S-BATCH @ SRICHAITANYA: Algebra

Explaination

Explanation for Question1: If n is an integer, what is the least value of n such that 1/3ⁿ<0 .01="" br="">1/3ⁿ<0 .01
3¹=3
3²=9
3³=27
3⁴=81
3⁵=243.
the least value that satisfies is 5.

Explanation for Question2:If x > 0 and |x|= 1/x, then x=
By substituting the options we get x=1.

Explanation for Question3:If the average of 10,14,and n is greater than or equal to 8 and less than or equal to 12, what is the least possible value of n?
8 <= (10+14+n)/3 <= 12
24 <= (10+14+n) <= 36
0 <= (10+14+n)/3 <= 12
the least possible value of n is 0.

Explanation for Question 4:If x(x²-4)=0, then find the possible values of x.
Byverifying the options -2,0,2 satisfies.

Explanation for Question 5:If 3x⁵-3=726, then find the value of x.
3x⁵-3=726
=>3x⁵=729
=>x⁵=243
=>x⁵=3⁵
x=3.

Explanation for Question 6: If 3k < 21 and 8k > 40 then what could be the value of K
by substituing the options k=5 satisfies.

Explanation for Question 7:
A rim has fewer than 11 spokes and more than 7 ,that are go from centre point of hub and they are equally spaced,What could be the possible smallest angle between any two adjacent spokes?
The possible number of spokes will be 8,9,10
there the possible angles are 360/10,360/9,360/8
36,40 and 45 are the possible answers

Explanation for Question8:If ab < 0 and c/a - d/b > ab then which of the following must be true?
(cb-ad)/ab>ab, when multiply with ab on both sides the inequality change (as ab is negative)
(cb-ad) < a²b²

Explanation for Question9:If I add seven times my age seven years from now to three times my age three years ago, I get 12 times my current age.How old I will be three years from now?
let the age be x=> 7(x+7) + 3 (x-3) = 12x
=> x=20

Explanation for Question 10:If |4x-2|= 22, then find the possible values of x².
|4x-2|= 22=>4x-2= 22 (or) 4x-2= -22
therefore x= 6 or -5=> x²=36 0r 25

Explanation for Question 11:If 2x²-5x+6=0, find the sum of the roots.(write in decimal form)
The sum of the roots of equation ax²+bx+c=0 is -b/a
answer is 5/2 =2.5(we have to express in decimal form)

Explanation for Question 12:

QUANT COMPARISION

(x-3y)(x+3y)=25

COLUMN A	COLUMN B<>
x²-9y²	18

column A is greater (x-3y)(x+3y)=25 => x²-9y²=25
column B is 18.

Explanation for Question 13:A vessel can hold x litres of oil. y litres of oil is removed when the vessel is full. Remaining oil is what part of vessel capacity?
Intial quantity =x, which is the capacity of the vessel
y litres is removed,leftover will be x-y
therefore (x-y)/x is the answer.

Explanation for Question 14:Eight years hence I will be thrice as old as I was four years ago. After how many years will I be 24 years?
Let the present age be x,(x+8)=3(x-4)
onsimplification we get x=10
After 14 years the age will become 24.

Explanation for Question 15:How many numbers between 1 and 100 including both are divisible by 3 and 5?
Multiples of 3 are 33
MUltiples of 5 are 20
common multiple i.e multiples of 15 are 6
therefore the answer is 33+20-6=47.

Explanation for Question 16:The sum of two Positive integers is 48.Which of the following cannot be the ratio of two numbers.
The sum must be factor of 48. hence the answer is 3:4 ( 7 is not a factor of 48)

Explanation for Question 17:Which of the following is equivalent to 13 < x < 33
by verifying the options |x-23|<10 data-blogger-escaped-div="" data-blogger-escaped-satisfies.="">

Explanation for Question 18:

QUANT COMPARISION

(x-y)(x+y)=48

COLUMN A	COLUMN B<>
x-y	x+y

In (x-y)(x+y)=48, when don't whether x is positive or negative at the same time we don't whether y is positive or negative.

Explanation for Question 19:If |x+3|+|y-2|+|z-1|=0 then find the value of x²+y²+z²?
When sum of the modulus of three terms is zero, then each term is equivalent to 0.
therefore x=-3,y=2,z=1 => x²+y²+z²=14.

Explanation for Question 20:(x+8)²+(y-5)²+(z-3)²=0,x,y,z are integers.Find x+y+Z.
When sum of the squares of three terms is zero, then each term is equivalent to 0.
therefore x=-8,y=5,z=3 => x+y+z=0.

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Algebra

QUANT COMPARISION

(x-3y)(x+3y)=25

QUANT COMPARISION

(x-y)(x+y)=48

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QUANT COMPARISION

(x-3y)(x+3y)=25

QUANT COMPARISION

(x-y)(x+y)=48