Oral puzzles

Jai Ganesh · 2006-04-17 02:38:42

116. The ratio of the common differences of two series in Arithmetic Progression is 4:9. If the ratio of their sums of the first 25 terms of the two series is 4:9, what is the ratio of their sums of the first 75 terms?

117. The number N=49!, that is 49x48x47x....4x3x2x1. How many times can the number N repeatedly be divided by 14 so that no reminder is obtained?

118. Taps A, B, and C are connected to a water tank and the rate of flow of water is 21 litres/hour, 28 litres/hour and 24 litres/hour respectively. Taps A and B fill the tank and tap C empties the tank. If all the three taps are opened simultaneously, the tank gets completely filled in 8 hours. What is the capacity of the tank?

119. The original price of an article is $ 3000. The price is discounted by 20% and then raised by 10%. What is the new price of the article?

120. A person claims to have earned a profit of 10%. But it was found that he had calculated the profit percent on Selling Price instead of Cost Price. What was his actual profit?

Jai Ganesh · 2006-04-17 16:17:05

121. A person has four hats, 6 shirts and 4 trousers. He is always with his hat on. He also has 3 ties, but doesn't always wear a tie. In how many different ways could he dress himself up for a party?

122. Brian and Desmond start from a point A towards B. Brian, the faster of the two, on reaching B, starts moving back to A on the same route. He meets Desmond, and then again starts going towards B. This continues until Desmond reaches point B. If the speeds of Brian and Desmond are 20 kilometers/hour and 15 kilometers/hour respectively, and the distance between A and B is 45 kilometers, what is the total distance covered by Brian?

123. A man jogging diametrically across a semi-circular track from X to Y takes 48 seconds lesser than he would take to cover the semi-circular path. His speed is 50 meters per minute. What is the radius of the semi-circular track?

Jai Ganesh · 2006-04-18 17:58:44

124. The length of a chord of a circle at a distance of 5 cm from the centre is 24 cm. What is the diameter of the circle?

125. What is the ratio of the areas of a square of side 6 cm and an equilateral triangle of side 6 cm?

126. The largest possible square is inscribed in a circle of circumeference

units. What is the area of the square?

127. If the areas of two spheres are in the ratio 4:9, what would be the ratio of their volumes?

128. The length of a hall is 4/3 times its breadth. If the area of the hall is 675 square meters, what is the difference between the lengt and breadth of the hall?

129. The volume of a cube is 216 cubic centimeters. It is moulded into a cuboid having one edge equal to 6 cm. What is the number of ways it can be done in such a way that the lengths of the sides are integral values?

130. 6x²+ax+7 when divided by x-2 gives remainder 13. What is the value of a?

131. What is the value of k for which the equation
2kx²-40x+25=0 has equal roots?

132. A cuboid is formed of 3 edges measuring 3 cm, 4 cm, and 5 cm. It is sliced into two identical solids by a plane through a diagonal of the smallest of the faces. What would the surface area of the sliced section be?

133. A solid body is made up of a cylinder of radius r and height r, a cone of base radius r and height r is fixed to the cylinder's one base and a hemisphere of radius r to its other base. If the value of r is 2 units, what would be the total volume of the body?

rm · 2006-04-19 14:37:44

124. 26
125. 4:sqrt(3)
126. 2
127. 8:27
128. 7.5
129. 4 ( not counting the case when it is left as it is )
130. -9
131. 8
132. 25
133. 2*pi*r^^3

rm · 2006-04-19 14:43:58

121. 4*6*4*4 ( assuming he won't go to the party without his shirt and trousers )
122. Brian takes 45/15 = 3 hrs. In this time D covers 3 x 20 = 60 Kms
123. 40/(Pi-2)

Jai Ganesh · 2006-04-19 16:10:29

rm,
all your answers are correct!

Jai Ganesh · 2006-04-19 16:24:08

134. The speed of a metro train is 54 kilometers per hour. However, the effective speed after including the time of stoppage at stations is 45 kilometers per hour. How many minutes an hour does the train stop?

135. A cone, hemisphere and cylinder have the same base and the heights of the cone and cylinder are equal to the base radius. What would be the ratio of volumes of the three solids?

136. What is the raminder when

is divided by 8?

137. A and B can weave a carpet in 10 days and 15 days respectively. They begine to work together but B leaves after 2 days. In how many days would A complete the work?

138. Two cars were sold for $ 9,900 each. In one transaction there was a gain of 10% and in the other, a loss of 10% was incurred. What was the net effect of the two transactions together?

139. What is the difference between the Simple Interest and Compund Interest compunded annually, bot the at the rate of 12% per annum, for two years?

140. Of the 30 students in a class, the average age of the first ten is 12.5 years and the average age of the next twenty is 13.1 years. What is the average age of the whole class?

Jai Ganesh · 2006-04-20 16:55:56

141. If

what is the value of
?

142. What is the remainder when

is divided by (x-2)?

143. If the value of

then what would be the value of

144. If p and q are the roots of the equation x²+ax+b=0, then what are the roots of the equation x²-ax+b=0?

145. 1 man or 2 women or 3 boys can do a piece of work in 55 days. In how many days would 1 man, 1 woman and 1 boy do the same work?

146. A circle of 5 cm radius is drawn and another circle of 3 cm radius is cut out of this circle. What is the radius of a circle which has the same area as the area of the bigger circle excluding the cut one?

147. What is the value of
(tan A + cot A + sec A)(tan A + cot A - sec A)?

148. A spherical iron ball is dropped into a cylindrical vessel of base diameter 14 cm. The water level increases by 9 1/3 cm. What is the radius of the ball?

149. The radius of a cylindrical cistern is 10 meters and its height is 15 meters. Initially the cistern is empty. The cistern is filled with water through a pipe whose diameter is 50 centimeters. Water is flowing out of the pipe with a velocity of 5 meters per second. How many minutes would it take for the cistern to be filled?

150. A sphere of radius 13 cm is cut by a plane whose distance from the center of the sphere is 5 cm. What is the circumference of the plane circular section?

Jai Ganesh · 2006-04-21 16:40:47

151. Two circles of diamters 74 cm and 40 cm have a common chord of length 24 cm. What is the distance between the centers of the circles?

152.Two complementary angles are such that two times the measure of one is equal to three times the measure of the other. What is the measure of the larger angle?

153. The mean of marks scored by the 100 students in a class was 72. The mean of the marks scored by the 70 boys was 75. What was the mean of the marks scored by the girls?

154. The number of students opting for Information Technology courses decreased by 23%. If the present number of students who opted for Information Technology courses is 1540, what was the original number of students who opted for the said course?

155. An investment triples itself in 30 years at simple interest. What is the rate of simple interest?

156. 76% of the students in a school are boys. If the number of girls is 204, what is the total number of students in the school?

157. A toy train travels on a circular path of radius 250 meters at the rate of 10 kilometers/hour. What is the angle moved with reference to the center of the circle in 9 seconds?

158. If sinA=cosA and A iss acute, what is tanA-cotA equal to?

159. If

what is the value of ?

160. If

what is the value of x?

Jai Ganesh · 2006-04-22 17:48:33

161. If

what is the value of tan²θ?

162. What is the maximum value of sinθ + cosθ?

163. From noon to 4.24 pm, what's the angle covered by the hour hand of the clock?

164. If

what is the value of x?

165. What is the value of

?

166. If

what is the value of x?

167. In the equation

one root is the reciprocal of the other. What is the alue of a?

168. If

waht is the value of x?

169. Find the samller of the two numbers whose sum is 35 and difference is 5.

170. If 2x-y=4 and x+y=5, what is the value of xy?

Jai Ganesh · 2006-04-23 16:22:40

171. What is the sum of all odd numbers from 1 to 32?

172. What is the unit digit in the product 207x781x39x94?

173. When a number is divided by 296, the remainder is 75. What would the remainder be when the number is divided by 37?

174. Which is the number nearest to 7671 that is exactly divisible by 38?

175. When two numbers are divided by a certain divisor, they give remainders of 35 and 30 respectively. When the sum of the two numbers is divided by the same divisor, the remainder obtained is 20. What is the divisor?

176. What is the value of y is 1y3y6 is divisible by 11?

177. Which is the largest positive integer which divides all integers of the form n³-n?

178. Which is the biggest even divisor of (2n+1)²-1where n is a natural number?

179. What is the last digit of

for any positive integer n?

180. How many positive integers less than or equal to 1200 are divisible by both 6 and 8?

krassi_holmz · 2006-04-24 02:05:56

180. 50

krassi_holmz · 2006-04-24 02:14:10

179. you said "for any positive integer n", so this digit must be the digit when n=1.

4.16+1=64+1=65=5(mod 10).
let f(x)=(2.4^n)^2.
We got that f(1)=4(mod 10).
Let for fixed k f(k)=4(mod 10).
Then, for k+1, we get:
f(k+1)=(2.4^(k+1))^2=f(k) 4^2
But
f(k) 4^2=4.4^2=64=4(mod 10),
so f(k+1)=4(mod 10).
Then the number is 5.

krassi_holmz · 2006-04-24 02:15:56

178. (2n+1)²-1=2n(2n+2)=4n(n+1), so 8/(2n+1)²-1

Jai Ganesh · 2006-04-24 02:22:55

Well done, krassi_holmz!
Your answers are all correct!

krassi_holmz · 2006-04-24 05:27:32

177.n^3-n=(n-1)n(n+1), divisible by 3!=6

krassi_holmz · 2006-04-24 05:29:14

176. What is the value of y is 1y3y6 is divisible by 11?
5.

krassi_holmz · 2006-04-24 05:32:14

175. When two numbers are divided by a certain divisor, they give remainders of 35 and 30 respectively. When the sum of the two numbers is divided by the same divisor, the remainder obtained is 20. What is the divisor?
a === 35 mod x
b === 30 mod x
(a + b) === 35 + 30 = 65 === 20 mod x,
so 65 === 20 mod x and x|65-20=45 and x>20, so x=45

krassi_holmz · 2006-04-24 05:34:09

174. Which is the number nearest to 7671 that is exactly divisible by 38?
7676.

Patrick · 2006-04-24 05:35:36

174. 7676
175. Not sure I understand this one, but: y=11?

Last edited by Patrick (2006-04-24 05:39:36)

krassi_holmz · 2006-04-24 05:36:22

173. When a number is divided by 296, the remainder is 75. What would the remainder be when the number is divided by 37?
x===75 (mod 296),
but 37|296, so:
x===75===1(mod 37)

krassi_holmz · 2006-04-24 05:38:46

172. What is the unit digit in the product 207x781x39x94?
207.781.39.94=592671222

krassi_holmz · 2006-04-24 05:40:33

171. What is the sum of all odd numbers from 1 to 32?
271

krassi_holmz · 2006-04-24 05:42:59

175. Not sure I understand this one, but: y=11?

y can't be 11 because the remainder must be > of the divisor.

krassi_holmz · 2006-04-24 05:45:49

170. If 2x-y=4 and x+y=5, what is the value of xy?
2x=4+y
x=(4+y)/2
(4+y)/2+y=5
4+y+2y=10
3y=6
y=2
x=6/2=3
xy=6

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