Problem of the Day 30.07.09

Find the sum of the digits of the least natural number N, such that the sum of the cubes of the four smallest distinct divisors of N is 2N?

1)  9                                2) 8                             3) 7                    4) 6                      5) 10

Bonus QUestion 28.07.09

Suppose K be the number of integers n such that (2^n+1)/n^2 is also an integer.
Then K is
a) 0               b) 1               c) 2              d) 3              e) none of these

Problem of the day 28.07.09

if a<b and 12²+4²+5²+3²=a²+b² the find (a+b)?

Problem of the day 27.07.09

Find the number of quadratic polynomials ax² + bx + c such that:

a) a, b, c are distinct.

b) a, b, c ε {1, 2, 3, ...2008}

c) x + 1 divides ax² + bx + c
a) 2013018            b) 2013021            c) 2014024             d) 2018040       e) none of these

Bonus Question 26.07.09

The perimeter of a right triangle is 60. The height to the hypotenuse is 12 what is the area?
(A) 75 (B) 144 (C) 150 (D) 300 (E) none of these

Problem Of the Day 26.07.09

If x² + y²= 1 and x, y are real numbers. Let p, q be the largest and smallest possible
value of x + y respectively. Then compute pq
a) 0                    b) 1/2         c) −1/2                          d) 2                           e) −2

Problem of the day 25.07.09

In 1896 lord Coin has decided to play a game. From the January 1 till December 31 every day he chooses among two match boxes an arbitrary one and placed a match from it to another box (if the chosen box was not empty). If the chosen box was empty then he placed a match from
the other box to the chosen one. What is the probability that after the December 31 the both boxes will have an equal number of matches if at the beginning each box had a) n = 400 b) n = 200 c) n = 100 matches?

Bonus Question 16.07.09

Find the number of solutions in distinct positive  integers of x^4+y^4=z^4

A) 0                 B) 1                  C) 2                         D) 3                E) More than 3

Problem of the day 17.07.09

Find the area of right angle triangle whose inradius is 4 and circumradius
is 10?
a) 28                   b) 56                    c) 96                     d) 192                   e) none of these

Problem of the day 16.7.09

What is the sum of the digits of a two digit number which is 32 less than the square of the product of its digits?

A. 12                   B. 11                 C. 10 .                     D. 9                           E.      8

Problem of the day 14.7.09

Given that 1025/1024=1.0009765625, find the sum of the digits of 5¹⁰?



(a)  36       (b) 40    (c) 50   (d) 102   (e) 41

Problem of The day 13.07.09

On a circle 26 equidistant points are marked. these points are joined to form a triangles. Of the triangles formed, how many of them will have their circumcenter on one of their sides.?

A) 318 B) 312 C) 288 d) 624 e) None of these

ONLINE CAT- Effects on Quant Section

In this blog, I will discuss how the ONLINE CAT changes QUANT Preparation.

CAT Goes Online!

With the CAT going online, there has been a surge of doubts and apprehensions in the minds of students. Some of them are being directed to me,  so I think its best to post it together for the benefit of one and all.

The Aftermath

I think with the online CAT being CBT ( Computer Based Test) and not compute adaptive, the effect on Quant section is less when compared to DI or VA sections. Still, the change is considerable.

The first change is in Quant, most of us solve it just by the side of Question and save time, of going to the rough pages. But, now everyone is at the same ground, so people who did write in font 6 lose some of their advantages. Now everyone has to first check the screen and solve it on paper, so everyone takes the same amount of  time in this step.

The Geometry Puzzle

For algebra, number theory, arithmetic and modern maths, there is no other recognisable change. As earlier you solved on question paper itself, now you will do it on rough sheet.

The major change is with geometry questions, the ones with figures given. It might happen, that you need to do some additional construction to get a clear picture, this will be cumbersome and add to the time taken to solve the question.  Even if the question does not need construction, but the nomenclature of angles will become a little difficult, like you could name angles 1, 2 etc and go fast and save time. Now, one has to be really careful with the angles or take the pain of redrawing the full figure, which might not be cakewalk either.

What to Do?

The general and most obvious trick is to avoid geometry, unless there is no other choice. The other trick is to practice doing the question without the need to draw the figure in full again. This can be only done, if we try and solve geometry sets on screen, and get used to doing it quick.  The habit of doing it on paper and pencil can backfire, if the paper comes geometry heavy.

One Last Advice

The last piece of advice is there is no reason to panic. If there is something for you, it is for everyone who is taking the test. How you go ahead and work, to tackle this issue, is what matters. What are you waiting for?

Good Luck!

Implex

Problems 8.07.09

I could not post due to some engagements. Here are a bunch of problems to compensate :)

Question 1)

A + B + C + D = D + E + F + G = G + H + I = 17 where each letter represent a number from 1 to 9. Find out number of ordered pairs (D,G) if letter A = 4.
a) 0                       b) 1                 c)2                        d) 3                 e) none of these

Question 2)

The sequence 1, 3, 4, 9, 10, 12..... includes all numbers that are a sum of one or more distinct powers of 3. Then the 50th term of the sequence is
a. 252                    b. 283                     c. 327                      d. 360                  e) none of these

Question 3)


Given that g(h(x)) = 2x² + 3x and h(g(x)) = x² + 4x − 4 for all
real x. WHich of the following could be the value of g(-4)?
a)1                     b) -1                          c) 2                 d) -2                   e) -3

Question 4)


If a, x, b and y are real numbers and ax+by = 4 and ax² +by² = 2 and
ax³ + by³= −3 then find (2x − 1)(2y − 1)
a)4                      b) 3                    c) 5                 d) -3          e) cannot be determined.

Question 5)


K1,K2,K3...K30 are thirty toffees. A child places these toffees on a circle, such that there are exactly n ( n is a positive integer) toffees placed between Ki and Ki+1 and no two toffees overlap each other. Find n
a)4                        b) 5                     c) 9                 d) 12                       e) 13

Question 6)
For the n found in previous  question, which of the two toffees are adjacently
placed on the circle? ( All other conditions remaining same)
a) K11 and K13                    b) K6 and K23                   c) K2 and K10              d) K11 and K18
e) K20 and K28

Problem Of The Day 04.07.2009

Let aabb be a 4-digit number (a≠0). How many such numbers are perfect squares?

A) 0   B) 1   C)  2   D) 3  E) 4

Problem of the Day 3.07.09

In a triangle ABC, perpendiculars BD and CE are drawn to the sides AC and AB. Points  D and E are joined, then the ratio of the area of ADE to the area of ABC is:

1) Cos²A 2) Sin²A 3) Cot²A 4) Tan²A  5) None of these

Problem of The Day 2.07.09

Two triangles are considered distinct if they cannot be superimposed on each other by rotation. How many distinct triangles, with integer sides,  exist, such that there perimeter is 30?

A) 19    B) 57    C) 114    d) 38    E) 36

Problem of the day 1.07.09

300! is divisible by (24!)^n. what is the max. possible integral value of n?