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1 votes
1 answer
4288
CAT 2003 | Question: 2-94
What is the sum of all two-digit numbers that give a remainder of $3$ when they are divided by $7?$ $666$ $676$ $683$ $777$
What is the sum of all two-digit numbers that give a remainder of $3$ when they are divided by $7?$$666$$676$$683$$777$
1 votes
1 answer
4289
CAT 2003 | Question: 2-93
If $\log_{10} x - \log_{10} \sqrt{x} = 2 \log_x 10$ then a possible value of $x$ is given by $10$ $\frac{1}{100}$ $\frac{1}{1000}$ None of these
If $\log_{10} x - \log_{10} \sqrt{x} = 2 \log_x 10$ then a possible value of $x$ is given by$10$$\frac{1}{100}$$\frac{1}{1000}$None of these
0 votes
1 answer
4293
CAT 2003 | Question: 2-89
If three positive real numbers $x, y, z$ satisfy $y – x = z – y$ and $x y z = 4,$ then what is the minimum possible value of $y?$ $2^{\frac{1}{3}}$ $2^{\frac{2}{3}}$ $2^{\frac{1}{4}}$ $2^{\frac{3}{4}}$
If three positive real numbers $x, y, z$ satisfy $y – x = z – y$ and $x y z = 4,$ then what is the minimum possible value of $y?$$2^{\frac{1}{3}}$$2^{\frac{2}{3}}$$2^...
0 votes
1 answer
4294
CAT 2003 | Question: 2-88
If both $a$ and $b$ belong to the set $\{1, 2, 3, 4\}$, then the number of equations of the form $ax^2 + bx + 1 = 0$ having real roots is $10$ $7$ $6$ $12$
If both $a$ and $b$ belong to the set $\{1, 2, 3, 4\}$, then the number of equations of the form $ax^2 + bx + 1 = 0$ having real roots is$10$$7$$6$$12$
0 votes
0 answers
4295
CAT 2003 | Question: 2-87
In the figure (not drawn to scale) given below, if $\text{AD = CD = BC},$ and $\measuredangle \text{BCE} = 96^{\circ}$, how much is $\measuredangle \text{DBC}?$ $32^{\circ}$ $84^{\circ}$ $64^{\circ}$ Cannot be determined
In the figure (not drawn to scale) given below, if $\text{AD = CD = BC},$ and $\measuredangle \text{BCE} = 96^{\circ}$, how much is $\measuredangle \text{DBC}?$$32^{\cir...
0 votes
1 answer
4304
CAT 2003 | Question: 2-78
If $x$ and $y$ are integers then the equation $5x + 19y = 64$ has no solution for $x < 300$ and $y < 0$ no solution for $x > 250$ and $y > – 100$ a solution for $250 < x < 300$ a solution for $– 59 < y < – 56$
If $x$ and $y$ are integers then the equation $5x + 19y = 64$ hasno solution for $x < 300$ and $y < 0$no solution for $x 250$ and $y – 100$a solution for $250 < x < 3...
0 votes
1 answer
4305
CAT 2003 | Question: 2-77
What is the remainder when $4^{96}$ is divided by $6?$ $0$ $2$ $3$ $4$
What is the remainder when $4^{96}$ is divided by $6?$ $0$$2$$3$$4$
0 votes
0 answers
4306
CAT 2003 | Question: 2-76
The length of the circumference of a circle equals the perimeter of a triangle of equal sides, and also the perimeter of a square. The areas covered by the circle, triangle, and square are $c, t,$ and $s,$ respectively. Then, $s > t > c$ $c > t > s$ $c > s > t$ $s > c > t$
The length of the circumference of a circle equals the perimeter of a triangle of equal sides, and also the perimeter of a square. The areas covered by the circle, triang...
0 votes
1 answer
4307
CAT 2003 | Question: 2-75
Using only $2, 5, 10, 25$ and $50$ paise coins, what will be the minimum number of coins required to pay exactly $78$ paise, $69$ paise and Rs $1.01$ to three different persons? $19$ $20$ $17$ $18$
Using only $2, 5, 10, 25$ and $50$ paise coins, what will be the minimum number of coins required to pay exactly $78$ paise, $69$ paise and Rs $1.01$ to three different ...
0 votes
1 answer
4308
CAT 2003 | Question: 2-74
If $\frac{1}{3} \log_3 \text{M} + 3 \log_3 \text{N} =1 + \log_{0.008} 5$, then $\text{M}^9 = \frac{9}{\text{N}}$ $\text{N}^9 = \frac{9}{\text{M}}$ $\text{M}^3 = \frac{3}{\text{N}}$ $\text{N}^9 = \frac{3}{\text{M}}$
If $\frac{1}{3} \log_3 \text{M} + 3 \log_3 \text{N} =1 + \log_{0.008} 5$, then$\text{M}^9 = \frac{9}{\text{N}}$$\text{N}^9 = \frac{9}{\text{M}}$$\text{M}^3 = \frac{3}{\te...
0 votes
1 answer
4309
CAT 2003 | Question: 2-73
A real number $x$ satisfying $1- \frac{1}{n} < x \leq 3 + \frac{1}{n}$ for every positive integer $n,$ is best described by $1 < x < 4$ $0 < x \leq 4$ $0 < x \geq 4$ $1 \leq x \leq 3$
A real number $x$ satisfying $1- \frac{1}{n} < x \leq 3 + \frac{1}{n}$ for every positive integer $n,$ is best described by$1 < x < 4$$0 < x \leq 4$$0 < x \geq 4$$1 \leq ...
0 votes
1 answer
4310
CAT 2003 | Question: 2-72
The number of roots common between $x^3 + 3 x^2 + 4x + 5 = 0$ and $x^3 + 2 x^2 + 7x +3 =0$ is $0$ $1$ $2$ $3$
The number of roots common between $x^3 + 3 x^2 + 4x + 5 = 0$ and $x^3 + 2 x^2 + 7x +3 =0$ is$0$$1$$2$$3$
0 votes
0 answers
4311
CAT 2003 | Question: 2-71
Let $\text{ABCDEF}$ be a regular hexagon. What is the ratio of the area of the triangle $\text{ACE}$ to that of the hexagon $\text{ABCDEF}?$ $\frac{1}{3}$ $\frac{1}{2}$ $\frac{2}{3}$ $\frac{5}{6}$
Let $\text{ABCDEF}$ be a regular hexagon. What is the ratio of the area of the triangle $\text{ACE}$ to that of the hexagon $\text{ABCDEF}?$$\frac{1}{3}$$\frac{1}{2}$$\fr...
0 votes
0 answers
4312
CAT 2003 | Question: 2-70
Consider the sets $T_n = \{n, n + 1, n + 2, n + 3, n + 4\}$, where $n = 1, 2, 3,\dots, 96.$ How many of these sets contain $6$ or any integral multiple thereof (i.e., any one of the numbers $6, 12, 18, \dots)?$ $80$ $81$ $82$ $83$
Consider the sets $T_n = \{n, n + 1, n + 2, n + 3, n + 4\}$, where $n = 1, 2, 3,\dots, 96.$ How many of these sets contain $6$ or any integral multiple thereof (i.e., any...
0 votes
1 answer
4313
CAT 2003 | Question: 2-69
The infinite sum $1 + \frac{4}{7} + \frac{9}{7^2} + \frac{16}{7^3} + \frac{25}{7^4} + \dots$ equals $\frac{27}{14}$ $\frac{21}{13}$ $\frac{49}{27}$ $\frac{256}{147}$
The infinite sum $1 + \frac{4}{7} + \frac{9}{7^2} + \frac{16}{7^3} + \frac{25}{7^4} + \dots$ equals$\frac{27}{14}$$\frac{21}{13}$$\frac{49}{27}$$\frac{256}{147}$
0 votes
1 answer
4318
CAT 2003 | Question: 2-62
If $|b| \geq 1$ and $x =\; – |a| b$, then which one of the following is necessarily true? $a – xb < 0$ $a – xb \geq 0$ $a – xb > 0$ $a – xb \leq 0$
If $|b| \geq 1$ and $x =\; – |a| b$, then which one of the following is necessarily true?$a – xb < 0$$a – xb \geq 0$$a – xb 0$$a – xb \leq 0$
0 votes
1 answer
4320
CAT 2003 | Question: 2-60
If $13x + 1 < 2$ and $z,$ and $z + 3 = 5y^2$, then $x$ is necessarily less than $y$ $x$ is necessarily greater than $y$ $x$ is necessarily equal to $y$ None of the above is necessarily true.
If $13x + 1 < 2$ and $z,$ and $z + 3 = 5y^2$, then$x$ is necessarily less than $y$$x$ is necessarily greater than $y$$x$ is necessarily equal to $y$None of the above is n...
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