Numbers
T is a set of 5 consecutive positive integers and G is a set of 7 consecutive positive integers such that sum of elements of set T and G is same. Find the difference between sums of non-identical elements of the two sets.
1. 9
2. 5
3.2
4. 0
Question of the day
Read the following information carefully and answer the questions given below it.
(1) P, Q,R,S and T are five friends.
(2) Q is elder to T, but not as tall as R.
(3) R is younger to P and is taller to S and T.
(4) P is taller to S and is not the tallest, but younger than T.
(5) S is elder to P but is shortest in the group.
Who among the following is the tallest?
In terms of age, we have T<Q, R<P, P<T, P<S, So we have: R<P<T<Q, P<S. In terms of height, Q<R, S<R, T<R, S<P. So R is the tallest.
See our previous ‘Puzzles of the Day’:
Number/Geometry
If the sum of all the interior angles of 8 polygons is 4320, then the total number of sides of all these polygons when written in base 3 is –
1. 1111
2. 220
3. 1210
4. 1110
Let these polygons have n1, n2, n3….. n8 sides. Sum of all the interior angles of a polygon with n sides is given by 180(n-2) Sum of all these angles = 4320 180(n1-2) + 180(n2-2) ……. 180(n8-2) = 4320 n1 + n2 + n3 +……..+ n8 = 40 Now, when 40 is converted to base 3, it becomes 1111.
See our previous ‘Questions of the Day’:
Algebra
In a sequence of integers, product of every 4 consecutive terms is same. It is given that 5th term is 5, 11th term is 11, 28th term is 28 and 102nd term is 102. Which of the following is not true?
1. Number of positive integral divisors of 2014th term is 8.
2. Number of zeroes at the end of product of first 100 terms of the sequence is 24.
3. None of the integer in the sequence is a perfect square.
4. Difference between 20th term and 3rd term is 20 – 3.
Sahrukh decided to quit his smoking habit one day, but he had 64 cigarettes with him. So he started smoking them one by one, to finish them. He had the habit of smoking only 1/4th of it and leaving the rest butt. Latter he found out that by joining 4 butts he can form 1 cigarette. So, how many cigarettes in all he smoked.
Algebra
Given that the three roots of x4 + ax2 + bx + c are -2, 3, 5. Find the value of a + b + c.
1. 6
2. -6
3. 125
4. 119
An agent code named Shaktiman emailed a code word to his head office. They are “AIS EUC RAO REI COS”. But four of these five words are fake and only one contains the information.
He also mailed a sentence as a clue – if I tell you any one character of the code word, you would be able to tell the number of vowels in the code word. Can you tell what the code word is?
The code word is RIE.
If you were told any one character of COS, then you would not be able to determine whether the number of vowels is one or two. e.g. if you were told S, there are two words with S – AIS with 2 vowels and COS with 1 vowel. So you would not be able to say the number of vowels.
Same arguments can be given for characters O and C.
Hence, the word with any one of M, O or C is not a code word i.e. AIS, EUC, RAO and COS are not the code word. Thus, REI is the code word.
R : two words – REI and RAO, both with 2 vowels
E : two words – REI and EUC, both with 2 vowels.
I : two words – REI and AIS, both with 2 vowels
See our previous ‘Puzzles of the Day’:
Let Tn = 1n + 2n + 3n + 4n. Find the number of values of n among first 100 positive integers such that Tn is divisible by 5.
- 48
- 50
- 67
- 75
See our previous ‘Questions of the Day’:
Quant Question Of The Day: 135
Quant Question Of The Day: 134
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