mathewhe/aqua_rat huggingface dataset:
Question: The ratio Q , by volume of soap to alcohol to water in a 76 litre solution is 2: 50: 100 . The solution is then altered by adding more soap, alcohol and water.After this alteration the ratio, by volume of soap to water in the solution doubles whereas the ratio, by volume of soap to water remains the same as before. What COULD BE the resulting volume.
(A) 79 litres
(B) 78 litres
(C) 77 litres
(D) 152 liters
(E) 304 litres
Rationale: I guess it should be
the ratio Q, by volume ofsoaptowaterin the solutiondoubleswhereas the ratio, by volume ofalocoholtowaterremains thesameas before
2:50: 100 => 1 : 25 : 50. If we add all the parts, we get 76 liters
So we have 1 liters of Soap, 25 liters of Alcohol and 50 liters of Water.
Now as per the Question, Soap : Water doubles but alcohol to water remains the same.
So Soap becomes 2 liters, Alcohol remains 25 liters and Water remains at 50 liters.
Hence 77 liters - Option C)
Answer: (C) 77 litres
Question: The length of a rectangular floor is more than its breadth by 200%. If Rs. 324 is required to paint the floor at the rate of Rs. 3 per sq m, then what would be the length of the floor?
(A) 76
(B) 15
(C) 18
(D) 16
(E) 19
Rationale: Let the length and the breadth of the floor be l m and b m respectively.
l = b + 200% of b = l + 2b = 3b
Area of the floor = 324/3 = 108 sq m
l b = 108 i.e., l * l/3 = 108
l2 = 324 => l = 18.
Answer: C
Answer: (C) 18
Question: A child must place 4 different toys in 5 different bins. If any of the toys can go in any of the bins, in how many ways can the child place the toys into the bins?
(A) 5^4
(B) 6^4
(C) 4^6
(D) 4^4
(E) 6^4-4^6
Rationale: there are 4 different bins and each of the toy can go to any of these bins..
so answer 5âˆ—5âˆ—5âˆ—5=5^4
ANSWER:A
Answer: (A) 5^4
Question: A tradesman by means of his false balance defrauds to the extent of 20%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?
(A) 48%
(B) 24%
(C) 44%
(D) 46%
(E) 84%
Rationale: g% = 20 + 20 + (20*20)/100
= 44%
Answer: C
Answer: (C) 44%
Question: Rohan spends 40% of his salary on food, 20% on house rent, 10% on entertainment and 10% on conveyance. If his savings at the end of a month are Rs. 2000. then his monthly salary is
(A) Rs. 10000
(B) Rs. 6000
(C) Rs. 8000
(D) Rs. 4000
(E) Rs. 2000
Rationale: Sol.
Saving = [100 - (40 + 20 + 10 + 10]% = 20%.
Let the monthly salary be Rs. x.
Then, 20% of x = 2000
â‡” 20 / 100x = 2000
â‡” x = 2000 Ã— 5 = 10000.
Answer A
Answer: (A) Rs. 10000
Question: The radius of the two circular fields is in the ratio 4: 5 the area of the first field is what percent less than the area of the second?
(A) 42%
(B) 39%
(C) 38%
(D) 36%
(E) 26%
Rationale: r = 4 Ï€r2 =16
r = 5 Ï€r2 = 25
25Ï€ â€“ 9Ï€
100 ---- ? => 36%.Answer:D
Answer: (D) 36%
Question: The operation is defined for all integers a and b by the equation ab = (a - 1)(b - 1). If x20 = 190, what is the value of x ?
(A) 10
(B) 12
(C) 11
(D) 13
(E) 14
Rationale: ab = (a - 1)(b - 1)
x20 = (x-1)(20-1) = 190 --> x-1=10 --> x=11
Answer: C
Answer: (C) 11
Question: An uneducated retailer marks all his goods at 50% above the cost price and thinking that he will still make 15% profit, offers a discount of 15% on the marked price. What is his actual profit on the sales?
(A) 12.50 %
(B) 27.50 %
(C) 14 %
(D) 14.50 %
(E) None
Rationale: Sol.
Let C.P. = Rs. 100. Then, marked price = Rs. 150.
S.P. = 85% of Rs. 150 = Rs. 127.5.
∴ Gain% = 27.50%.
Answer B
Answer: (B) 27.50 %
Question: Julie had 90 currency notes in all, some of which are of Rs 80 denomination and the remaining of Rs 50 denomination. The total amount of all these currency notes was Rs. 6000. How much amount (in Rs) did she have in the denomination of Rs 50?
(A) 56
(B) 35
(C) 30
(D) 45
(E) 40
Rationale: Let the number of 50-rupee notes = x
Then, the number of 80-rupee notes = (90 – x)
50x + 80(90 – x) = 6000 : x = 40
ANSWER:E
Answer: (E) 40
Question: John bought Bicycles at 6 for Rs 10000.What is the profit or loss Percentage after selling Bicycles at 5 for Rs 10000.
(A) 30%
(B) 50%
(C) 20%
(D) 60%
(E) None
Rationale: C.P. of 6 Bicycles = Rs10000
C.P. of 1 Bicycle = Rs10000/6=Rs 5000/3
S.P. of 5 Bicycles = Rs10000
S.P of 1 Bicycle= Rs 2000
Therefore, Profit Percentage={(2000-5000/3)/(5000/3)}100=20%
Answer: Option C
Answer: (C) 20%
Question: Look at this series: 70, 71, 76, __, 81, 86, 90, 91, ... What number should fill the blank?
(A) 70
(B) 71
(C) 80
(D) 96
(E) 84
Rationale: 70,71,76
80,81,86
90,91,96
ANSWER:C
Answer: (C) 80
Question: A container contains 40lit of milk. From this container
4 lit of milk was taken out and replaced by water.
This process was repeated further two times.
How much milk is now contained by the container?
(A) 19.16 lit
(B) 29.16 lit
(C) 9.16 lit
(D) 26.16 lit
(E) 16.6 lit
Rationale: Amount of milk left after 3 operations = 40(1-4/40)3lit
=(40*9/10*9/10*9/10)
= 29.16 lit
ANSWER : B 29.16 lit
Answer: (B) 29.16 lit
Question: Aravind had $ 2100 left after spending 30 % of the money he took for shopping. How much money did he
take along with him?
(A) 3000
(B) 3300
(C) 3400
(D) 3700
(E) 4000
Rationale: Let the money he took for shopping be m.
Money he spent = 30 % of m
= 30/100 × m
= 3/10 m
Money left with him = m – 3/10 m = (10m – 3m)/10 = 7m/10
But money left with him = $ 2100
Therefore 7m/10 = $ 2100
m = $ 2100× 10/7
m = $ 21000/7
m = $ 3000
Therefore, the money he took for shopping is $ 3000.
A)
Answer: (A) 3000
Question: If s,u, and v are positive integers and 2s=u+2v, which of the following must be true?
i. u>v
ii. u is not equal to v
iii. s=u
(A) None
(B) I only
(C) II only
(D) III only
(E) II and III
Rationale: Notice two things: 1. we are asked to find out which of the following MUST be true, not COULD be true and 2. s, u, and v are positive integers.
Given: 2s=2u+2v --> s=u+v. Now, since s, u, and v are positive integers then s is more than either u or v, so I is never true and III is always true. As for II: it's not necessarily true, for example 4=2+2. So, we have that only option I must be true.
Answer: B
Answer: (B) I only
Question: If x% of y is 100 and y% of z is 200, then find the relation between x and z.
(A) z = x
(B) 2z = x
(C) z = 2x
(D) None of above
(E) z = 2y
Rationale: Explanation:
It is , y% of z = 2(x% of y)
=> yz/100 = 2xy/100
=> z = 2x
Option C
Answer: (C) z = 2x
Question: A trader bought a car at 10% discount on its original price. He sold it at a 40% increase on the price he bought it. What percent of profit did he make on the original price?
(A) 118
(B) 110
(C) 112
(D) 126
(E) 115
Rationale: Original price = 100
CP = 80
S = 80*(140/100) = 126
100 - 126 = 26%
Answer: D
Answer: (D) 126
Question: Kay and Larry race around a running track. Kay runs at a constant rate of one lap every 9 minutes and Larry runs at a constant rate of one lap every 11 minutes. If they both start at the same time, how many minutes will it take for Kay to get exactly one lap ahead of Larry?
(A) 41.5
(B) 43.5
(C) 45.5
(D) 47.5
(E) 49.5
Rationale: Let x be the number of minutes it takes for Kay to get one lap ahead.
Then Kay ran x/9 laps and Larry ran x/11 laps.
x/9 = 1+x/11
11x=99+9x
2x=99
x=49.5
The answer is E.
Answer: (E) 49.5
Question: A certain roller coaster ride has between 80 and 110 people waiting in line to board. If riders are let on only in groups of 5 there will be 2 riders that do not get on. If the riders are let on only in groups of 6 all riders will be able to get on the roller coaster. How many riders are in the line?
(A) 82
(B) 87
(C) 90
(D) 102
(E) 110
Rationale: let 'x' be the number of riders. Given
x=5k+2 and x=6q also x is between 80-110
so multiples of 5= 80, 85, 90, 95, 100, 105, 110
multiples of 6= 84, 90, 96, 102, 108
Condition: If riders are let on only in groups of 5 there will be 2 riders that do not get on. If the riders are let on only in groups of 6 all riders will be able to get on the roller coaster.
only value satisfying this condition within a group of 80-110 riders is 102.
ANSWER:D
Answer: (D) 102
Question: If the operation € is defined for all x and y by the equation x € y = 2*x*y, then 8 € (4 € 5) =
(A) 80
(B) 120
(C) 160
(D) 640
(E) 760
Rationale: working inside out,
(4 € 5) = 2*4*5 = 40
8 € 40 = 2*8*40 = 640
Hence, answer is D
Answer: (D) 640
Question: The ratio of the volumes of two cubes is 729 : 343. What is the ratio of their total surface areas?
(A) 81 : 49
(B) 81 : 122
(C) 81 : 124
(D) 81 : 126
(E) 81 : 129
Rationale: Ratio of the sides = 3√729 : 3√343 = 9 : 7
Ratio of surface areas = 9^2 : 7^2 = 81 : 49
Answer: Option A
Answer: (A) 81 : 49
Question: A jogger running at 9 km/hr along side a railway track is 240 m ahead of the engine of a 150 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?
(A) 39 sec
(B) 87 sec
(C) 36 sec
(D) 16 sec
(E) 11 sec
Rationale: Speed of train relative to jogger = 45 - 9 = 36 km/hr.
= 36 * 5/18 = 10 m/sec.
Distance to be covered = 240 + 150 = 390 m.
Time taken = 390/10 = 39 sec.
Answer: A
Answer: (A) 39 sec
Question: In a certain province in France there are 11 cities. If a single road segment connects only two cities, how many road segments are required in order to connect the cities so that each city is connected to all other cities with a single road segment?
(A) 55
(B) 105
(C) 330
(D) 143
(E) 156
Rationale: 1 city needs 10 roads to connect directly to the rest => 11 city needs 11*10 roads.
One road is counted twice => the number of road needed is 11*10/2 = 55
Answer A
Answer: (A) 55
Question: In the number 10,0AB, A and B represent the tens and units digits, respectively. If 11,0AB is divisible by 55, what is the greatest possible value of B × A?
(A) 0
(B) 5
(C) 10
(D) 15
(E) 25
Rationale: You should notice that 55*2=110 so 11,000 is divisible by 55: 55*200=11,000 (or you can notice that 11,000 is obviously divisible by both 5 and 11 so by 55) --> B*A=0*0=0. Next number divisible by 55 is 11,000+55=11,055: B*A=5*5=15 (next number won't have 110 as the first 3 digits so we have only two options 0 and 25).
Answer: E.
!
Please post PS questions in the PS subforum:gmat-problem-solving-ps-140/
Please post DS questions in the DS subforum:gmat-data-sufficiency-ds-141/
No posting of PS/DS questions is allowed in the mainMath forum.
D
Answer: (D) 15
Question: In a shower, 5 cm of rain falls. The volume of water that falls on 1.5 hectares of ground is
(A) 75 cu. m
(B) 750 cu. m
(C) 7500 cu. m
(D) 75000 cu. m
(E) None of these
Rationale: Solution
Area = (1.5 × 10000) m2 = 45000 m2.
Depth = m = m.
∴ Volume = (area × depth) = m3 = 750 m3.
Answer B
Answer: (B) 750 cu. m
Question: If a point (x,y) is randomly selected within the square shown in the figure above, (the vertices are on 1,1 1,-1, -1,1 -1,-1) what are
the Q odds that x^2+y^2>1?
(A) 1. pi/4
(B) 2. pi/16
(C) 3. Q=1-pi/4
(D) 4. Q=1-pi/16
(E) 5.4-pi
Rationale: area of the square will be 4, and the area of circle with center (0,0) and radius 1 will be pi.
then succesful outcomes = 4 - pi (the area where x2+y2 will be greater than 1)
total outcomes = 4
therefore probability = (4-pi)/4
C
Answer: (C) 3. Q=1-pi/4
Question: Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. If the faster train passes the slower train in 36 seconds,what is the length of each train?
(A) 50 m
(B) 80 m
(C) 76 m
(D) 58 m
(E) 90 m
Rationale: let length of each train = x m
total distance while passing the slower train = (x+x) = 2x m
relative speed = (46-36) = 10 km/hr
=10*5/18 = 50/18 m/s
time = 36 sec
2x/36 = 50/18 => x=50
ANSWER A
Answer: (A) 50 m
Question: The probability that A speaks truth is 23/35 and that of B speaking truth is 35/47. What is the probability that they agree in stating the same fact?
(A) 1553/1645
(B) 1262/2535
(C) 1257/1835
(D) 1903/1735
(E) None of these
Rationale: If both agree stating the same fact, either both of them speak truth of both speak false.
Probability = 23/35 * 35/47 + 22/35 * 34/47
= 805/1645 + 748/1645 = 1553/1645
ANSWER:A
Answer: (A) 1553/1645
Question: The measures of the 2 acute angles of a triangle are in the ratio of 4 : 6. What arethe measures of the 2 angles?
(A) 20°
(B) 70°
(C) 110°
(D) 120°
(E) 54°
Rationale: If the ratio of the two angles is 4:6, then the measures of two angles can be written as 4x and 6x. Also the two acute angles of a triangle is equal to 90°. Hence
4x + 6x = 90
10x = 90
x = 9
Measures of the two acute angles are
4x = 4 × 9 = 36°
6x = 6 × 9 = 54°
E
Answer: (E) 54°
Question: Car Z travels 51 miles per gallon of gasoline when driven at a constant rate of 45 miles per hour, but travels 20 percent fewer miles per gallon of gasoline when driven at a constant rate of 60 miles per hour. How many miles does car Z travel on 10 gallons of gasoline when driven at a constant rate of 60 miles per hour?
(A) 320
(B) 375.2
(C) 400
(D) 408
(E) 440
Rationale: The question stem asks us for the distance possible with 10 gallons of fuel at a constant speed of 60 miles per hour. We therefore first calculate the fuel efficiency at that speed.
The stem tells us that at 45 miles/hour, the car will run 51 miles/gallon and at 60 miles/hour, that distance decreases by 20%. We can therefore conclude that the car will travel 40.8 miles/gallon at a constant speed of 60 miles/gallon. With 10 gallons of fuel, the car can therefore travel 40.8 miles/gallon * 10 gallons = 408 miles.
Answer D.
Answer: (D) 408
Question: Find the value of y from (12)^3 x 6^4 ÷ 432 = y?
(A) 2356
(B) 3454
(C) 4656
(D) 3456
(E) 5184
Rationale: Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184
432 12 x 62
E
Answer: (E) 5184
Question: The proportion of water to alcohol in Solution A is 4:1 and the proportion of water to alcohol in Solution B is 2:3. If an equal amount of each solution is mixed together, what is the concentration of alcohol in the new solution?
(A) 39%
(B) 40%
(C) 41%
(D) 42%
(E) 43%
Rationale: Let V be the total volume of the new solution.
Then a volume of V/2 was added from each solution A and B.
The amount of alcohol added to the new solution was:
(1/5)(V/2)+(3/5)(V/2)=V/10+3V/10=4V/10=2V/5.
The concentration of alcohol is 2/5=40%
The answer is B.
Answer: (B) 40%
Question: The average marks scored by Ganesh in English, Science, Mathematics and History is less than 17 from that scored by him in English, History, Geography and Mathematics. What is the difference of marks in Science and Geography scored by him?
(A) 40
(B) 50
(C) 60
(D) 68
(E) None of these
Rationale: E+H+G+M/4âˆ’E+S+M+H/4=17
â‡’ G - S = 68
Answer D
Answer: (D) 68
Question: Tea worth Rs.126 per kg are mixed with a third variety in the ratio 1: 1 : 2. If the mixture is worth Rs.133 per kg, the price of the third variety per kg will be
(A) Rs.169.50
(B) Rs.1700
(C) Rs. 175.50
(D) Rs. 155.50
(E) None
Rationale: Solution
Since first second varieties are mixed in equal proportions, so their average price = Rs.(126+135/2) = Rs.130.50
So, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find x.
x-133/22.50 = 1 =â€º x - 133 = 22.50 =â€º x=155.50.
Hence, price of the third variety = Rs.155.50 per kg.
Answer D
Answer: (D) Rs. 155.50
Question: In an election, candidate A got 80% of the total valid votes. If 15% of the total votes were declared invalid and the total numbers of votes is 560000, find the number of valid vote polled in favor of candidate.
(A) 330000
(B) 340000
(C) 380800
(D) 356000
(E) 357000
Rationale: Total number of invalid votes = 15 % of 560000
= 15/100 × 560000
= 8400000/100
= 84000
Total number of valid votes 560000 – 84000 = 476000
Percentage of votes polled in favour of candidate A = 80 %
Therefore, the number of valid votes polled in favour of candidate A = 80 % of 476000
= 80/100 × 476000
= 38080000/100
= 380800
C)
Answer: (C) 380800
Question: Monica and Miya's age are in 2:5. Find teh age of Monica if the sum of their age is 28.
(A) 10 years
(B) 14 years
(C) 20 years
(D) 8 years
(E) 12 years
Rationale: Let the age of Monica be 2x and Miya be 5x.
2x + 5x = 28
x = 4
Monica's age is 8 years
Answer : D
Answer: (D) 8 years
Question: A boy has twelve trousers and 14 shirts. In how many different ways can he select a trouser and a shirt?
(A) 238 ways
(B) 287 ways
(C) 266 ways
(D) 168 ways
(E) 121 ways
Rationale: Explanation:
The boy can select one trouser in 12 ways.
The boy can select one shirt in 14 ways.
The number of ways in which he can select one trouser and one shirt is 12 * 14 = 168 ways.
Answer: D
Answer: (D) 168 ways
Question: A bag contains 12 white and 18 black balls. 2balls are drawn in succession. What is the probability that first is white and second is black?
(A) 21/145
(B) 36/145
(C) 3/145
(D) 2/119
(E) 2/189
Rationale: The probability that first ball is white:
=12C130C1=12C130C1
=1230=1230
=25=25
Since, the ball is not replaced; hence the number of balls left in bag is 29.
Hence, the probability the second ball is black:
=18C129C1=18C129C1
=1829=1829
Required probability,
=(25)×(1829)=(25)×(1829)
=36/145
B
Answer: (B) 36/145
Question: When all the students in a school are made to stand in rows of 45, 40 such rows are formed. If the students are made to stand in rows of 40, how many such rows will be formed ?
(A) 31
(B) 36
(C) 45
(D) 40
(E) 21
Rationale: Explanation:
Total number of students = 45 x 40
When arranged in rows of 40, number of rows formed are,
= 45.
Answer: C
Answer: (C) 45
Question: Joe needs to paint all the airplane hangars at the airport, so he buys 360 gallons of paint to do the job. During the first week, he uses 1/4 of all the paint. During the second week, he uses 1/4 of the remaining paint. How many gallons of paint has Joe used?
(A) 18
(B) 157
(C) 175
(D) 216
(E) 250
Rationale: Total paint initially = 360 gallons
Paint used in the first week = (1/4)*360 = 90 gallons.
Remaning paint = 270 gallons
Paint used in the second week = (1/4)*270 = 67 gallons
Total paint used = 157 gallons.
Option B
Answer: (B) 157
Question: If Peter reads at a constant rate of 1 pages every 5 minutes, how many seconds will it take him to read N pages?
(A) 300
(B) 2N
(C) 5/2*N
(D) 24N
(E) 150
Rationale: Peter would read 1 page in 5/1 minutes
Peter would read N page in (5/1)*N min i.e. (5/2)*N*60 Seconds = 300N Seconds.
Option A is the correct Answer.
Answer: (A) 300
Question: If y is 60 percent greater than x, then x is what percent less than y?
(A) 30%
(B) 37.5%
(C) 45.5%
(D) 50%
(E) 55.5%
Rationale: y = 1.6x
x = y/1.6 = 10y/16 = y - (3/8)*y
3/8 is 37.5%.
The answer is B.
Answer: (B) 37.5%
Question: A reduction of 40% in the price of apples would enable a man to obtain 64 more for Rs.40, what is reduced price per dozen?
(A) 1
(B) 3
(C) 6
(D) 7
(E) 10
Rationale: B
40*(40/100) = 16 --- 64
? --- 12 => Rs.3
Answer: (B) 3
Question: A merchant has 100 lbs of sugar, part of which he sells at 6% profit and the rest at 17% profit. He gains 10 % on the whole. Find how much is sold at 6% profit?
(A) 70 lbs
(B) 40 lbs
(C) 30 lbs
(D) 50 lbs
(E) 64 lbs
Rationale: These types ofweighted averagequestions can be solved in a variety of ways, so you can choose whichever method you find easiest/fastest. Here's another variation on the Weighted Average Formula:
A = # of pounds sold at 6% profit
B = # of pounds sold at 17% profit
A+B = 100 pounds
(.06A + .17B)/(A+B) = .10
.06A + .17B = .1A + .1B
.07B = .04A
7B = 4A
7/4 = A/B
So, for every 7 pounds of A, we have 4 pounds of B.
With 100 pounds total, we have 64 pounds of A and 36 pounds of B.
option E
Answer: (E) 64 lbs
Question: When the positive integer x is divided by 9,the remainder is 5.What is the remainder when 6x is divided by 9?
(A) 0
(B) 1
(C) 3
(D) 4
(E) 6
Rationale: i tried plugging in numbers
x = 9q+5
x = 14
6x = 84
6x/9= 9*9 + 3
remainder is 3.
Answer is C.
Answer: (C) 3
Question: Find the one which does not belong to that group?
(A) 16
(B) 36
(C) 22
(D) 64
(E) 4
Rationale: Explanation:
16, 36, 64 and 4 are perfect squares but not 22.
Answer:C
Answer: (C) 22
Question: In a certain province in France there are 17 cities. If a single road segment connects only two cities, how many road segments are required in order to connect the cities so that each city is connected to all other cities with a single road segment?
(A) 30
(B) 105
(C) 330
(D) 136
(E) 156
Rationale: 1 city needs 16 roads to connect directly to the rest => 17 city needs 17*14 roads.
One road is counted twice => the number of road needed is 17*16/2 = 136
Answer D
Answer: (D) 136
Question: A woman has $252,125 in her savings account. What is the least amount of money (in whole number of dollars) that she must add to her account if she wants to split this money evenly among her nine children?
(A) $1
(B) $2
(C) $3
(D) $4
(E) $11
Rationale: To find the least amount the woman should add to her saving account to split the money evenly among her 9 children,
she needs to make the total divisible by 9
Simply add the individual digits of the total = 2+5+2+1+2+5=17
If you add 1 , the number is divisible by 9 (17+ 1)
Correct Option : A
Answer: (A) $1
Question: If the numerator of a fraction is increased by 20% and its denominator is diminished by 25% value of the fraction is 2/15. Find the original fraction?
(A) 1/12
(B) 1/18
(C) 1/42
(D) 1/15
(E) 1/17
Rationale: X * (120/100)
---------------- = 2/15
Y * (75/100)
X/Y = 1/12
Answer: A
Answer: (A) 1/12
Question: how many number x (x being an integer) with 10<=x<=99 are 18 more than sum of their digits?
(A) 12
(B) 9
(C) 8
(D) 18
(E) 10
Rationale: Let the no. be 10y+z.
then,
10y+z= y+z+18
=> Y=2
So the no. are 20, 21, 22, 23, 24, 25, 26, 27, 28, 29. Total nos. 10
ANSWER:E
Answer: (E) 10
Question: x+(1/x) = 3.5 find x^2 + (1/x^2)
(A) 2.25
(B) 3.25
(C) 10.25
(D) 5.25
(E) 6.25
Rationale: squaring on both sides (x+1/x)^2=3.5^2
x^2+1/X^2=12.25-2
x^2+1/X^2=10.25
ANSWER:C
Answer: (C) 10.25
Question: What will be the compound interest on a sum of Rs. 35,000 after 3 years at the rate of 12% p.a.?
(A) s:10123.19
(B) s:14172.48
(C) s:10123.20
(D) s:10123.28
(E) s:10123.12
Rationale: Amount
= [35000 * (1 + 12/100)3]
= 35000 * 28/25 * 28/25 * 28/25
= Rs. 49172.48
C.I. = (49172.48 - 35000)
= Rs:14172.48
Answer: B
Answer: (B) s:14172.48
Question: Tom drives his car at a speed of 40kmph and reaches his destination in 5hrs and John covers the same distance in 8 hours. If speed of Tomis increased by 10kmph and speed of Ram is increased by 15kmph, what would be the difference between the times taken by them to cover the distance?
(A) 2 hour
(B) 1 hour
(C) 3 hour
(D) 4 hour
(E) 5 hour
Rationale: Distance covered by Ravi at a speed of 40 kmph in 5 hours
ð Distance= Speed x Time = 40 x 5= 200 km
Ram covers same distance in 8 hours => Speed of Rama =
Distance
Time
= 200/8
= 25 kmph.
Ravi speed is increased by 10 kmph => New speed of Ravi = 40+10 = 50 kmph
Ram speed is increased by 15 kmph =>New speed of Ram = 25+15 = 40 kmph.
Therefore, time taken by Ravi to cover 200 km at 50 kmph = 200/50
= 4 hours
Time taken by Ram to cover 200 km at 40 kmph = 200/40
= 5 hours B)
Required time difference = 5 hours – 4 hours = 1 hour
B
Answer: (B) 1 hour
Question: A train 490 m long, running with a speed of 63 km/hr will pass a tree in?
(A) 18 sec
(B) 16 sec
(C) 76 sec
(D) 15 sec
(E) 28 sec
Rationale: Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 490 * 2/35 = 28 sec
Answer:E
Answer: (E) 28 sec
Question: In how many ways the word ENGINEERING can be arranged so that no vowel come together???
(A) 273000
(B) 283000
(C) 293000
(D) 263000
(E) 253000
Rationale: Total no. of ways ENGINEERING can be arranged is
E=3, N=3, G=2, I=2, R=1
=> 11!/(3!*3!*2!*2!) => 277200
No. of ways vowels come together
Vowels ==> (eieei)ngnrng =>
eieei can be considered as 1 letter ... so 1!
ngnrng = 6!
eieei can be arranged as 5!/(3!*2!)
ngnrng can be arranged as 6!/(3!*2!)
So (1!+6 !)*5!/(3!*2!*3!*2!)
=> 4200
So no. of ways vowels not come together
=> 277200 - 4200 = 273000
ANSWER:A
Answer: (A) 273000
Question: Car A takes 10 min lesser than Car B which is travelling at an average speed of 40mph to cover a distance of 60 miles. What is the average speed of car A?
(A) 30
(B) 35
(C) 45
(D) 50
(E) 55
Rationale: Time taken by Car B to cover 60 miles=60/40=1.5 hrs=90 min
Time taken by Car A to cover 60 miles=80min
Average speed of Car A=60/80= 0.75 miles per min= 45 miles per hour.
Answer: C
Answer: (C) 45