Consider a n + 1 = 1 1 + 1 a n a_{n+1} =\frac{1}{1+\frac{1}{a_{n}}} a n + 1 = 1 + a n 1 1 for n = 1 , 2 , . . . . . , 2008 , 2009 n = 1,2, ....., 2008, 2009 n = 1 , 2 , . . . . . , 2 0 0 8 , 2 0 0 9 where a 1 = 1 a_{1} = 1 a 1 = 1 . Find the value of a 1 a 2 + a 2 a 3 + a 3 a 4 + . . . + a 2008 a 2009 a_{1}a_{2} + a_{2}a_{3} + a_{3}a_{4} + ... + a_{2008}a_{2009} a 1 a 2 + a 2 a 3 + a 3 a 4 + . . . + a 2 0 0 8 a 2 0 0 9 .

Aman has come to the market with Rs. 100. If he buys 5 kilograms of cabbage and 4 kilograms of potato, he will have Rs. 20 left; or else, if he buys 4 kilograms of cabbage and 5 kilograms of onion, he will have Rs. 7 left. The per kilogram prices of cabbage, onion and potato are positive integers (in rupees), and any type of these vegetables can only be purchased in positive integer kilogram, or none at all.

Question 3.

Aman decides to buy only onion, in whatever maximum quantity possible (in positive integer kilogram), with the money he has come to the market with. How much money will he be left with after the purchase?

Rs. 12

Rs. 9

Rs. 7

Rs. 5

Rs. 1

Question 4.

Aman decides to buy only onion and potato, both in positive integer kilogram, in such a way that the money left with him after the purchase will be insufficient to buy a full kilogram of either of the two vegetables.
If all such permissible combinations of purchases are equally likely, what is the probability that Aman buys more onion than potato?

$\frac{3}{10}$

$\frac{5}{6}$

$\frac{2}{9}$

$\frac{7}{20}$

$\frac{4}{10}$

Question 5.

The addition of 7 distinct positive integers is 1740. What is the largest possible “greatest common divisor” of these 7 distinct positive integers?

140

None of the above.

Question 6.

ABC is a triangle and the coordinates of A, B and C are (a, b-2c), (a, b+4c) and (-2a,3c) respectively where a, b and c are positive numbers.
The area of the triangle ABC is:

6abc

9abc

6bc

9ac

None of the above

Question 7.

Let x and y be two positive integers and p be a prime number. If x (x - p) - y (y + p) = 7p, what will be the minimum value of x - y?

None of the above

Question 8.

Consider $a_{n+1} =\frac{1}{1+\frac{1}{a_{n}}}$ for $n = 1,2, ....., 2008, 2009$ where $a_{1} = 1$ . Find the value of $a_{1}a_{2} + a_{2}a_{3} + a_{3}a_{4} + ... + a_{2008}a_{2009}$ .

$\frac{2009}{1000}$

$\frac{2009}{2008}$

$\frac{2008}{2009}$

$\frac{6000}{2009}$

$\frac{2008}{6000}$

Question 9.

Raju and Sarita play a number game. First, each one of them chooses a positive integer independently. Separately, they both multiply their chosen integers by 2, and then subtract 20 from their resultant numbers. Now, each of them has a new number. Then, they divide their respective new numbers by 5. Finally, they added their results and found that the sum is 16. What can be the maximum possible difference between the positive integers chosen by Raju and Sarita?

None of the above

Question 10.

Wilma, Xavier, Yaska and Zakir are four young friends, who have a passion for integers. One day, each of them selects one integer and writes it on a wall. The writing on the wall shows that Xavier and Zakir picked positive integers, Yaska picked a negative one, while Wilma’s integer is either negative, zero or positive. If their integers are denoted by the first letters of their respective names, the following is true:
$W^{4}+X^{3}+Y^{2}+Z\leq4$
$X^{3}+Z\geq2$
$W^{4}+Y^{2}\leq2$
$Y^{2}+Z\geq3$
Given the above, which of these can $W^{2}+X^{2}+Y^{2}+Z^{2}$ possibly evaluate to?

Great Job! continue working on more practice questions?

Question 1.

Find z, if it is known that:
a: $-y^2 + x^2 = 20$
b: $y^3 - 2x^2 - 4z \geq -12$ and
c: x, y and z are all positive integers

Any integer greater than 0 and less than 24

We need one more equation to find z

Question 2.

The topmost point of a perfectly vertical pole is marked A. The pole stands on a flat ground at point D. The points B and C are somewhere between A and D on the pole. From a point E, located on the ground at a certain distance from D, the points A, B and C are at angles of 60, 45 and 30 degrees respectively. What is AB : BC : CD?

$(3 + \sqrt 3) : (1 + \sqrt 3) : 1$

$(3 - \sqrt 3) : 1 : (\sqrt 3 - 1)$

1 : 1 : 1

$(3 - \sqrt 3) : (\sqrt 3 - 1) : 1$

$(\sqrt 3 - 1) : 1 : (3 - \sqrt 3)$

Question 3.

Consider the four variables A, B, C and D and a function Z of these variables, $Z = 15A^2 - 3B^4 + C + 0.5D$ It is given that A, B, C and D must be non-negative integers and thatall of the following relationships must hold:
i) $2A + B \leq 2$
ii) $4A + 2B + C \leq 12$
iii) $3A + 4B + D \leq 15$
If Z needs to be maximised, then what value must D take?

Question 4.

Let P be the point of intersection of the lines
3x + 4y = 2a and 7x + 2y = 2018
and Q the point of intersection of the lines
3x + 4y = 2018 and 5x + 3y = 1
If the line through P and Q has slope 2, the value of a is:

4035

1/2

3026

1009

Question 5.

Let C be a circle of radius $\sqrt{20}$ cm. Let L1, L2 be the lines given by 2x − y −1 = 0 and x + 2y−18 = 0, respectively. Suppose that L1 passes through the center of C and that L2 is tangent to C at the point of intersection of L1 and L2. If (a,b) is the center of C, which of the following is a possible value of a + b?

Question 6.

If the diagonals of a rhombus of side 15 cm are in the ratio 3:4, find the area of the rhombus.

54 sq. cm.

108 sq. cm.

144 sq. cm.

200 sq. cm.

None of the above

Question 7.

The number of boys in a school was 30 more than the number of girls. Subsequently, a few more girls joined the same school. Consequently, the ratio of boys and girls became 3:5. Find the minimum number of girls, who joined subsequently.
Assume that there was at least one girl at the start.

Solution not possible

Question 8.

If $2 \leq |x - 1| \times |y + 3| \leq 5$ and both $x$ and $y$ are negative integers, find the number of possible combinations of $x$ and $y$ .

Question 9.

If f(x) = ax + b, a and b are positive real numbers and if f(f(x)) = 9x + 8, then the value of a + b is:

None of the above

Question 10.

Hari’s family consisted of his younger brother (Chari), younger sister (Gouri), and their father and mother. When Chari was born, the sum of the ages of Hari, his father and mother was 70 years. The sum of the ages of four family members, at the time of Gouri’s birth, was twice the sum of ages of Hari’s father and mother at the time of Hari’s birth. If Chari is 4 years older than Gouri, then find the difference in age between Hari and Chari.

5 years

6 years

7 years

8 years

9 years

Great Job! continue working on more practice questions?

XAT Linear Equations Practice Questions With Solutions

XAT Quantitative Ability & Data Interpretation Linear Equations Practice Questions

Question 1.

Question 2.

Question 3.

Aman decides to buy only onion, in whatever maximum quantity possible (in positive integer kilogram), with the money he has come to the market with. How much money will he be left with after the purchase?

Question 4.

Question 5.

The addition of 7 distinct positive integers is 1740. What is the largest possible “greatest common divisor” of these 7 distinct positive integers?

Question 6.

ABC is a triangle and the coordinates of A, B and C are (a, b-2c), (a, b+4c) and (-2a,3c) respectively where a, b and c are positive numbers. The area of the triangle ABC is:

Question 7.

Let x and y be two positive integers and p be a prime number. If x (x - p) - y (y + p) = 7p, what will be the minimum value of x - y?

Question 8.

Question 9.

Question 10.

Question 1.

Find z, if it is known that:a: −y2+x2=20-y^2 + x^2 = 20−y2+x2=20b: y3−2x2−4z≥−12y^3 - 2x^2 - 4z \geq -12y3−2x2−4z≥−12 andc: x, y and z are all positive integers

Question 2.

Question 3.

Question 4.

Let P be the point of intersection of the lines3x + 4y = 2a and 7x + 2y = 2018and Q the point of intersection of the lines3x + 4y = 2018 and 5x + 3y = 1If the line through P and Q has slope 2, the value of a is:

Question 5.

Question 6.

If the diagonals of a rhombus of side 15 cm are in the ratio 3:4, find the area of the rhombus.

Question 7.

The number of boys in a school was 30 more than the number of girls. Subsequently, a few more girls joined the same school. Consequently, the ratio of boys and girls became 3:5. Find the minimum number of girls, who joined subsequently.Assume that there was at least one girl at the start.

Question 8.

If 2≤∣x−1∣×∣y+3∣≤52 \leq |x - 1| \times |y + 3| \leq 52≤∣x−1∣×∣y+3∣≤5 and both xxx and yyy are negative integers, find the number of possible combinations of xxx and yyy.

Question 9.

If f(x) = ax + b, a and b are positive real numbers and if f(f(x)) = 9x + 8, then the value of a + b is:

Question 10.

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ABC is a triangle and the coordinates of A, B and C are (a, b-2c), (a, b+4c) and (-2a,3c) respectively where a, b and c are positive numbers.
The area of the triangle ABC is:

Find z, if it is known that:
a: $-y^2 + x^2 = 20$
b: $y^3 - 2x^2 - 4z \geq -12$ and
c: x, y and z are all positive integers

Let P be the point of intersection of the lines
3x + 4y = 2a and 7x + 2y = 2018
and Q the point of intersection of the lines
3x + 4y = 2018 and 5x + 3y = 1
If the line through P and Q has slope 2, the value of a is:

The number of boys in a school was 30 more than the number of girls. Subsequently, a few more girls joined the same school. Consequently, the ratio of boys and girls became 3:5. Find the minimum number of girls, who joined subsequently.
Assume that there was at least one girl at the start.

If $2 \leq |x - 1| \times |y + 3| \leq 5$ and both $x$ and $y$ are negative integers, find the number of possible combinations of $x$ and $y$ .