1. Out of three people (P, Q, R) in a group, two are selected for a task, such that:

i. The shorter of P and Q is the older of the two selected.

ii. The younger of Q and R is the shorter of the two selected.

iii. The taller of P and R is the younger of the two selected.

Who is not selected?

 Difficult
A. P
B. Q
C. R
D. Can’t be determined

View Answer

Answer: Option C

Explanation:

The various possibilities are:

Possibility Older Younger Taller Shorter
1 P Q P Q
2 P Q Q P
3 Q P Q P
4 Q P P Q
5 Q R Q R
6 Q R R Q
7 R Q R Q
8 R Q Q R
9 P R P R
10 P R R P
11 R P R P
12 R P P R

 

From i, 1 & 3 are eliminated. Also, R is eliminated as an older candidate -> 7,8,11,12 are also eliminated.

From ii, 6 & 8 are eliminated. Also, P is eliminated as the shorter candidate -> 2, 3, 10, 11 are eliminated.

From iii, 9 & 11 are eliminated. Also, Q is eliminated as the younger candidate -> 1, 2, 7, 8 are eliminated.

We are left with 4 and 5. Now 4 satisfies all a, b and c. However, in case of 5:

From i, Q is shorter than P -> Q<P —– ❶

From ii, R is shorter than Q -> R<Q —– ❷

From iii, R is taller than P -> R>P —– ❸

Not possible, because from ❶ & ❷

R<Q<P (in terms of height)

But from ❸ R>P

Hence only possibility is 4. -> ‘R’ is not selected

2. A detective keeps the following code for his secret box: B E G B C E B G
He realizes the need to change this five-year-old code and replace it with a new one such that:
i. The code comprises five letters of the English alphabet.
ii. The product of the five letters of the code is the same as that of all the letters of the previous code, where the product is calculated using the numerical values of the respective letters corresponding to their position in the English alphabet measured from A to Z. For example, A is 1 and Z is 26.
iii. The new code has no third letter of the alphabet because 3 is his unlucky number.
iv. The new code has its letter in alphabetical order when the first letter and the second letter are interchanged.
v. The new code repeats only one of the letters, with a numerical value more than 10.
vi. The product of the first two letters of the new code is a single digit number.
What is the new code?		 Difficult
A. AFNNY
B. FANNY
C. FANYN
D. Can’t be determined

View Answer

Answer: Option B

Explanation:

The previous code is

B E G B C E B G, which has 3 Bs, 2 Es, 2 G, and 1 C. The numerical values of these letter are: B = 2, C = 3, E = 5, G = 7

Therefore, the product of these letters is 2*2*2*5*5*7*7*3 =29400

Now, the only letter which can be repeated corresponds to 2*7, because others will have a value less than 10 or more than 26, which is not possible. For example, 5*7 is not possible as the value of a letter can’t be more than 26; 2, 5 or 7 can’t be repeated as the letter which repeats should have a value more than 10

-> The letter which repeats should have a value 2*7 = 14. So, out of three 2s and two 7s, two 2s and two 7s are adjusted as two Ns (N = 14). Thus, out of 5 letters in the code, two are the 2 Ns.

Now, we are left to choose from the expression: 2*5*5*3, and we are left with three distinct letters. The various possibilities are:

  1. 2, 3, 5*5
  2. 2, 5, 5*3
  3. 1, 2*3, 5*5 (note that 1 doesn’t alter the product)
  4. 1, 2*5, 3*5

Out of these 1 is eliminated because the code can’t have the 3rd letter of the English alphabet; 2 & 4 are eliminated because in that case, when the letters are arranged alphabetically, the product of 1st and 2nd letter is a two-digit number, which contradicts condition vi.

So, we are left with 3. Now, the letters of the code will have the following numerical values: 1, 16, 14, 14, 25 (product is 29400)

Applying condition iv, the letters will be arranged in the following sequence w.r.t their numerical values: 6, 1, 14, 14, 25

So, the code is F A N N Y

3. Solve the following figure logic by completing the arithmetic operations defined under ‘ACROSS’ and ‘DOWN’:  Difficult
 

ACROSS DOWN
1.One half of 28-Down

2.29-Across minus 6-Across

6.The sum of its first and fourth digits is the product of its two centre digits

8.Digits of 16-Down rearranged

9.Two more than 18-Across

10.Same digit repeated

12.Its second digit is three times its first digit

14.6-Down times 19-Down

16.Two times 32-Across

17.19-Down plus 30-Down

18.26-Across plus 28-Down

19.26-Across times 30-Down

21.20-Down times 30-Down

24.Digits of 4-Down reversed

25.Ten times 30-Down

26.Two less than 12-Across

27.6-Down minus 25-Across

29.Its first digit times its second equals the sum of its last two digits

31.Consecutive digits in some order

32.Four times 1-Across

 1.Two times 30-Down

2.Square of 25-Across

3.11-Down times 30-Down

4.12-Across plus 26-Across

5.Square of 19-Down

6.Square of 1-Down

7.Consective digits in some order

11.First digit of 27-Across

13.Seven times 30-Down

15.Consective digits in some order

16. Square of 30-Down

18. 20-Down times 28-Down

19.Two times 1-Down

20.Square of 28-Down

21.Digits of 28-Down reversed

22.Three different multiples of three

23.1-Down times 21-Down

25.Three more than 25-Across

28.1-Down plus 30-Down

30.Its second digit is four times its first digit

 

View Answer

Answer:

Explanation:

Note that 30-Down is either 14 or 28, because second digit is 4 times the 1st digit. However, 13-Down is 7 times 30-Down and 13-Down is a two-digit number -> 30-Down is 14, and 13-Down is 98. Once we fill these boxes, the grid can be simply completed by following the instructions. The completed grid is shown above.