How many triples (x, y, z) of rational numbers satisfy the following system of equations?
x + y + z = 0
xyz + z = 0
xy + yz + xz + y = 0
(a) 1 (b) 2 (c) 3 (d) 4 (e) 5
A coin has a probability of 1/3 for coming up heads and 2/3 for coming up tails. On average, how many flips of this coin are needed to guarantee both heads and tails appear at least once?
(a) 2.25 (b) 2.5 (c) 3 (d) 3.5 (e) 5
A farmer has 12 plots of land, arranged in a row. To ensure viability of the soil, the farmer never uses two adjacent plots at the same time. This season, the farmer wishes to plant one plot of each of the following: corn, wheat, soybeans, and rice. Each crop is assigned its own plot of land. How many ways can the farmer allocate plots of land for these crops?
(a) 1680 (b) 3024 (c) 5040 (d) 7920 (e) 11880
I have twenty Rs. 3 stamps and twenty RS. 5 stamps. Using one or more of these stamps, how many different amounts of postage can I make?
(a) 150 (b) 152 (c) 154 (d) 396 (e) 400
How many different quadruples (x1, x2, x3, x4) satisfy the equation x1 + x2 + x3 + x4 = 18, where each xi is a positive integer
(a) 83 (b) 172 (c) 256 (d) 344 (e) 352
For what values of k does the equation log(kx) = 2 log(x + 1) have only one real root?
Among all collections of distinct positive integers whose sum is 20, let n be the largest possible product. What is the sum of the digits of n ?
Let x, y, and z be positive real numbers which satisfy the following equations:
x^2 + xy + y^ 2 = 3
y^ 2 + yz + z^ 2 = 1
z^ 2 + zx + x^ 2 = 4:
What is the value of the expression xy + yz + zx ?
The squares of a 2×500 chessboard are coloured black and white in the standard alternating pattern. k of the black squares are removed from the board at random. What is the minimum value of k such that the expected number of pieces the chessboard is divided into by this process is at least 20?
Details and assumptions
The squares removed from the chessboard are not counted as pieces.
A piece of the chessboard is a set of squares joined together along edges. Being connected at corners of squares is not sufficient for two squares to be in the same piece.
in a company 605 employees are male. of these 40% earn more than 50K/year.If 36%of the total employees of the company draw more than 50K/yr, what is the % of women who are drawing less than 50K/yr
Consider four digit numbers for which the first two digits are equal and the last two digits are also equal. How many such numbers are perfect squares.
I have reduced the number to 11(100x+y). What next?
The answer is 1.
Thanks guize.
The two roots of the quadratic equation x 2^2 - 85x + c = 0 are prime numbers. What is the value of c?
In a bag, out of 10 mangoes, 4 are rotten. 2 mangoes are taken out together. if one of them is good, probability that other is also good is:
1. 1/3 2. 8/15 3. 5/18 4. 2/3
Any shortcut to do such division to find approx value
A cube is cut in two equal parts along a plane parallel to one of its faces. One piece is then coloured red on the two larger faces and green on the remaining, while the other is coloured green on two smaller adjacent faces and red on the remaining. Each is then cut into 32 cubes of same size and mixed up.What is the number of cubes with at least one green face each ?
a.36
b.32
c.38
d.48
please explain it
A person borrowed Rs.5000 at 12%rate for 3 years compounded quatrely..what is the final amount after 3 years
How many pairs of positive integers m , n satisfy 1/m+ 4/n=1/12 where n is an odd integer less than 60?
the answer is 3.
O is the centre and arc ABC subtends an angle of 130 degree at O.AB is extended to P.Then angle PBC is
75
65
70
80
easy one -
ab + bc + ac = 120 .. how many different combinations of A B C are possible . when all are prime ?