If a* = (2a + 6)/4, and a = 3b + 1, then a* equals
A)0.5b + 1.5
B)1.5b + 2
C)1.5b - 2
D)6b + 7
E)b - 1/3
a*= (6b +2+6)/4 = (6b+8)/4
hence the answer is option B
Showing posts with label ALGEBRA. Show all posts
Showing posts with label ALGEBRA. Show all posts
Thursday, October 21, 2010
Tuesday, August 17, 2010
GMAT Question of the day
A box contains 90 nuts each of 100 gms and 100 bolts each of 150 gms. If the entire box weighs 35.5 kg., then the weight of the empty box is :
A)10 kg
B)10.5 kg
C)11 kg
D)11.5 kg
E)None of the above
Total weight of nuts = 90*100 = 9 Kg
Total weight of bolts = 100*150 = 15 Kg
Total weight of box with nuts and bolts = 35.5 Kg
So the Answer is D
A)10 kg
B)10.5 kg
C)11 kg
D)11.5 kg
E)None of the above
Total weight of nuts = 90*100 = 9 Kg
Total weight of bolts = 100*150 = 15 Kg
Total weight of box with nuts and bolts = 35.5 Kg
So the Answer is D
Saturday, July 31, 2010
GMAT Question of the Day
19. If A2 + B2 = 15 and AB = 10, what is the value of the expression
(A – B)2 + (A + B)2 ?
(a) 10.
(b) 20.
(c) 30.
(d) 60.
(e) 70.
(A – B)2 + (A + B)2
=A2 – 2AB + B2 + A2 + 2AB + B2
=2(A2 + B2)
=30.
The best answer is C.
(A – B)2 + (A + B)2 ?
(a) 10.
(b) 20.
(c) 30.
(d) 60.
(e) 70.
(A – B)2 + (A + B)2
=A2 – 2AB + B2 + A2 + 2AB + B2
=2(A2 + B2)
=30.
The best answer is C.
Friday, July 30, 2010
GMAT Question of the Day
The value of some stock X changes according to the following method:
At the end of each month her value is doubled but due to commission the stock’s value is decreases by Rs.10. If the value at the beginning of January is Rs.A, what would be her value at the end of February?
(a) 4A – 10.
(b) 4A – 20.
(c) 4A – 30.
(d) 4A – 40.
(e) 4A – 50 .
At the end of January her value is 2A – 10.
At the end of February her value is (2 x (2A – 10) – 10
= 4A – 30).
The best answer is C.
At the end of each month her value is doubled but due to commission the stock’s value is decreases by Rs.10. If the value at the beginning of January is Rs.A, what would be her value at the end of February?
(a) 4A – 10.
(b) 4A – 20.
(c) 4A – 30.
(d) 4A – 40.
(e) 4A – 50 .
At the end of January her value is 2A – 10.
At the end of February her value is (2 x (2A – 10) – 10
= 4A – 30).
The best answer is C.
Thursday, July 29, 2010
GMAT Question of the Day
A Cell divides into two each round hour. If at a certain round hour, two Cells were placed in a jar, how many Cells will be in the jar in N hours?
(a) 2N
(b) 22N
(c) 2N+1
(d) 2N-1
(e) 2N
Let’s find the number of Cells in the first hours.
After one hour (N=1) there will be 4 Cells.
After two hours (N=2) there will be 8 Cells.
After three hours (N=3) there will be 16 Cells.
Therefore the formula that fits this series is 2N+1.
The best answer is C.
(a) 2N
(b) 22N
(c) 2N+1
(d) 2N-1
(e) 2N
Let’s find the number of Cells in the first hours.
After one hour (N=1) there will be 4 Cells.
After two hours (N=2) there will be 8 Cells.
After three hours (N=3) there will be 16 Cells.
Therefore the formula that fits this series is 2N+1.
The best answer is C.
Monday, July 12, 2010
GMAT Question of the day
Define x∇y by the equation x∇y = xy − y . Then 2∇ 3 =
(A) 1
(B) 3
(C) 12
(D) 15
(E) 18
From the above definition, we know that x∇y = xy − y .
So we replace x with 2 and y with 3 in the definition:
2∇3 = 2 ⋅ 3 − 3 = 3 .
Hence, the answer is (B).
(A) 1
(B) 3
(C) 12
(D) 15
(E) 18
From the above definition, we know that x∇y = xy − y .
So we replace x with 2 and y with 3 in the definition:
2∇3 = 2 ⋅ 3 − 3 = 3 .
Hence, the answer is (B).
Friday, March 19, 2010
GMAT Question of the Day
I decided to walk down the escalator of a tube station. I did some quick calculation in my mind. I found that if I walk down twenty-six steps, I require thirty seconds to reach the bottom. However, if I am able to step down thirty-four stairs I would only require eighteen seconds to get to the bottom. If the time is measured from the moment the top step begins to descend to the time I step off the last step at the bottom,
can you tell the height of the stair way in steps?
(a) 44
(b) 48
(c) 46
(d) 42
Let speed of the escalator be x steps per second.
In 30 second the escalator will come down by 30 x steps and in 18 seconds it will come down by 18 x steps.
Since height of the stair way is same 26 + 30(x) = 34 + 18(x)
x = 2/3.
Height of the stair way = 26 + 30 (2/3)
= 46 steps.
can you tell the height of the stair way in steps?
(a) 44
(b) 48
(c) 46
(d) 42
Let speed of the escalator be x steps per second.
In 30 second the escalator will come down by 30 x steps and in 18 seconds it will come down by 18 x steps.
Since height of the stair way is same 26 + 30(x) = 34 + 18(x)
x = 2/3.
Height of the stair way = 26 + 30 (2/3)
= 46 steps.
Monday, March 8, 2010
GMAT Question of the day
If x^4 = 2y^2 and 4y = 8, what is the value of x^4 + 2y?
A)8
B)10
C)12
D)14
x^4+2y is the given expression.
Since x^4 is equal to 2y the expression becomes 2y +2y = 4y =8 .
So the answer is option A
A)8
B)10
C)12
D)14
x^4+2y is the given expression.
Since x^4 is equal to 2y the expression becomes 2y +2y = 4y =8 .
So the answer is option A
Thursday, February 18, 2010
GMAT Question of the day
The numerator of a fraction is a multiple of two nos. One of the nos. is greater
than other by 2. The greater no. is smaller than the denominator by 1. If the
denominator is given as 5 + c (c is a constant), then the minimum value of the
fraction is
(a) 2
(b) –2
(c) –1/2
(d) 1/2
The fraction can be written as F = (4 + c) (2 + c) / (5 + c)
Put 5 + c = t or c = t – 5
∴ F = (t – 3) (t – 1)/t
= (t^2 – rt + 3)/t
= (t^2 – 4t + 4 – 1)/t
= (t – 2)^2/ t – 1/t
Hence, the given expression is minimum, if the square term is equal to zero
∴(t-2)/t = 0 or t = 2
Hence answer is A
than other by 2. The greater no. is smaller than the denominator by 1. If the
denominator is given as 5 + c (c is a constant), then the minimum value of the
fraction is
(a) 2
(b) –2
(c) –1/2
(d) 1/2
The fraction can be written as F = (4 + c) (2 + c) / (5 + c)
Put 5 + c = t or c = t – 5
∴ F = (t – 3) (t – 1)/t
= (t^2 – rt + 3)/t
= (t^2 – 4t + 4 – 1)/t
= (t – 2)^2/ t – 1/t
Hence, the given expression is minimum, if the square term is equal to zero
∴(t-2)/t = 0 or t = 2
Hence answer is A
Wednesday, February 3, 2010
GMAT Question of the day
If (a + 1/a)^2 = 3, then a^3 + 1/a^3 equals
(a) 0
(b) 3√3
(c) 10√3/3
(d) 6√3
(a + 1/a)^2 = 3 or (a + 1/a) = 3^(1/2) and we know that
(a + 1/a)^3 = a^3 + 1/a^3 + 3(a + 1/a)
⇒ (a3 +1/a3) = 3√ 3 – 3/3 = 0
(a) 0
(b) 3√3
(c) 10√3/3
(d) 6√3
(a + 1/a)^2 = 3 or (a + 1/a) = 3^(1/2) and we know that
(a + 1/a)^3 = a^3 + 1/a^3 + 3(a + 1/a)
⇒ (a3 +1/a3) = 3√ 3 – 3/3 = 0
Monday, September 7, 2009
ALGEBRAIC EXPRESSIONS
How to evaluate an Algebric Expression?
To evaluate an algebraic expression all we need to do is just to replace the given values
for the unknowns and calculate according to the rules for the order of operations.
2
Example: To find the value of y + 3y - 1 when x = -1, replace -1 for y:
(-1)(-1) + 3(-1) - 1 = 1 -3 -1 = -3.
To evaluate an algebraic expression all we need to do is just to replace the given values
for the unknowns and calculate according to the rules for the order of operations.
2
Example: To find the value of y + 3y - 1 when x = -1, replace -1 for y:
(-1)(-1) + 3(-1) - 1 = 1 -3 -1 = -3.
Tuesday, August 11, 2009
GMAT - FACTORING ALGEBRAIC EXPRESSIONS
1. Factoring the Difference of Squares
The difference of squares.
2 2
a - b = (a -b) (a + b)
2
a - 9, for example, factors to (a - 3)(a + 3).
2. Factoring the Square of a Binomial
Learn to recognize polynomials that are squares of binomials:
2 2 2
a + 2ab + b = (a + b)
2 2 2
a - 2ab + b = (a -b)
2 2
For example, 4x + 12x + 9 factors to (2x + 3)
2 2
n - 10n + 25 factors to (n -5).
3 . Simplifying an Algebraic Fraction
Simplifying an algebraic fraction is a similar to simplifying a numerical fraction: cancel out common factors in numerator and denominator.
2
a + 7a + 12
____________
2
a - 9
2
a + 7a + 12 = (a + 3) (a + 4)
2
a - 9 = (a + 3) (a - 3)
Thus, we can cancel out the identical expressions (a + 3) in the numerator and denominator, leaving us with (a + 4) /(a - 3).
Tuesday, July 21, 2009
GMAT Question of the day
For which of the following functions is f(a+b)= f(a) + f(b) for all positive numbers a and b?
a. f(x) = x*x
b. f(x) = x + 1
c. f(x) = sq. root of x
d. f(x) = 2/x
e. f(x) = -3x
src="http://pagead2.googlesyndication.com/pagead/show_ads.js">
We can find the answer by replacing the value of x by a, b & (a+b)
a. (a+b)*(a+b) != a*a + b*b
b. a + b + 1 != a + 1 + b + 1
c. sqrt(a+b) != sqrt(a) + sqrt(b)
d. 2/(a+b) != 2/a + 2/b
e. -3(a+b) = -3a - 3b (TRUE)
Hence the answer is option E
a. f(x) = x*x
b. f(x) = x + 1
c. f(x) = sq. root of x
d. f(x) = 2/x
e. f(x) = -3x
src="http://pagead2.googlesyndication.com/pagead/show_ads.js">
We can find the answer by replacing the value of x by a, b & (a+b)
a. (a+b)*(a+b) != a*a + b*b
b. a + b + 1 != a + 1 + b + 1
c. sqrt(a+b) != sqrt(a) + sqrt(b)
d. 2/(a+b) != 2/a + 2/b
e. -3(a+b) = -3a - 3b (TRUE)
Hence the answer is option E
Tuesday, June 9, 2009
ALGEBRA
What is algebra ?
Algebra is the world of the unknown ie, it deals with variables whose value are unknown.
In the following expression
2+x =5
x is a variable and we call the above as algebric expression.
Much of algebra deals with making the unknown known ie, solving equations so that variables can be replaced constant numbers.
So we need to know some of the terms that are basic for algebra
Constant :A numerical quantity that does not change.
Variable: An unknown quantity can be represented by any alphabet in English ,x or y are common .
Coefficient: A coefficient is a number that appears next to a variable
Term: The product of a constant and a variable. Every algebraic term is the product of a constant and a variable raised to some power.
Expression: A combination of terms. Expressions don’t include an equal sign that differentiates expressions from equations. Expressions can’t be solved unless we know all the variables values but they can be simplified.
Equation. Two expressions linked by an equal sign.
Algebra is the world of the unknown ie, it deals with variables whose value are unknown.
In the following expression
2+x =5
x is a variable and we call the above as algebric expression.
Much of algebra deals with making the unknown known ie, solving equations so that variables can be replaced constant numbers.
So we need to know some of the terms that are basic for algebra
Constant :A numerical quantity that does not change.
Variable: An unknown quantity can be represented by any alphabet in English ,x or y are common .
Coefficient: A coefficient is a number that appears next to a variable
Term: The product of a constant and a variable. Every algebraic term is the product of a constant and a variable raised to some power.
Expression: A combination of terms. Expressions don’t include an equal sign that differentiates expressions from equations. Expressions can’t be solved unless we know all the variables values but they can be simplified.
Equation. Two expressions linked by an equal sign.
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