For a real number x the condition ∣ 3 x − 20 ∣ + ∣ 3 x − 40 ∣ = 20 \mid3x-20\mid+\mid3x-40\mid=20 ∣ 3 x − 2 0 ∣ + ∣ 3 x − 4 0 ∣ = 2 0 necessarily holds if

10 < x < 15 10<x<15 1 0 < x < 1 5

The shortest distance of the point ( 1 2 , 1 ) (\frac{1}{2},1) ( 2 1 , 1 ) from the curve y = I x -1I + I x + 1I is

2 \sqrt{2} 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z">

3 2 \sqrt{\frac{3}{2}} 2 3 <path d="M983 90l0 -0c4,-6.7,10,-10,18,-10 H400000v40H1013.1s-83.4,268,-264.1,840c-180.7,572,-277,876.3,-289,913c-4.7,4.7,-12.7,7,-24,7s-12,0,-12,0c-1.3,-3.3,-3.7,-11.7,-7,-25c-35.3,-125.3,-106.7,-373.3,-214,-744c-10,12,-21,25,-33,39s-32,39,-32,39c-6,-5.3,-15,-14,-27,-26s25,-30,25,-30c26.7,-32.7,52,-63,76,-91s52,-60,52,-60s208,722,208,722c56,-175.3,126.3,-397.3,211,-666c84.7,-268.7,153.8,-488.2,207.5,-658.5c53.7,-170.3,84.5,-266.8,92.5,-289.5zM1001 80h400000v40h-400000z">

Let f ( x ) = 2 x − 5 f(x) =2x-5 f ( x ) = 2 x − 5 and g ( x ) = 7 − 2 x g(x) =7-2x g ( x ) = 7 − 2 x . Then |f(x)+ g(x)| = |f(x)|+ |g(x)| if and only if

5 2 ≤ x ≤ 7 2 \frac{5}{2}\leq x\leq\frac{7}{2} 2 5 ≤ x ≤ 2 7

5 2 < x < 7 2 \frac{5}{2}<x<\frac{7}{2} 2 5 < x < 2 7

x ≤ 5 2 x\leq\frac{5}{2} x ≤ 2 5 or x ≥ 7 2 x\geq\frac{7}{2} x ≥ 2 7

x < 5 2 x<\frac{5}{2} x < 2 5 or x ≥ 7 2 x\geq\frac{7}{2} x ≥ 2 7

CAT Modulus Practice Questions With Solutions

CAT Quant Modulus Practice Questions

VARC DILR

Question 1.

Let $0 \leq a \leq x \leq 100$ and $f(x) = \mid x - a \mid + \mid x - 100 \mid + \mid x - a - 50\mid$ . Then the maximum value of f(x) becomes 100 when a is equal to

A

25

B

100

C

50

D

0

Question 2.

The largest real value of a for which the equation $\mid x + a \mid + \mid x - 1 \mid = 2$ has an infinite number of solutions for x is

A

-1

B

0

C

1

D

2

Question 3.

The number of integers n that satisfy the inequalities $\mid n - 60 \mid < \mid n - 100 \mid < \mid n - 20 \mid$ is

A

21

B

19

C

18

D

20

Question 4.

If r is a constant such that $\mid x^2 - 4x - 13 \mid = r$ has exactly three distinct real roots, then the value of r is

A

17

B

21

C

15

D

18

Question 5.

For a real number x the condition $\mid3x-20\mid+\mid3x-40\mid=20$ necessarily holds if

A

$10<x<15$

B

$9<x<14$

C

$7<x<12$

D

$6<x<11$

Question 6.

If $3x+2\mid y\mid+y=7$ and $x+\mid x \mid+3y=1$ then $x+2y$ is:

A

$-\frac{4}{3}$

B

$\frac{8}{3}$

C

$0$

D

$1$

Question 7.

In how many ways can a pair of integers (x , a) be chosen such that $x^{2}-2\mid x\mid+\mid a-2\mid=0$ ?

A

6

B

5

C

4

D

7

Question 8.

The product of the distinct roots of $\mid x^2 - x - 6 \mid = x + 2$ is

A

−16

B

-4

C

-24

D

-8

Question 9.

The shortest distance of the point $(\frac{1}{2},1)$ from the curve y = I x -1I + I x + 1I is

A

1

B

0

C

$\sqrt{2}$

D

$\sqrt{\frac{3}{2}}$

Question 10.

Let $f(x) =2x-5$ and $g(x) =7-2x$ . Then |f(x)+ g(x)| = |f(x)|+ |g(x)| if and only if

A

$\frac{5}{2}<x<\frac{7}{2}$

B

$x\leq\frac{5}{2}$ or $x\geq\frac{7}{2}$

C

$x<\frac{5}{2}$ or $x\geq\frac{7}{2}$

D

$\frac{5}{2}\leq x\leq\frac{7}{2}$

CAT Modulus Practice Questions With Solutions

CAT Quant Modulus Practice Questions

Question 1.

Let $0 \leq a \leq x \leq 100$ and $f(x) = \mid x - a \mid + \mid x - 100 \mid + \mid x - a - 50\mid$ . Then the maximum value of f(x) becomes 100 when a is equal to

Question 2.

The largest real value of a for which the equation $\mid x + a \mid + \mid x - 1 \mid = 2$ has an infinite number of solutions for x is

Question 3.

The number of integers n that satisfy the inequalities $\mid n - 60 \mid < \mid n - 100 \mid < \mid n - 20 \mid$ is

Question 4.

If r is a constant such that $\mid x^2 - 4x - 13 \mid = r$ has exactly three distinct real roots, then the value of r is

Question 5.

For a real number x the condition $\mid3x-20\mid+\mid3x-40\mid=20$ necessarily holds if

Question 6.

If $3x+2\mid y\mid+y=7$ and $x+\mid x \mid+3y=1$ then $x+2y$ is:

Question 7.

In how many ways can a pair of integers (x , a) be chosen such that $x^{2}-2\mid x\mid+\mid a-2\mid=0$ ?

Question 8.

The product of the distinct roots of $\mid x^2 - x - 6 \mid = x + 2$ is

Question 9.

The shortest distance of the point $(\frac{1}{2},1)$ from the curve y = I x -1I + I x + 1I is

Question 10.

Let $f(x) =2x-5$ and $g(x) =7-2x$ . Then |f(x)+ g(x)| = |f(x)|+ |g(x)| if and only if

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CAT Modulus Practice Questions With Solutions

CAT Quant Modulus Practice Questions

Question 1.

Let 0≤a≤x≤1000 \leq a \leq x \leq 1000≤a≤x≤100 and f(x)=∣x−a∣+∣x−100∣+∣x−a−50∣f(x) = \mid x - a \mid + \mid x - 100 \mid + \mid x - a - 50\midf(x)=∣x−a∣+∣x−100∣+∣x−a−50∣. Then the maximum value of f(x) becomes 100 when a is equal to

Question 2.

The largest real value of a for which the equation ∣x+a∣+∣x−1∣=2\mid x + a \mid + \mid x - 1 \mid = 2∣x+a∣+∣x−1∣=2 has an infinite number of solutions for x is

Question 3.

The number of integers n that satisfy the inequalities ∣n−60∣<∣n−100∣<∣n−20∣\mid n - 60 \mid < \mid n - 100 \mid < \mid n - 20 \mid∣n−60∣<∣n−100∣<∣n−20∣ is

Question 4.

If r is a constant such that ∣x2−4x−13∣=r\mid x^2 - 4x - 13 \mid = r∣x2−4x−13∣=r has exactly three distinct real roots, then the value of r is

Question 5.

For a real number x the condition ∣3x−20∣+∣3x−40∣=20\mid3x-20\mid+\mid3x-40\mid=20∣3x−20∣+∣3x−40∣=20 necessarily holds if

Question 6.

If 3x+2∣y∣+y=73x+2\mid y\mid+y=73x+2∣y∣+y=7 and x+∣x∣+3y=1x+\mid x \mid+3y=1x+∣x∣+3y=1 then x+2yx+2yx+2y is:

Question 7.

In how many ways can a pair of integers (x , a) be chosen such that x2−2∣x∣+∣a−2∣=0x^{2}-2\mid x\mid+\mid a-2\mid=0x2−2∣x∣+∣a−2∣=0 ?

Question 8.

The product of the distinct roots of ∣x2−x−6∣=x+2\mid x^2 - x - 6 \mid = x + 2∣x2−x−6∣=x+2 is

Question 9.

The shortest distance of the point (12,1)(\frac{1}{2},1)(21​,1) from the curve y = I x -1I + I x + 1I is

Question 10.

Let f(x)=2x−5f(x) =2x-5f(x)=2x−5 and g(x)=7−2xg(x) =7-2xg(x)=7−2x. Then |f(x)+ g(x)| = |f(x)|+ |g(x)| if and only if

Other Topics of that Section

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Popular Degrees

Popular Specializations

Management Colleges in States

Management Colleges in Cities

Popular Management Exams

Management Colleges by College Type

Let $0 \leq a \leq x \leq 100$ and $f(x) = \mid x - a \mid + \mid x - 100 \mid + \mid x - a - 50\mid$ . Then the maximum value of f(x) becomes 100 when a is equal to

The largest real value of a for which the equation $\mid x + a \mid + \mid x - 1 \mid = 2$ has an infinite number of solutions for x is

The number of integers n that satisfy the inequalities $\mid n - 60 \mid < \mid n - 100 \mid < \mid n - 20 \mid$ is

If r is a constant such that $\mid x^2 - 4x - 13 \mid = r$ has exactly three distinct real roots, then the value of r is

For a real number x the condition $\mid3x-20\mid+\mid3x-40\mid=20$ necessarily holds if

If $3x+2\mid y\mid+y=7$ and $x+\mid x \mid+3y=1$ then $x+2y$ is:

In how many ways can a pair of integers (x , a) be chosen such that $x^{2}-2\mid x\mid+\mid a-2\mid=0$ ?

The product of the distinct roots of $\mid x^2 - x - 6 \mid = x + 2$ is

The shortest distance of the point $(\frac{1}{2},1)$ from the curve y = I x -1I + I x + 1I is

Let $f(x) =2x-5$ and $g(x) =7-2x$ . Then |f(x)+ g(x)| = |f(x)|+ |g(x)| if and only if