Numbers
For how many integral values of n, n2 + 8n + 49/ (n + 4) is always an integer.
1. 8
2. 16
3. 4
4. None of these
Question of the day
Given the following facts:
D is younger than F and older than G.
J is younger than C and older than E.
A is younger than I and older than C.
F is younger than B and older than H.
I is younger than G and older than J.
H is older than G.
Who is the Youngest?
Geometry
Increasing the radius of a cylinder by 6 units increased the volume by y cubic units. Increasing the height of the cylinder by 6 units also increases the volume by y cubic units. If the original height is 2, then the original radius is:
1. 2
2. 4
3. 6
4. 6π
5. 8
Counting and Probability
Four standard six-sided dice are rolled. Find the probability that, for each pair of dice, the product of the two numbers rolled on those dice is a multiple of 4.
1. 1/108
2. 31/432
3. 1/16
4. 13/69
If any two of the dice show an odd number, then this is impossible, so at most one of the dice can show an odd number. We take two cases: Case 1: If exactly one of the dice shows an odd number, then all three other dice must show a multiple of 4; which can only be the number 4: The probability that this occurs is 4 × ½ × (1/6)3 = 1/108 Case 2: If all of the dice show even numbers, then the condition is satisfied. The probability that this occurs is (1/2)4 = 1/16 The total probability is: 1/108 + 1/16 = 31/432
Numbers
What is the sum of the digits of the largest prime factor of 49 + 94 ?
1. 17
2. 16
3. 9
4. None of the above
Q, R, S and T are related to each other.
(1) T is Q’s brother or only daughter.
(2) Q or R is S’s only son.
(3) R or S is T’s sister.
(4) One of the four is the opposite gender from each of the other three.
How are they related to each other?
From (1) and (3), T can not be the only daughter and have a sister (R or S). Hence, T is T’s brother i.e. D is a Male. From (3), let’s say that R is T’s sister i.e. R is Female. From (2), Q is S’s only son i.e. Q is Male. But T is Q’s brother which means that Q is not S’s only son. Hence, our assumption was wrong. Thus, S is T’s sister i.e. S is Female. And R must be S’s only son. Now it is clear that T & R are Males and S is Female. Q must be a Male as only one of them is of opposite sex from each of the other three. And he is S & T’s brother.
Geometry
Triangle ABC is isosceles, and ∠ABC = x°. If the sum of the possible measures of ∠BAC is 240°, find x.
There are three possible triangles: either ∠ABC = ∠BCA, in which case ∠BAC = 180° −2x, ∠ABC = ∠BAC, in which case ∠BAC = x, or ∠BAC = ∠BCA, in which case ∠BAC = (180−x)°/ 2 . These sum to (540−3x)°/ 2 , so we have (540−3x)°/2 = 240
⇒ x =20°
See our previous ‘Questions of the Day’:
Quant Question Of The Day: 157
Quant Question Of The Day: 156
At the entrance to a members club stands a stranger seeking admission. A friend told him that it’s easy to get in. You just have to answer a question corrcetly! Answering wrong, however, will result in being shot! To live a little longer, the man waits in a back alley near the entrance for people to go in. After a while a man comes to the entrance. The door warden asks him: “Twelve?” to which he replies “Six!” and goes in. “That’s easy.” our friend thinks, but he waits a little longer. Another man comes to the door. “Six?” the door warden asks, to which he replies “Three!” and goes in. “That’s too good to be true” our friend thinks, and he was not right. Because, when asked “Four?”, he answered “Two!” and was found dead in the alley. What was the correct answer?
The answer is the number of letters in the word spoken by the door warden. “Twelve” contains “Six” letters i.e. T, W, E, L, V, E “Six” contains “Three” letters i.e. S, I, X Similarly, “Four” contains “Four” letters i.e. F, O, U, R.
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