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Saket wanted to add two two-digit numbers. Instead, he multiplied them and obtained $$629$$. The sum of the two two-digit numbers is
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Saket wanted to add two two-digit numbers. Instead, he multiplied them and obtained $$629$$. The sum of the two two-digit numbers is
Factorising gives $$629=17 \times 37$$. Both factors are two-digit numbers, and their sum is $$17+37=54$$.
The sum of three integers is $$1$$ and their product is $$36$$. The greatest of these three integers is
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The sum of five consecutive even numbers is $$150$$. When written in ascending order, the fourth number is
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The price of a cell phone is decreased by $$25\%$$. What percentage increase in the decreased price is required to restore the original price?
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A rectangular carpet is placed in an $$8\text{ m} \times 8\text{ m}$$ room as shown. What fraction of the floor is not covered?
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$$p$$ and $$p+1$$ are both prime numbers. Then the value of $$\frac{p(p+1)}{2p+1}$$ lies between
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Real numbers $$a,b,c,d$$ satisfy $$a-2023=b+2024=c-2025=d+2026$$. The greatest among $$a,b,c,d$$ is
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In the adjoining figure, $$AD=AE$$. The measure of $$\angle EAD$$ is
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The largest three-digit number exactly divisible by the HCF of $$24$$ and $$36$$ is $$n$$. Then $$n+4$$ equals
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In the given figure, $$AB$$, $$HG$$, $$CD$$ and $$FE$$ are parallel. Also, $$AB=6$$, $$GH=4$$, $$CD=5$$, $$FE=9$$ and $$BC=8$$. The distances between each indicated pair of parallel lines are $$3$$. The area of the complete figure is
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The number of pairs of two-digit square numbers whose sum or difference is also a square is
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There are $$20$$ people around a table. Each person shakes hands with the person immediately to the left and the person immediately to the right. The total number of handshakes is
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In the adjoining figure, $$A,B,C,D$$ are the vertices of a square of side $$3$$ units. All the semicircles are equal. The area of the shaded region in square units is
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Two box types $$A$$ and $$B$$ hold $$38$$ and $$20$$ candles respectively. Exactly $$288$$ candles fill all the boxes. If $$m$$ boxes are of type $$A$$ and $$n$$ boxes are of type $$B$$, then $$\frac{m}{n}$$ is
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For a positive integer $$r$$, let $$[r]$$ denote the sum of its divisors other than $$1$$ and $$r$$ itself. For example, $$[6]=2+3=5$$. The value of $$[[[12]]]$$ is
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The fraction $$\frac{(2 \times 3 \times 4)+(4 \times 6 \times 8)+(6 \times 9 \times 12)+\cdots+(20 \times 30 \times 40)}{(1 \times 2 \times 3)+(2 \times 4 \times 6)+(3 \times 6 \times 9)+\cdots+(10 \times 20 \times 30)}$$ reduces to
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In the adjoining figure, $$ABCD$$ is a rectangle, and $$AE$$ and $$CF$$ are quadrants. The length of the rectangle is twice its breadth. Taking $$\pi=\frac{22}{7}$$, the shaded area is $$21\text{ cm}^2$$. The area of the rectangle is
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The number $$m$$ has $$2,5,6$$ as factors, and the number $$n$$ has $$4,8$$ as factors. The smallest possible value of $$m+n$$ is
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Bus route $$X$$ arrives every $$15$$ minutes and bus route $$Y$$ arrives every $$40$$ minutes. Both buses have arrived now. They will next arrive simultaneously after how many hours?
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In the adjoining figure, $$\angle ABC=60^\circ$$ and $$\angle ACB=80^\circ$$. $$AD$$ bisects $$\angle A$$. Through $$C$$, a line making an angle of $$\frac{\angle A}{2}$$ with $$BC$$ is drawn. It intersects the bisector and the perpendicular from $$B$$ to $$AD$$ as shown. The value of $$x$$ in degrees is
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For real numbers $$a$$ and $$b$$, define $$a \ast b=\left(a+\frac{b}{2}\right)\left(b+\frac{a}{2}\right)$$. The value of $$(2 \ast 8)\ast2$$ is
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A two-digit number has repeated digits. The number of such numbers having exactly $$4$$ positive divisors is
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The salaries of Peter and Ali are in the ratio $$3 \colon 2$$. Their expenditures are in the ratio $$5 \colon 3$$, and each saves Rs. $$5000$$. Peter's income in rupees is
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In the given figure, $$\angle A \colon \angle B \colon \angle C=14 \colon 3 \colon 1$$. The two additional lines are drawn as described in the figure. The measure of $$\angle EGF$$ in degrees is
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Five people have different odd amounts of money, each less than Rs. $$100$$. The largest possible total amount in rupees is
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The cost price of $$10$$ articles equals the selling price of $$9$$ articles. The profit percentage is $$11\frac{1}{a}\%$$. The value of $$a$$ is
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When $$2\frac{6}{11}$$ of $$1\frac{2}{7}$$ is divided by $$3\frac{3}{11}$$, the result is
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Two cell phones are sold at the same selling price. One gives a $$10\%$$ gain and the other gives a $$10\%$$ loss. The overall percentage loss is
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An office employee works for $$4$$ consecutive days and then has one day off, repeating this pattern. Today is an off-day and a Sunday. The minimum number of days the employee must work before another off-day falls on Sunday is
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In the adjoining figure, triangle $$BCD$$ is equilateral. If $$\angle AFB=90^\circ$$ and $$AH$$ bisects $$\angle FAE$$, then the measure of $$\angle HGE$$ in degrees is
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