# Recent questions tagged cat1997

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These questions are based on the following data:A thief flees City $A$ in a car towards City $B$ on a stretch of straight road, $300$ kilometres long, at the speed of $60...

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In the given figure, $EADF$ is a rectangle and $ABC$ is a triangle whose vertices lie on the sides of $EADF$. $AE = 22,BE = 6,CF = l6$ and $BF = 2$. Find the length of th...

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In the adjoining figure, points $A, B, C$ and $D$ lie on the circle. $AD = 24$ and $BC =12$. What is the ratio of the area of the triangle $CBE$ to that of the triangle $...

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Boston is $4$ hours ahead of Frankfurt and two hours behind India. X leaves Frankfurt at $06:00$ p.m. on Friday and reaches Boston the next day. After waiting there for t...

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At Weird Holiday Company, an employee gets a holiday on those days whose first letter is the same as the first letter of the employee’s name. All other days are working...

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In a rectangle, the difference between the sum of the adjacent sides and the diagonal is half the length of the longer side. What is the ratio of the shorter to the longe...

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In a triangle $ABC$, points $P, Q$ and $R$ are the mid-points of the sides $AB, BC$ and $CA$ respectively. If the area of the triangle $ABC$ is $20$ sq units, find the ar...

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The value of each of a set of silver coins varies as the square of its diameter if thickness remains constant, and it varies as the thickness if the diameter remains cons...

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$A, B$ and $C$ are defined as follows:$A=(2.000004)\div [(2.000004)^{2}+(4.000008)]$$B=(3.000003)\div [(3.000003)^{2}+(9.000009)]$$C=(4.000002)\div [(4.000002)^{2}+(8.000...

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The adjoining figure shows a set of concentric squares.If the diagonal of the innermost square is $2$ units, and if the distance between the corresponding corners of any ...

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$ABC$ is a three-digit number in which $A>O$. The value of $ABC$ is equal to the sum of the factorials of its three digits. What is the value of $B$?$9$$7$ $4$ $2$

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For these questions, the following functions have been defined:$la(x,y,z) = min(x+y, y+z)$ $le (x,y,z) = max(x–y, y–z)$ $ma(x,y,z)=(1/2) [le(x,y,z)+la(x,y,z)]$For $x ...

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For these questions, the following functions have been defined:$la(x,y,z) = min(x+y, y+z)$$le (x,y,z) = max(x–y, y–z)$$ma(x,y,z)=(1/2) [le(x,y,z)+la(x,y,z)]$What is t...

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For these questions, the following functions have been defined:$la(x,y,z) = min(x+y, y+z)$$le (x,y,z) = max(x–y, y–z)$$ma(x,y,z)=(1/2) [le(x,y,z)+la(x,y,z)]$Given tha...

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P, Q and R are three consecutive odd numbers in ascending order. If the value of three times P is three less than two times R, find the value of R.$5$$7$$9$$11$

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AB is the diameter of the given circle, while points C and D lie on the circumference as shown. If AB is $15$ cm, AC is $12$ cm and BD is $9$ cm, find the area of the qua...

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A man earns $x$% on the first $2000$ rupees and $y$% on the rest of his income. If he earns Rs $700$ from Rs $4000$ and Rs $900$ from Rs $5000$ of income, find $x$.$20$$1...

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A survey of $200$ people in a community who watched at least one of the three channels – BBC, CNN and DD showed that $80$% of the people watched DD, $22$% watched BBC, ...

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A survey of 200 people in a community who watched at least one of the three channels – BBC, CNN and DD showed that $80$% of the people watched DD, $22$% watched BBC, an...

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Which of the following is true?$_{7}^{3^{2}} = (7^{3})^{2}$$_{7}^{3^{2}} (7^{3})^{2}$$_{7}^{3^{2}} < (7^{3})^{2}$None of these

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If $m$ and $n$ are integers divisible by $5$, which of the following is not necessarily true?$m–n$ is divisible $5$.$m^{2}-n^{2}$ is divisible by $25$.$m+n$ is divisibl...

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The sum of the areas of two circles which touch each other externally is $153\pi$. If the sum of their radii is $15$, find the ratio of the larger to the smaller radius.$...

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If the roots, $x_{1}$ and $x_{2}$ of the quadratic equation $x^{2}-2x+c=0$ also satisfy the equation $7x_{2}-4x_{1}=47$, then which of the following is true? $c=-15$$x_{1...

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The average marks of a student in ten papers are $80$. If the highest and the lowest scores are not considered, the average is $81$. If his highest score is $92$, find th...

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$P$ and $Q$ are two integers such that $P \times Q = 64$. Which of the following cannot be the value of $P+Q$?$20$$65$$16$$35$

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A candidate was asked to find $7/8$th of a positive number; he found $7/18$th of the same by mistake. If his answer was $770$ less than the correct one, then the original...

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An express train moving at the rate of $80$ km per hour overtakes completely a good train twice as long and moving on a parallel line in the same direction at the rate of...

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Fresh grapes contain $90$% water by weight while dried grapes contain $20$% water by weight. The weight of dry grapes available from $20$ kg of fresh grapes will be.$2$ k...

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A dry fruit seller purchased 3 kinds of nuts at the rate of Rs. $100$/kg, Rs. $80$/kg and Rs. $60$/kg. He then mixed them, respectively, in the ratio $3:4:5$ by weight an...

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How many values of the natural number $n$ are possible so that the expression $(16n^{2}+7n+6)/n$ is also a natural number?Infinitely many$3$$4$None of thesed & c

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After a discount of $11.11$%, a trader still makes a gain of $14.28$%. At how many percent above the cost price does he mark his goods?$28.56$% $35$%$22.22$%None of these...

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If $\log_{2}[ \log_{7} (x^{2}-x+37)]=1$ then what could be the value of $x$?$3$$5$$4$None of these$c$

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In how many ways can the eight directors, the Vice chairman and the Chairman of a firm be seated at around- table, if the Chairman has to sit between the Vice- chairman a...

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A student gets an aggregate of 60% marks in five subjects in the ratio $10:9:8:7:6$. If the passing marks are $50$% of the maximum marks and each subjects has the same ma...

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There are $60$ students in a class. These students are divided into three groups $A, B$ and $C$ of $15, 20$ and $25$ students each. The groups $A$ and $C$ are combined to...

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