Recent questions tagged cat2001

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122
Euclid has a triangle in mind, Its longest side has length $20$ and another of its sides has length $10.$ Its area is $80.$ What is the exact length of its third side?$\s...
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124
If $a, b, c$ and $d$ are four positive real numbers such that $abcd = 1,$ what is the minimum value of $(1 + a)(1 + b)(1 + c)(1 + d)?$$4$$1$$16$$18$
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128
All the page numbers from a book are added, beginning at page $1.$ However, one page number was mistakenly added twice. The sum obtained was $1000.$ Which page number was...
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129
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133
In a number system the product of $44$ and $11$ is $1034.$ The number $3111$ of this system, when converted to the decimal number system, becomes$406$$1086$$213$$691$
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134
If $09/12/2001$ happens to be Sunday, then $09/12/1971$ would have been aWednesday TuesdaySaturday Thursday
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137
$m$ is the smallest positive integer such that for any integer $n m,$ the quantity $n^3 – 7n^2 + 11n – 5$ is positive. What is the value of $m?$$4$$5$$8$None of thes...
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138
$x$ and $y$ are real numbers satisfying the conditions $2 < x < 3$ and $–8 < y < –7.$ Which of the following expressions will have the least value?$x^2y$$xy^2$$5xy$No...
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140
Anita had to do a multiplication. Instead of taking $35$ as one of the multipliers, she took $53.$ As a result, the product went up by $540.$ What is the new product?$105...
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144
In the above diagram, $\text{ABCD}$ is a rectangle with $\text{AE = EF = FB}.$ What is the ratio of the area of the triangle $\text{CEF}$ and that of the rectangle?$\frac...
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146
Of $128$ boxes of oranges, each box contains at least $120$ and at most $144$ oranges. The number of boxes containing the same number of oranges is at least$5$$103$$6$Can...
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147
A red light flashes $3$ times per minute and a green light flashes $5$ times in two minutes at regular intervals. If both lights start flashing at the same time, how many...
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148
If $x 5$ and $y < −1,$ then which of the following statements is true?$(x + 4y) 1$$x − 4y$$−4x < 5y$None of these
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149
Let $x, y$ and $z$ be distinct integers, $x$ and $y$ are odd and positive, and $z$ is even and positive. Which one of the following statements cannot be true?$(x − z)^2...
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150