine what effect this supposition would have on the possible positions in which Y can appear in the recital schedule.

The correct response is (D): Y can play as late as sixth. The diagram below shows a recital order that meets all the conditions and has Y performing in the sixth position:

One strategy for arriving at this solution is to work backward to see which position is the latest in which we can place Y and at the same time produce a recital schedule that meets all the conditions.

Using that approach, we immediately see that Y cannot play as late as seventh, because of the condition that "Neither T nor Y can play seventh." Backing up and placing Y sixth, we can begin to fill in the schedule, as follows:

This schedule has five empty slots, into which we must fit players T, V, W, X, and Z. The following is a series of reasoning steps that can be used:

1. From our analysis of the previous question, we know that players T, W, and X cannot play seventh, but that Z can, so we can tentatively place Z in the seventh slot.
2. We also know that "Either Y or Z must play immediately after W plays." If we place W in the fifth slot, this condition will be met.
3. By placing V in the second slot, we can meet the condition that "V must play either immediately after or immediately before U plays."
4. We must place the remaining two players, T and X, in the two remaining slots, the first and the fourth. Because the first condition states that "X cannot play first...," we will place X in the fourth slot and T in the first. These positions will meet the conditions that apply to T and X: T will avoid playing seventh and X will play before W.
5. Since Y can play as late as sixth, response (D) is the correct solution.

This question deals with the awarding of grants during the quarters of a calendar year. As an aid in visualizing this problem, we can set up a simple table with columns representing the four quarters. Since the fifth condition in the passage states that "[a] wildlife preservation grant is awarded in the second quarter," we know that all possible solutions for any question based on the passage must include a wildlife preservation grant awarded in the second quarter, which we can represent like this:

The particular question here begins with the added supposition that "a wildlife preservation grant and a youth services grant are awarded in the same quarter of a particular calendar year." One possible way this could be satisfied is to have a youth services grant awarded in the second quarter in addition to the wildlife grant awarded in that quarter:

Another possibility would be to have a wildlife preservation grant and a youth services grant both being awarded in some quarter other than the second quarter. Given the condition that "[n]o grants in the same area are awarded in the same quarter or in consecutive quarters," the only quarter in which a wildlife preservation grant could be awarded in addition to the second quarter is the fourth quarter. So the only alternative way to satisfy the added supposition is if both a wildlife preservation grant and a youth services grant are awarded in the fourth quarter:

So far, then, we've determined that for this question there must be a youth services grant awarded in the second quarter or the fourth quarter.

Each of the incorrect answer choices for this question is a statement that could be true. The question asks you to identify the exception; that is, you need to find the statement that cannot be true. The correct answer choice is (D), which states: "A youth services grant is awarded in the third quarter." This could not be true without violating the third condition, which specifies that "[n]o grants in the same area are awarded in the same quarter or in consecutive quarters." We saw above that a youth services grant must either be awarded in the second quarter or the fourth quarter. On either possibility, awarding a youth services grant in the third quarter would result in two consecutive quarters where the youth services grant is awarded:

or:

In both cases, two youth services grants would be awarded in consecutive quarters, in violation of the third condition.

To see that each of the other answer choices could be true, it will suffice to construct a possible outcome for each one that is consistent with the supposition given in the question and the conditions in the passage. Consider the following possible outcome:

A quick check of the conditions shows that this satisfies all of the conditions for the problem:

• A wildlife preservation grant and a youth services grant are awarded in the same quarter of a particular calendar year.
• Grants are awarded in all four areas. (The table includes at least one of each of the four letters — M, T, W, and Y.)
• No more than six grants are awarded. (The table contains exactly six entries.)
• No grants in the same area are awarded in the same quarter or in consecutive quarters. (In the table above, only T and M are repeated, and neither repetition appears in the same or consecutive columns.)
• Exactly two medical services grants are awarded. (The table contains exactly two M's, in columns 2 and 4.)
• A wildlife preservation grant is awarded in the second quarter.

Notice that in this possible outcome, a medical services grant is awarded in the second quarter (answer choice (A)) and a theater arts grant is awarded in the first quarter (answer choice (B)). So answer choices (A) and (B) are both incorrect.

Now consider the following possible outcome:

A check of the conditions shows that this satisfies the supposition and all of the conditions. In this outcome, a theater arts grant is awarded in the second quarter (answer choice (C), so answer choices (C) is also incorrect.

This question adds a new supposition to the original set of conditions — "P is not selected to attend the retirement dinner." The task is to determine all of the different possible selections that are compatible with this new supposition. A compatible solution is one that violates neither the new supposition nor the original conditions.

Since the second condition states "[e]ither N or P must be selected...," we can infer from the new supposition (P is not selected) and the second condition (either N or P, but not both, is selected) that N is selected. And since N is selected, we know from the third condition that L is selected. In other words every acceptable selection must include both L and N.

We are now in a good position to enumerate the groups of four which would be acceptable selections. The first condition specifies that either J or K, but not both, must be selected. So you need to consider the case where J (but not K) is selected and the case in which K (but not J) is selected. Let's first consider the case where J (but not K) is selected. In this case, Q is not selected, since the fourth condition tells you that if K is not selected, then Q cannot be selected either. Since exactly four people must be selected, and since P, K, and Q are not selected, M, the only remaining person, must be selected. Since M's selection does not violate any of the conditions or the new supposition, N, L, J, and M is an acceptable selection; in fact, it is the only acceptable selection when K is not selected. So far we have one acceptable selection, but we must now examine what holds in the case where K is selected.

Suppose that K is selected. In this case J is not selected, but Q may or may not be selected. If Q is selected, it is part of an acceptable selection — N, L, K, and Q. If Q is not selected, remembering that J and P are also not selected, M must be selected. This gives us our final acceptable selection — N, L, K, and M.

Thus there are exactly three different groups of four which make up acceptable selections, and (C) is the correct response.

The way in which this question is phrased is rather complex, and so it is important to get very clear what exactly is being asked. Unlike other questions which give you a new supposition to consider in conjunction with the original conditions, this question asks you to determine what is needed, in addition to the original conditions, to guarantee that only one group of four is acceptable.

One way to approach this question is to consider each option individually, and determine for each option whether only one acceptable group of four can be selected when the pair indicated in the option is selected. You may wish to vary the order in which the options are considered according to personal preferences. In the discussion here, we will consider the answer choices in order from (A) through to (E).

Choice (A): When both J and L are selected, K cannot be selected (first condition). Consequently Q cannot be selected (fourth condition). More than one group of four is acceptable under these circumstances, however: J, L, M, and N may be selected, and J, L, M, and P may be selected.

Choice (B): When K and M are both selected, J cannot be selected (first condition). Other than that, anyone else could be selected. This leaves more than one acceptable group of four. K, L, M, and N may be selected; K, L, M, and P may be selected; and K, M, P, and Q may be selected.

Choice (C): When L and N are both selected, P cannot be selected (second condition), but, as in the case of option (B), anyone else can be selected. This leaves more than one acceptable group of four: J, L, M, and N may be selected; K, L, M, and N may be selected; and K, L, N, and Q may be selected.

Choice (D): When M and Q are both selected, K must be selected (fourth condition), and hence J cannot be selected (first condition). Furthermore, N cannot be selected: if N were selected, then L would also have to be selected (third condition), and this would violate the restriction that exactly four people are to be selected. And since N cannot be selected, P must be selected (second condition). Thus when M and Q are both selected, both K and P must be selected as well, and only one group of four — K, M, P, and Q — is acceptable. (D) is therefore the correct response.

This problem is concerned with determining the order in which six activities will be performed. As with many questions involving relative ordering or ranking, it is likely that you will find it useful to diagram the various relationships given in the passage.

The first condition in the passage tells us that grocery shopping has to be immediately after hedge trimming, which we can abbreviate as follows:

1. HG

The second condition tells us that kitchen cleaning has to be earlier than grocery shopping, which we can abbreviate as follows, where "..." is used to represent "earlier than" (which means any time before, including immediately before):

2. K ... G

The third condition tells us that motorbike servicing has to be earlier than laundry, and the fourth condition tells us that motorbike servicing has to be either immediately before or immediately after jogging. These conditions can be abbreviated as follows, where the / symbol is used to represent "or":

3. M ... L
4. MJ / JM

Notice that the information specified in these four conditions can be collapsed into two ordering statements:

I. K ... HG (first and second conditions)
II. MJ / JM ... L (third and fourth conditions)

Question 7 introduces the new supposition "laundry is earlier than kitchen cleaning":

L ... K

This new supposition works to further collapse the ordering statements in I and II to the single statement below; that is, if L must be earlier than K, then we know that the activities must be ordered like this:

MJ / JM ... L ... K ... HG

So, with the addition of the new supposition, there are exactly two possible orderings of the six activities, differing only with respect to whether motorbike servicing is immediately before or immediately after jogging:

Question 7 asks what position hedge trimming must be in, given the new supposition. What we see here is that hedge trimming must be the fifth activity performed, and so answer choice (A) is correct.