The following are a few sample analytical reasoning questions to practice your skills.
Sample Question #1
A committee must select five out of eight employees — A, B, C, D, E, F, G, and H — for an upcoming project. The committee must adhere to the following conditions:
1. If both A and B are selected, C must also be selected.
2. If D is selected, neither G nor H can be selected.
3. If E is selected, F must also be selected.
4. Exactly two of G, H, and A must be selected.
Question: If both D and H are selected, which one of the following is a pair of employees neither of whom could be selected?
A) A, B
B) B, C
C) C, E
D) E, F
E) F, G
This question asks you to assume that both D and H are selected and determine a pair of employees who could not be selected based on this condition.
Condition 4 states that exactly two out of G, H, and A must be selected. Since H is one of the selected employees, we know that G and A cannot both be selected:
Condition 2 states that if D is selected, neither G nor H can be selected. As we have assumed that D is selected, it follows that G cannot be selected:
From the given conditions, we have determined that G and A are employees who cannot be selected if both D and H are selected. Therefore, answer choice (A) – A, B – is the correct answer.
To rule out the other answer choices, let’s consider each one:
Answer choice (B) – B, C: Since we have assumed that D and H are selected, B can still be selected, and C must be selected if A and B are selected. Therefore, (B) is incorrect.
Answer choice (C) – C, E: This pair is not affected by the selection of D and H. Both C and E could still be selected. Therefore, (C) is incorrect.
Answer choice (D) – E, F: The selection of D and H does not affect this pair. Both E and F could still be selected. Therefore, (D) is incorrect.
Answer choice (E) – F, G: The selection of D and H does not affect this pair. Both F and G could still be selected. Therefore, (E) is incorrect.
Hence, the correct answer is (A) – A, B.
Sample #2
A bakery is deciding on which cakes to display in their showcase. They have eight different cakes: A, B, C, D, E, F, G, and H. The bakery must choose exactly five cakes to display, following the following conditions:
If both A and C are displayed, then G must also be displayed. If H is displayed, then neither B nor D can be displayed. If E is displayed, then F must also be displayed. Of the three cakes B, D, and G, exactly two are displayed.”
Question 1: If both B and D are displayed, which one of the following is a pair of cakes that cannot be displayed together?
A) A, C
B) A, G
C) C, E
D) F, G
E) G, H
This question involves the bakery’s decision to display five cakes out of eight options. The question requires you to suppose that both B and D are displayed and determine which pair of cakes cannot be displayed together.
The fourth condition given in the passage on which this question is based states that exactly two of B, D, and G are displayed. Since the question asks us to suppose that both B and D are displayed, we know that G cannot be displayed: Displayed: B, D Not displayed: G The second condition states that if H is displayed, then neither B nor D can be displayed. Here, since B is displayed, we know that H cannot be displayed. Thus, adding this to what we’ve determined so far, we know that G and H are a pair of cakes that cannot be displayed together if both B and D are displayed: Displayed: B, D Not displayed: G, H
Answer choice (E) is therefore the correct answer.
To provide further clarification, let’s go over the incorrect answer choices. Each of the incorrect answer choices can be ruled out by finding a possible scenario where at least one of the cakes listed in that answer choice is displayed.
Answer choice (A) lists the pair A and C. We know that if both A and C are displayed, then G must also be displayed. Here’s a possible scenario: Displayed: A, C, G Since G is displayed, it follows the conditions stated in the passage. Therefore, A and C can be displayed together, making answer choice (A) incorrect.
Answer choice (B) lists the pair A and G. We’ve already established that G cannot be displayed if both B and D are displayed. Therefore, answer choice (B) is incorrect.
Answer choice (C) lists the pair C and E. We know that if E is displayed, then F must also be displayed. Here’s a possible scenario: Displayed: B, D, E, F Since both E and F are displayed, it follows the conditions stated in the passage. Therefore, C and E can be displayed together, making answer choice (C) incorrect.
Answer choice (D) lists the pair F and G. We’ve already established that G cannot be displayed if both B and D are displayed. Therefore, answer choice (D) is incorrect.
Thus, answer choice (E) is the only pair that cannot be displayed together, satisfying the given conditions.
Sample #3
A panel of six judges—A, B, C, D, E, and F—is evaluating five paintings to be included in an art exhibition. The judges must adhere to the following conditions:
Either A or B must select at least one painting, but not both. Either D or E must select exactly two paintings, but not both. If C selects a painting, then D must also select a painting. F cannot select a painting unless both A and C have selected a painting.
Question: If A does not select any paintings, which of the following statements must be true?
A) B must select at least one painting. B) C must select a painting. C) D must select exactly two paintings. D) E must select exactly two paintings. E) F must select at least one painting.
This question introduces a new condition—”A does not select any paintings.” The task is to determine which statements must be true given this new condition while also considering the original conditions.
Since either A or B must select at least one painting, and A is not selecting any, it follows that B must select at least one painting. This confirms statement (A).
If C selects a painting, then D must also select a painting, according to the third condition. However, there is no information given in the question about whether C selects a painting or not. Therefore, we cannot definitively conclude that statement (B) must be true.
The second condition states that either D or E must select exactly two paintings, but not both. Since A is not selecting any paintings, it does not affect this condition. Thus, statement (C) cannot be concluded to be true.
Similar to statement (C), the second condition is unaffected by A not selecting any paintings. Therefore, statement (D) cannot be definitively determined to be true.
Finally, according to the fourth condition, F cannot select a painting unless both A and C have selected a painting. Since A is not selecting any paintings, F cannot select a painting either. Thus, statement (E) must be true.
In conclusion, statements (A) and (E) are the only ones that can be determined to be true given the new condition, and therefore the correct answer is (A) and (E).