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mathematics | In a garden, there are five blue flowers, five red flowers,five green flowers, and five pink flowers. What is the probability that a florist will choose three flowers of the same color when randomly picking three flowers? | [
"11/10",
"3/95",
"31/10",
"3/55",
"1/16"
]
| P(all the same color) = P(1st flower is ANY colorAND2nd flower is same as firstAND3rd flower is also the same color)
= P(1st flower is ANY color)xP(2nd flower is same as 1st)ANDP(3rd flower is the same color)
= 1x4/20x3/19
= 3/95
Answer: B
The answer is: B | B |
mathematics | If k is the greatest positive integer such that 3^k is a divisor of 15! then k = | [
"3",
"4",
"5",
"6",
"7"
]
| For solving this type of tasks we can use such approach
15 / 3 = 5
15 / 3^2 = 1 and remainder
and 3^3 is more than 15 so we stop on second exponent
5 + 1 = 6
so maximum value of k = 6
And answer is D
The answer is: D | D |
mathematics | Find the number of square tiles to cover the floor of a room measuring 4 m * 9 m leaving 0.25 m space around the room. A side of square tile is given to be 25 cms? | [
"388",
"476",
"557",
"2885",
"271"
]
| 3 1/2 * 8 1/2 = 1/4 * 1/4 * x => x = 476
Answer: B
The answer is: B | B |
mathematics | In a certain business school class, p students are accounting majors, q students are finance majors, r students are marketing majors, and s students are strategy majors. If pqrs = 1365, and if 1< p < q < r < s, how many students in the class are marketing majors? | [
"3",
"5",
"7",
"11",
"17"
]
| pqrs = 1365 = 3 * 5 * 7 * 13
Since 1< p < q < r < s, the number of students who are marketing majors is r = 7.
The answer is C.
The answer is: C | C |
mathematics | A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is? | [
"187 m",
"768 m",
"237 m",
"150 m",
"287 m"
]
| Let the length of the train be x meters and its speed be y m/sec.
They, x / y = 15 => y = x/15
x + 100 / 25 = x / 15
x = 150 m.
Answer: D
The answer is: D | D |
mathematics | The positive difference between Sam and Lucy’s ages is b, and the sum of their ages is x. If Lucy is older than Sam, then which of the following represents Lucy’s age? | [
"(x-b)/2",
"b - x/2",
"2b+ x",
"(x + b)/2",
"(b - x)/2"
]
| let Lucy's age be L and sam's age be S
as given,
L-S=b-- 1
L+S=x --2
adding both the equations 2L=a+z
L= (b+x)/2 answer is D
The answer is: D | D |
mathematics | Given that there are 4 basketball players per team, how many ways can you select 2 basketball players from 3 teams if no more than one player can be selected from each team? | [
"15",
"30",
"48",
"75",
"90"
]
| 2 teams can be selected from 3 teams in 3C2 ways = 3 ways
as the condition is that the 2 players should be from different teams
one player can be chosen from 1st team in 5 ways
similarly another player can be chosen from 2nd team in 5 ways
Total number of ways to choose the player = 4 * 4 * 3 = 48 ways
Correct Answer - C
The answer is: C | C |
mathematics | It takes a boat 3 hours to travel down a river from point A to point B, and 5 hours to travel up the river from B to A. How long would it take the same boat to go from A to B in still water? | [
"9 hours and 45 minutes",
"3 hours and 45 minutes",
"1 hours and 45 minutes",
"6 hours and 45 minutes",
"8 hours and 45 minutes"
]
| Let: S be the speed of the boat in still water, r be the rate of the water current and d the distance between A and B.
d = 3(S + r) : boat traveling down river
d = 5(S - r) : boat traveling up river
3(S + r) = 5(S - r)
r = S / 4 : solve above equation for r
d = 3(S + S/4) : substitute r by S/4 in equation B
d / S = 3.75 hours = Let: S be the speed of the boat in still water, r be the rate of the water current and d the distance between A and B.
d = 3(S + r) : boat traveling down river
d = 5(S - r) : boat traveling up river
3(S + r) = 5(S - r)
r = S / 4 : solve above equation for r
d = 3(S + S/4) : substitute r by S/4 in equation B
d / S = 3.75 hours = 3 hours and 45 minutes.
correct answer B
The answer is: B | B |
mathematics | A can do a certain work in 12 days. B is 60% more efficient than A. How many days does B alone take to do the same job? | [
"15/2",
"14/2",
"15/4",
"14/4",
"13/4"
]
| Let the total units of work done be 60.
Units of work done by A in one day = 5.
Given, B is 60% more efficient than A.
Thus, B will be able to finish 8 units of work in a day.
Therefore, time taken by B alone to complete the total work = 60/8 =15/2 days.
ANSWER:A
The answer is: A | A |
mathematics | Graph G has a line of symmetry of x = –5. Graph G passes through the point (3, 3). What is the x-coordinate of another point that must have a y-coordinate of 3? | [
"–8",
"–7",
"–5",
"–4",
"-13"
]
| Line of symmetry is X=-5; one point is (3,3)
Right side distance =5+3(distance from origin) = 8; therefore Left side distance should be same from line of symmetry =8;
therefore left side co-ordinate=8+5(distance from origin) = 13; as the X coordinate is in 2nd quadrant hence -13
Therefore answer is E
The answer is: E | E |
mathematics | A train of 45 carriages, each of 60 meters length, when an engine also of 60 meters length is running at a speed of 60 kmph. In what time will the train cross a bridge 1.5 km long? | [
"6",
"3",
"4.2",
"9",
"4"
]
| D = 45 * 60 + 1500 = 4200 m
T = 4200/60 * 18/5 = 252 sec = 4.2 mins
Answer:C
The answer is: C | C |
mathematics | A train crosses a platform of 150 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train? | [
"150m",
"278m",
"286m",
"121m",
"112m"
]
| Length of the train be ‘X’
X + 150/15 = X + 250/20
4X + 600 = 3X + 750
X = 150m
Answer: A
The answer is: A | A |
mathematics | If John invested $ 1 at 5 percent interest compounded annually, the total value of the investment, in dollars, at the end of 6 years would be | [
"(1.5)^4",
"4(1.5)",
"(1.05)^6",
"1 + (0.05)^4",
"1 + 4(0.05)"
]
| f John invested $ 1 at 5 percent interest compounded annually, the total value of the investment, in dollars, at the end of 6 years would be
1(1.05)^6
1.05^6
C. (1.05)^6
The answer is: C | C |
mathematics | In a class,9 students like to play Basketball and 8 like to play Cricket. 6 students like to play on both Basketball and Cricket. How many students like to play Basketball or Cricket or both? | [
"12",
"11",
"16",
"18",
"22"
]
| Draw a Venn Diagram yourself !
B + C - BC = Number of students that play either Basketball or Cricket
9 +8 - 6 = 11
B)
The answer is: B | B |
mathematics | What will be the day of the week 15th August, 2010? | [
"Tuesday",
"Saturday",
"Monday",
"Sunday",
"Friday"
]
| 15th August, 2010 = (2009 years + Period 1.1.2010 to 15.8.2010)
Odd days in 1600 years = 0
Odd days in 400 years = 0
9 years = (2 leap years + 7 ordinary years) = (2 x 2 + 7 x 1) = 11 = 4 odd days.
Jan. Feb. Mar. Apr. May. Jun. Jul. Aug.
(31 + 28 + 31 + 30 + 31 + 30 + 31 + 15) = 227 days
227 days = (32 weeks + 3 days) 3 odd days.
Total number of odd days = (0 + 0 + 4 + 3) = 7 = 0 odd days.
Given day is Sunday
Answer is D.
The answer is: D | D |
mathematics | The average of 11 numbers is 12.9. If the average of first six is 12.5 and that of the last six is 11.4 the sixth number is? | [
"10.5",
"11.5",
"12.5",
"13.5",
"14.5"
]
| 1 to 11 = 11 * 12.9 = 141.9
1 to 6 = 6 * 15.5 = 93
6 to 11 = 6 * 11.4 = 68.4
93 + 68.4 = 161.4 – 149.9 = 11.5
6th number = 11.5
ANSWER:B
The answer is: B | B |
mathematics | What is the sum of all 3 digit positive integers that can be formed using the digits 1, 4, and 7, if the digits are allowed to repeat within a number? | [
"10,655",
"11,988",
"12,433",
"13,766",
"14,322"
]
| The number of these 3-digit numbers is 3*3*3 = 27
Each digit 1, 4, and 7 will appear in the ones, tens, and hundreds place 9 times each.
The sum equals 9(111) + 9(444) + 9(777) = 11,988
The answer is B.
The answer is: B | B |
mathematics | In how many ways can the letters of the word AGENDA be rearranged such that the vowels always appear together? | [
"6!/2!",
"3!*3!",
"4!/2!",
"(4! *3!)/2!",
"3!*3!/2"
]
| In the word ABACUS , there are 3 vowels - 2 A's and E
Number of ways the letters of word AGENDA be rearranged such that the vowels always appear together
= (4! * 3! )/2!
We can consider the the 3 vowels as a single unit and there are 3 ways to arrange them . But since 2 elements of vowel group are identical we divide by 2! .
The entire vowel group is considered as a single group .
Answer D
The answer is: D | D |
mathematics | There are 3 numbers A, B and C. If A:B = 3/4, B:C = 4/5, C:D = 5/6, then A:D will be? | [
"1 : 2",
"3 : 5",
"5 : 7",
"6 : 11",
"5 : 3"
]
| Sol. A : B = 3 : 4, B : C = 4 : 5, C : D = 5 : 6
∴A∶B∶C∶D= 3 : 4 : 5 : 6.
Thus, A : D = 3 : 6 or, 1 : 2
A
The answer is: A | A |
mathematics | A fruits marks his fruit baskets 40% more than the real price and allows 15% discount. His profit is: | [
"16%",
"17%",
"18%",
"19%",
"20%"
]
| Let the CP = 100 Rs.
Mark Price = 140
Discount = 15%
Selling price 85/100 × 140
Hence profit = 19%
Answer: D.
The answer is: D | D |
mathematics | A 15% stock yielding 12% is quoted at: | [
"s. 83.33",
"s. 110",
"s. 112",
"s. 125",
"s. 140"
]
| Income of Rs 12 on investment of Rs 100
Income of Rs 15 on investment of ?
= (15*100)/12=125
ANSWER:D
The answer is: D | D |
mathematics | A train 50m long takes 6 sec to cross a man walking at 5kmph in a direction opposite to that of the train. Find the speed of the train? | [
"15kmph",
"25kmph",
"35kmph",
"45kmph",
"55kmph"
]
| Let the speed of the train be x kmph
Speed of the train relative to man = x+5 = (x+5)*5/18 m/sec
50/[(x+5)*5/18] = 6
30(x+5) = 900
x = 25kmph
Answer is B
The answer is: B | B |
mathematics | How many liters of a 40% iodine solution need to be mixed with 35 liters of a 20% iodine solution to create a 32% iodine solution? | [
"35",
"49",
"100",
"102",
"140"
]
| Solution 1:
Assume the iodine solution to be mixed = x lts.
Iodine = 0.4x lts, Water = 0.6x lts.
Solution 2: 35 liters of a 20% iodine solution
Iodine = 7 lts, Water = 28 lts.
Total iodine = 0.4x + 7
Total water = 0.6x + 28
The resultant is a 35% idoine solution.
Hence (0.4x + 7) / (x + 35) = 32/100
40x + 700 = 32x + 1120
8x = 820
x = 102 lts
Correct Option: D
The answer is: D | D |
mathematics | In an election between two candidates, 70% of the voters cast their votes, out of which 4% of the votes were declared invalid. A candidate got 6552000 votes which were 75% of the total valid votes. Find the total number of votes enrolled in that election. | [
"13000000",
"12500",
"14000",
"12000",
"None of these"
]
| Explanation :
Solution: let the total number of votes enrolled be x. then, number of votes cast = 70% of x. valid votes = 96% of(70% of x). .'. 75% of(96% of (70% of of x)) = 6552000.
(75/100 * 96/100 * 70/100 * x) = 6552000.
=> x = (6552000*100*100*100)/(75*96*70) = 13000000
Answer : A
The answer is: A | A |
mathematics | Cost of 16 mirror and 8 comb is Rs.336 and the cost of 4 mirror and 4 comb is Rs.96. Find the cost of each mirror? | [
"10",
"18",
"20",
"21",
"22"
]
| Let the cost of each pen and pencil be 'p' and 'q' respectively.
16m + 8c = 336 --- (1)
4m + 4c = 96
8m + 8c = 192 --- (2)
(1) - (2) => 8p = 144
=> m = 18
B
The answer is: B | B |
mathematics | The average speed of a car decreased by 3 miles per hour every successive 8-minutes interval. If the car traveled 4.4 miles in the fifth 8-minute interval, what was the average speed of the car, in miles per hour, in the first 8 minute interval? | [
"45",
"48",
"51",
"54",
"57"
]
| (4.4 miles / 8 minutes)*60 minutes/hour = 33 mph
Let x be the original speed.
x - 4(3) = 33
x = 45 mph
The answer is A.
The answer is: A | A |
mathematics | Ramesh can complete a work in 12 days, working 7 hours a day. Suresh can complete the same work in 8 days, working 9 hours a day. If Ramesh and Suresh work together working 7 hours a day, in how many days can they complete the work? | [
"5 * 7 / 13",
"5 * 7 / 19",
"5 * 7 / 11",
"5 * 7 / 19",
"5 * 6 / 11"
]
| Explanation:
Ramesh can finish the work in 12 * 7 = 84 hours
Amount of work he can complete in 1 hour = 1/84
Suresh can finish the same work in 8 * 9 = 72 hours
Amount of work he can complete in 1 hour = 1/72 hours
Work done by both of them in 1 hour =
= 1/84 + 1/72 = 13/504
Ramesh and Suresh together can complete the work in 504/13 hours.
i.e. 504/13 * 1/7 = 72/13 days
i.e. 5 * 7 / 13 days
ANSWER: A
The answer is: A | A |
mathematics | The number of bacteria in a petri dish increased by 50 percent every 2 hours. If there were 108 million bacteria in the dish at 1: 00 p.m., at what time were there 32 million bacteria in the dish? | [
"7: 00 p.m.",
"8: 00 p.m.",
"6: 00 a.m.",
"8: 00 a.m.",
"10: 00 a.m."
]
| Given:
The number of bacteria in a petri dish increased by 50 percent every 2 hours
There were 108 million bacteria in the dish at 2: 00 p.m
Since the bacteria is increasing by 50% every 2 hours, this means that the number is multiplied by 1.5 every 2 hours.
Required: At what time were there 32 million bacteria in the dish?
Assume that there were n intervals of 2 hours between 32 million and 108 million.
32 * (1.5)^n = 108
(3/2)^n = 108/32 = 27/8 = (3/2)^3
Hence n = 3 intervals.
Each interval was of 2 hours. Therefore, the number of hours = 6
Subtracting 6 hours from 1 PM, we get 7 AM as the answer.
Option A
The answer is: A | A |
mathematics | The average of 8 numbers is 21. If each of the number is multiplied by 8, the average of the new set of numbers is : | [
"168",
"667",
"288",
"1991",
"111"
]
| Average of new numbers = (21×8)=168
Answer:A
The answer is: A | A |
mathematics | The sum of ages of 5 children born 4 years different each is 70 yrs. What is the age of the Elder child? | [
"8",
"9",
"22",
"17",
"18"
]
| Let the ages of children be x, (x + 4), (x + 8), (x + 12) and (x + 16) years.
Then, x + (x + 4) + (x + 8) + (x + 12) + (x + 16) = 70
5x = 30
x = 6
x+16= 6+16= 22
Answer : C
The answer is: C | C |
mathematics | Eight people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire cost of the car, then the share of each of the remaining persons increased by: | [
"1by7",
"1/8",
"1/9",
"7/8",
"1/5"
]
| Original share of 1 person = 1/8
New share of 1 person = 1/7
Increase =(1/7-1/8) = 1/56
Required fraction = (1/56)/(1/8)
= (1/56)*8
= 1/7
ANSWER:A
The answer is: A | A |
mathematics | If Rs.420 amount to Rs.540 in 4 years, what will it amount to in 6 years at the same rate % per annum? | [
"s.575",
"s.595",
"s.590",
"s.600",
"s.585"
]
| 80 = (420*4*R)/100
R = 7.14%
I = (420*6*7.14)/100 = 180
420 + 180 = 600
ANSWER:D
The answer is: D | D |
mathematics | Entry fee in an exhibition was Rs. 1. Later, this was reduced by 25% which increased the sale by 20%. The percentage increase in the number of visitors is : | [
"33",
"37",
"60",
"28",
"27"
]
| Explanation:
Let the total original sale be Rs. 100. Then, original number of visitors = 100.
New number of visitors = 120/0.75 = 160.
Increase % = 60 %.
Answer: C) 60 %
The answer is: C | C |
mathematics | When positive integer x is divided by positive integer y, the remainder is 9. If x/y = 96.45, what is the value of y? | [
"96",
"75",
"48",
"20",
"12"
]
| Guys, one more simple funda.
5/2= 2.5
now .5 x2 =1 is the remainder
25/4 = 6.25
now .25x4=1 is the remainder
32/5=6.4
now.4x5 = 2 is the remainder
given x/y = 96.45 and remainder is 9
So .45 X y = 9
hence y= 20
Ans D
The answer is: D | D |
mathematics | A shoe store sells Adidas shoes for $60 each and Puma shoes for $50 each. On every Adidas shoe the restaurant makes a profit of $10 while on every Puma shoe it makes a profit of $8. If on a given day the storest's sales amounted to $1600, which of the following cannot be the profit made on that day? | [
"262",
"260",
"258",
"256",
"254"
]
| $254 is the only option that does not fit into a combination of Adidas and Puma sales profits, given the total sales of the day. Answer: E
The answer is: E | E |
mathematics | If the remainder is 10 when positive integer n is divided by 14, what is the remainder when n is divided by 7? | [
"0",
"1",
"2",
"3",
"4"
]
| Assume x is quotient here,
n=14x+7 ----------(1)
and n=7x+ ?
We can also write equation (1) as:
n=(14x+7)+3.
ie 7(2x+1)+3 ie the first term is perfectly divisible by 7.
So,the remainder left is 3.
So,answer (D) is right choice.
The answer is: D | D |
mathematics | Harkamal purchased 10 kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper? | [
"A)1190",
"B)1065",
"C)1070",
"D)1075",
"E)1080"
]
| Cost of 10 kg grapes = 70 × 10 = 700.
Cost of 9 kg of mangoes = 55 × 9 = 490.
Total cost he has to pay = 700 + 490 = 1190
A
The answer is: A | A |
mathematics | If 2/3rd of the contents of a container evaporated on the 1st day. And 1/4th of the remaining evaporated on the second day. What part of the contents of the container is left at the end of the second day? | [
"1/4",
"1/12",
"1/18",
"1/6",
"1/2"
]
| After first day, 1/3 of the contents remain.
After second day,
(1/3) - (1/4(2/3)) = (1/3) - (1/6) = 1/6 of the contents remain
ANSWER:D
The answer is: D | D |
mathematics | A batsman makes a score of 87 runs in the 17th inning and thus increases his averages by 3. What is his average after 17th inning? | [
"25",
"31",
"27",
"29",
"39"
]
| Let the average after 17 innings = x
Total runs scored in 17 innings = 17x
Average after 16 innings = (x-3)
Total runs scored in 16 innings = 16(x-3)
Total runs scored in 16 innings + 87 = Total runs scored in 17 innings
=> 16(x-3) + 87 = 17x
=> 16x - 48 + 87 = 17x
=> x = 39
Answer is E.
The answer is: E | E |
mathematics | In an objective test, a correct answer scores 4 marks, and a wrong answer scores 2 marks. A student scores 480 marks from 150 questions. how many answers are correct? | [
"90",
"80",
"70",
"60",
"50"
]
| if all ans. right the marks=4*150=600
but score=480
wrong attempt marks=600-480=120
wrong ans.=120/2=60
right ans.=150-60=90.
ANSWER:A
The answer is: A | A |
mathematics | If x is 12 percent greater than 70, then x = | [
"78.4",
"91.0",
"88.0",
"70.4",
"71.2"
]
| 12% of 70 = (70*0.11) = 8.4
12% greater than 70 = 70 + 8.4 = 78.4
Answer is clearly A.
The answer is: A | A |
mathematics | If x^2 – x = 2, then one possible value of x – 4 = | [
"-9",
"-5",
"-3",
"-1",
"5"
]
| x^2 –x = 2
i.e. x^2 – x - 2 = 0
i.e. x^2 +x -2x -2 = 0
i.e. (x-2)(x+1) = 0
i.e. x = 2 or -1
i.e. x-4 = 2-4 or -1-4
i.e. x-4 = -2 or -5
Answer: Option B
The answer is: B | B |
mathematics | If 60! is written out as an integer, with how many consecutive 0’s will that integer end? | [
"6",
"12",
"14",
"42",
"56"
]
| Soln:-
60/5+60/52=12+2=14
Answer: C
The answer is: C | C |
mathematics | A room of 6m 44cm long and 3m 00cm broad is to be paved with square tiles. Find the least number of square tiles required to cover the floor. | [
"12076",
"12070",
"12077",
"12075",
"12074"
]
| Explanation:
area of the room = 644 * 300sq cm
size of largest square tile = H.C.F of 644cm and 300cm= 4cm
area of 1 tile = 4*4 sq cm
no. of tiles required = (644*300) / (4 * 4) = 12075
Answer: D) 12075
The answer is: D | D |
mathematics | What is the equation of a circle of radius 5 units centered at (3, 2)? | [
"x^2 + y^2 + 6x – 4y = 23",
"x^2 + y^2 - 6x + 4y = 23",
"x^2 + y^2 + 6x + 4y = 23",
"x^2 + y^2 - 6x – 4y = - 12",
"x^2 + y^2 - 6x – 4y = 12"
]
| the equation of a circle with center at (a,b) and radius R is (X-a)^2+(Y-b)^2=R^2
=> answer = (X-3)^2+(Y-2)^2=5^2
solving,,we get the equation in answer choice E.
The answer is: E | E |
mathematics | In a certain game, each player scores either 2 points or 5 points. If n players score 2 points and m players score 5 points, and the total number of points scored is 50, what is the least possible positive R difference between n and m? | [
"1",
"3",
"5",
"7",
"9"
]
| We have equation 2n + 5m = 50
We have factor 2 in first number and we have factor 5 in second number.
LCM(2, 5) = 10
So we can try some numbers and we should start from 5 because it will be less list than for 2
2 * 5 = 10 and n should be equal 20
4 * 5 = 20 and n should be equal 15
6 * 5 = 30 and n should be equal 10
8 * 5 = 40 and n should be equal 5
10 * 5 = 50 and n should be equal 0
third variant give us the mininal difference
n - m = 10 - 6 = 4
And there is some mistake in my way of thinking because we don't have such answer )
If we change the task and will seek for difference between m and n
than minimal result R will be 8 - 5 = 3
And answer B
The answer is: B | B |
mathematics | A can finish a work in 12days, B in 9days and C in 2days, B and C start the work but are forced to leave after 3 days. The remaining work was done by A in? | [
"10days",
"12days",
"6days",
"7days",
"5days"
]
| B+C 1day work = 1/9 + 1/12 = 7/36
work done by B and C in 3days = 7/36 * 3 = 7/12
Remaining work = 1 - 7/12 = 5/12
1/24 work is done by A in 1day
5/12 work is done by A in 12*5/12 = 5days
Answer is E
The answer is: E | E |
mathematics | 7^1+7^2+7^3+...........+7^2015 find out how many numbers present which unit place contain 3 ? | [
"504",
"505",
"506",
"507",
"508"
]
| 7^3,7^7,7^11,7^15,7^19.........7^2015 contains last digit=3.
Now,we see
3,7,11,15....2015 are in AP
tn=a+(n-1)d
2015=3+(n-1)4
2015=3+4n-4
4n=2016
n=504
ANSWER:A
The answer is: A | A |
mathematics | a;b = 8: 10, b:c = 7: 9, a:b:c = ? | [
"56 : 70: 80",
"56 : 70: 70",
"56 : 70: 60",
"56 : 70: 95",
"56 : 70: 90"
]
| a;b = 8: 10
b:c = 7: 9
a:b:c =56 : 70: 90
Answer : E
The answer is: E | E |
mathematics | 2,3,5,8,13,21,34,? | [
"57",
"58",
"55",
"54",
"56"
]
| Each number is the sum of the previous two numbers, ie 18 + 29 = 55.
Answer : C
The answer is: C | C |
mathematics | A geometric shape is obtained by combining a square of side 8 cm and a semicircle of diameter 8cm. What is the perimeter of the shape obtained? | [
"28.32",
"36.57",
"44.57",
"48.93",
"54.24"
]
| Circumference of the semicircle= πxD/2 = (22/7)x4 = 12.57
Perimeter of the square plot = 3x8 = 24
Perimeter of the shape=36.57cm
Answer: B
The answer is: B | B |
mathematics | How many distinct integer values of n satisfy the inequality||n-3| + 4| ≤ 11? | [
"15",
"16",
"17",
"8",
"19"
]
| so i can write this as In-3I+4<=11
or In-3I<=7
so n can have -4 to 10 = 8 true values....
D
The answer is: D | D |
mathematics | How many multiples of 3 are there between 81 and 358? | [
"94",
"95",
"93",
"97",
"98"
]
| 3 * 27 = 81
3 * 119 = 357
Total multiples of 3 = (119 - 27) + 1
= 93
Answer is C.
The answer is: C | C |
mathematics | Which of the following CANNOT be the least common multiple of two positive integers x and y | [
"xy",
"x",
"y",
"x + y",
"x - y^2"
]
| The least common multiple of two positive integers cannot be less than either of them. Therefore, since x - y^2 is less than x, it cannot be the LCM of a x and y.
Answer: E
The answer is: E | E |
mathematics | A pipe can fill a cistern in 20 minutes whereas the cistern when fill can be emptied by a leak in 30 minutes. When both pipes are opened, find when the cistern will be full? | [
"17 minutes",
"87 minutes",
"60 minutes",
"27 minutes",
"11 minutes"
]
| 1/20 - 1/30 = 1/60
60 minutes
Answer:C
The answer is: C | C |
mathematics | A number is doubled and 5 is added. If the resultant is trebled, it becomes 135. What is that number? | [
"12",
"29",
"20",
"15",
"99"
]
| Explanation:
Let the number be x.
Therefore,
3(2x + 5) = 135
6x + 15 = 135
6x = 120
x = 20
ANSWER:C
The answer is: C | C |
mathematics | Sides of a rectangular park are in the ratio 3: 2 and its area is 3750 sq m, the cost of fencing it at 20 ps per meter is? | [
"s.122",
"s.129",
"s.125",
"s.95",
"s.121"
]
| 3x * 2x = 3750 => x = 25
2(75 + 20) = 190 m
190 * 1/2 = Rs.95
Answer:D
The answer is: D | D |
mathematics | A cistern is normally filled in 4 hrs,but takes 2 hrs longer to fill because of a leak on its bottom,if Cistern is full ,how much time citern would empty? | [
"10 hours",
"20 hours",
"30 hours",
"40 hours",
"12 hours"
]
| If leakage/hour=1/x, then 1/4 -1/x= 1/6, solving 1/x=1/12
So in 12 hours full cistern will be empty.
ANSWER:E
The answer is: E | E |
mathematics | One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill tank in 38 min, then the slower pipe alone will be able to fill the tank in? | [
"229",
"787",
"152",
"128",
"121"
]
| Let the slower pipe alone fill the tank in x min.
Then, faster pipe will fill it in x/3 min.
1/x + 3/x = 1/38
4/x = 1/38 => x = 152 min.
Answer: C
The answer is: C | C |
mathematics | Five children, Anaxagoras, Beatrice, Childeric, Desdemona, and Ethelred, sit randomly in five chairs in a row. What is the probability that Childeric and Ethelred sit next to each other? | [
"1/30",
"1/15",
"1/5",
"2/5",
"7/20"
]
| Total no of empty space is 5 so total no of ways A B C D and E can sit is 5 !
Solution 1:
Now condition is C&E will sit together
If they sit at 1st and 2nd place . # of ways will be 1*3! but C&E can be either at 1 or at 2 so # of ways will be 1*3!*2!
Similarly they can sit together at position 2 and 3 or 3 and 4 or 4 and 5
So total # ways will be 1*3!*2! + 1*3!*2! + 1*3!*2! + 1*3!*2! = 4 *1*3! *2 !
So probability is (4! * 2! ) / 5! = 2/5
Solution 2:
Consider C*E as 1 person . So we have 4 ppl and 4 places . # of ways they can sit is 4!
C&E can sit as C&E or E&C so total # of ways is 4! * 2!
So probability will be 2/5
Answer:D
The answer is: D | D |
mathematics | A dress on sale in a shop is marked at $D. During the discount sale its price is reduced by 15%. Staff are allowed a further 10% reduction on the discounted price. If a staff member buys the dress what will she have to pay in terms of D ? | [
"0.965D",
"0.760D",
"0.765D",
"0.865D",
"4.765D"
]
| Explanation:
If the price is reduced by 15 %, then the new price will be 0.85D
If this new price is further reduced by 10%, the discounted price will be 0.9 x 0.85D = 0.765D
Answer: C
The answer is: C | C |
mathematics | A train passes a man standing on a platform in 8 seconds and also crosses the platform which is 276 metres long in 20 seconds. The length of the train (in metres) is: | [
"184",
"176",
"175",
"96",
"None of these"
]
| Explanation:
Let the length of train be L m.
Acc. to question
(276+L)/20 = L/8
2208+8L=20L
L= 2208/12 = 184 m
Answer A
The answer is: A | A |
mathematics | rahul played weel in this season.his current batting averagge is 53.if he score 78 runs in today match.his batting average will become 58.how many matches had he played in this season. | [
"4",
"10",
"9",
"6",
"5"
]
| 53x+78=58(x+1)
=>5x=20
=>x=4
ANSWER:A
The answer is: A | A |
mathematics | Tom invested Rs. 15000 @ 8% per annum for two years. If the interest is compounded half-yearly, then the amount received by Tom at the end of the year will be? | [
"17,546.75",
"17,547.40",
"17,547.88",
"17,548.32",
"17,548.80"
]
| P = Rs. 15000; R = 8% p.a. = 4% per half-year; T = 2 years = 4 half-year
Amount = [15000 * (1 + 4/100)4]
= (15000 * (1.04)4) = Rs. 17547.88
Answer: C
The answer is: C | C |
mathematics | Manie spent 2⁄5 of her money on new clothes and then deposited 1⁄2 of what remained into her savings account. If she then had $21 left, how much did she have at the start? | [
"$30",
"$35",
"$70",
"$105",
"$210"
]
| Manie spent 2⁄5 of her money on new clothes but if you see 21 is half of 3/5 money so 210 is too huge to be correct..
solution..
let the money be x..
2/5 is used...
1/2 of remaining 3/5 is put in savings account and remaining half is 21..
so 1/2 * 3/5 *x=21..
x=21*2*5/3=70..
C
The answer is: C | C |
mathematics | Car A runs at the speed of 65km/hr & reaches its destination in 8hr. Car B runs at the speed of 70 km/h & reaches its destination in 5h. What is the respective ratio of distances covered by Car A & Car B? | [
"11 : 6",
"52 : 35",
"13 : 7",
"15 : 6",
"13 : 6"
]
| Sol. Distance travelled by Car A = 65 × 8 = 520 km
Distance travelled by Car B = 70 × 5 = 350 km
Ratio = 520/350 = 52 : 35
B
The answer is: B | B |
mathematics | What is the sum E of all 3 digit numbers that leave a remainder of '2' when divided by 3? | [
"897",
"164,850",
"164,749",
"149,700",
"156,720"
]
| The series is => 101+...998
Number of terms => 300
sum => 300/2 * [101+998]
hence sum E=> 164850 i.e. option B
The answer is: B | B |
mathematics | 150 is what percent of 60 ? | [
"250%",
"20%",
"50%",
"200%",
"500%"
]
| 60*x=150 --> x=2.5 -->2.5 expressed as percent is 250%.
Answer: A.
The answer is: A | A |
mathematics | In an examination, the percentage of students qualified to the students appeared from school 'P' is 70%. In school 'Q', the number of students appeared is 30% more than the students appeared from school 'P' and the number of students qualified from school 'Q' is 50% more than the students qualified from school 'P'. What is the % of students qualified to the number of students appeared from school 'Q' ? | [
"80.76%",
"75.5%",
"60.50%",
"43 %",
"None of these"
]
| Explanation:
Number of students appeared from school 'P' = 100, say
Number of students qualified from school 'P' = 70
and Number of students appeared from school 'Q' = 130
Number of students qualified from school 'Q' = 50% more than those qualified from school 'P'.
= 70 + 35 = 105 % of students qualified to the number of students appeared from school B = 105 / 130 * 100
= 80.76%
ANSWER A
The answer is: A | A |
mathematics | If two letters are chosen at random (without replacement) from the word JUPITER, what is the probability that none of the letters are vowels? | [
"1/7",
"2/7",
"3/14",
"5/14",
"11/21"
]
| The number of ways to choose two letters is 7C2 = 21
The number of ways to choose two consonants is 4C2 = 6.
P(no vowels) = 6/21 = 2/7
The answer is B.
The answer is: B | B |
mathematics | If 6 (A's capital) = 8 (B's capital) = 10 (C's capital). Then the ratio of their capitals is: | [
"20:15:33",
"20:25:33",
"20:15:12",
"20:15:09",
"20:15:11"
]
| Explanation:
6A = 8B = 10 C
A:B:C = 1/6:1/8:1/10
= 20:15:12
Answer: C
The answer is: C | C |
mathematics | The least number of five digits which is exactly divisible by 12,15 and 18 is : | [
"10010",
"10015",
"10020",
"10080",
"None of these"
]
| Solution
Least number of 5 digits is 10000. L.C.M. of 12, 15 and 18 is 180.
On dividing 1000 by 180, the remainder is 100.
∴ Required number = 10000 + (180 - 100) = 10080. Answer D
The answer is: D | D |
mathematics | Train W leaves New York at 7:00 am traveling to Boston at 80mph. Train B leaves Boston at 7:45 am traveling to New York at 70 mph on a parallel track. If the distance between New York and Boston is 210 miles, at what time will the two trains pass each other? | [
"8:15 am",
"8:45 am",
"9:00 am",
"9:30 am",
"Cannot be determined from the information given"
]
| train W will cover 60 kms in 45 min at 7:45, the time when train B starts...
distance left to cover is 210-60=150..
combined speed=80+70=150..
so the trains meet in 1 hour i.e. 7:45 + 1 hr=8:45
B
The answer is: B | B |
mathematics | Eighty percent of the lights at Hotel California are on at 8 p.m. a certain evening. However, forty percent of the lights that are supposed to be off are actually on and ten percent of the lights that are supposed to be on are actually off. What percent Z of the lights that are on are supposed to be off? | [
"22(2/9)%",
"16(2/3)%",
"11(1/9)%",
"10%",
"5%"
]
| Is the Answer D.
let me try..
Let the light which are supposed to be OFF = SO
Let the light which are supposed to be ON = SN
Let the light which are ACTUALLY OFF = AO
Let the light which are ACTUALLY ON = AN
Let the total no. of lights be 100,
So ACTUALLY ON lights = 80
And ACTUALLY OFF lights = 20
Also given >> forty percent of the lights that are supposed to off are actually on >>> (40/100)*SO are ACTUALLY ON
it means >>> (60/100)*SO are ACTUALLY OFF
Also given >> ten percent of the lights that are supposed to be on are actually off >>> (10/100)*SN are ACTUALLY OFF
it means >>> (90/100)*SN are ACTUALLY ON
So, Total ACTUALLY ON lights = (40/100)*SO + (90/100)*SN = 80
and Total ACTUALLY OFF lights = (60/100)*SO + (10/100)*SN = 80
From here we get SO = 20
we need to find: What percent of the lights that are on are supposed to be off >>> So light ACTUALLY ON are 80 and light which are ACTUALLY ON, which are supposed to be OFF = (40/100)*SO = 8.
So (8/80)*100 Z= 10%.D
The answer is: D | D |
mathematics | A cistern is filled by a tap in 8 1/2 hours. Due to leak in the bottom of the cistern, it takes half an hour longer to fill the cistern. If the cistern is full how many hours will it take the leak to empty it? | [
"133",
"143",
"153",
"163",
"173"
]
| filling rate - leak rate = net rate
1/8.5 - leak rate = 1/9
leak rate = 2/17 - 1/9 = 1/153
The answer is C.
The answer is: C | C |
mathematics | Can you find the missing number in the sequence given below?
11 15 19 12 16 ? 13 17 21 14 18 22 | [
"20",
"21",
"22",
"23",
"24"
]
| Solution:
20
Explanation :
The sequence is given in the puzzle is :
11 15 19 12 16 ? 13 17 21 14 18 22
Let's break the given series as below:
11 15 19
12 16 ?
13 17 21
14 18 22
Now read the number from left hand side from top to bottom as :
So the number that will replace '?' is 20.
Answer A
The answer is: A | A |
mathematics | Series F(n) is such that i*F(i) = j*F(j) for any pair of positive integers (i, j). If F(1) is a positive integer, which of the following is possible?
I. 2*F(100) = F(99) + F(98)
II. F(1) is the only integer in the series
III. The series does not contain negative numbers | [
"I only",
"II only",
"IIII only",
"IIIII only",
"I, IIIII"
]
| First thing I want to understand is this relation: i*F(i) = j*F(j) for any pair of positive integers. I will take examples to understand it.
When i = 1 and j = 2, F(1) = 2*F(2)
So F(2) = F(1)/2
When i = 1 and j = 3, F(1) = 3*F(3)
So F(3) = F(1)/3
I see it now. The series is: F(1), F(1)/2, F(1)/3, F(1)/4 and so on...
II and III are easily possible. We can see that without any calculations.
II. F(1) is the only integer in the series
If F(1) = 1, then series becomes 1, 1/2, 1/3, 1/4 ... all fractions except F(1)
III. The series does not contain negative numbers
Again, same series as above applies. In fact, since F(1) is a positive integer, this must be true.
I. 2*F(100) = F(99) + F(98)
2*F(1)/100 = F(1)/99 + F(1)/98 (cancel F(1) from both sides)
2/100 = 1/99 + 1/98
Not true hence this is not possible
Answer (D)
The answer is: D | D |
mathematics | The CI on Rs. 30,000 at 7% per year is Rs. 4347. The period is? | [
"1 years",
"2 years",
"3 years",
"4 years",
"5 years"
]
| Amount = Rs. (30000 + 4347) = Rs. 34347.
Let the time be n years.
Then, 30000 1 + 7 n = 34347
100
107 n = 34347 = 11449 = 107 2
100 30000 10000 100
n = 2 years
B
The answer is: B | B |
mathematics | A person travels from K to L a speed of 50 km/hr and returns by increasing his speed by 50%. What is his average speed for both the trips ? | [
"55 kmph",
"58 kmph",
"60 kmph",
"66 kmph",
"70 kmph"
]
| Explanation:
Speed on return trip = 150% of 50 = 75 km/hr.
Average speed = (2 x 50 x 75)/(50 + 75) = 60 km/hr.
ANSWER IS C
The answer is: C | C |
mathematics | If Rs.1000 be invested at interest rate of 5% & the interest be added to the principal every 10 yrs, then the no. of yrs in which it will amount to Rs.2000 is: | [
"15",
"17 1/3",
"16 2/3",
"19 2/5",
"21 1/5"
]
| Total time= (10+6 2/3) = 16 2/3 years
C
The answer is: C | C |
mathematics | Cindy wants to buy dolls for her playhouse. Each doll costs $10. Cindy's mother gives her $30 to spend. How many dolls can Cindy buy with the money her mother gave her? | [
"5",
"10",
"2",
"1",
"3"
]
| E. 3
The answer is: E | E |
mathematics | Look at this series: 201, 202, 204, 207, ... What number should come next? | [
"211",
"205",
"209",
"210",
"212"
]
| A
The answer is: A | A |
mathematics | How many even number in the range between 15 to 100 inclusive are not divisible by 3 | [
"29",
"30",
"31",
"33",
"46"
]
| We have to find the number of terms that are divisible by 2 but not by 6( as the question asks for the even numbers only which are not divisible by 3)
For 2,
16,18...100
using AP formula, we can say 100 = 16 + (n-1) *2
or n=43.
For 6,
18,...96
using AP formula, we can say 96 = 18 + (n-1) *6
or n=14.
Hence, only divisible by 2 but not 3 = 43-14 = 29. hence, Answer A
The answer is: A | A |
mathematics | If x is the interest on y and y is the interest on z, the rate and time is the same on both the cases. What is the relation between x, y and z? | [
"Y2=XY",
"X2=YZ",
"Y2=XZ",
"Z2=XZ",
"Y2=XZ"
]
| X = (Y*NR)/100 Y = (Z*NR)/100
X/Y = NR/100 Y/Z = NR/100
X/Y = Y/Z
Y2 = XZ
Answer:C
The answer is: C | C |
mathematics | If 2x +3y = 30 and (x+y)/y = 11/8, then find the value of 5y + 6x | [
"72",
"58",
"64",
"29",
"28"
]
| Explanation:
The given equations are :
2x + 3y = 30 --------- (i)
and, (x+y)/y = 11/8
8x + 8y = 11y
8x – 3y =0 ----(ii)
Adding (i) & (ii), we get : 10 x = 30 or x = 3.
Put x = 3 in (i), we get : y = 8
Therefore, 5y + 6x = (5 * 8 + 6 * 3) = 40 + 18 = 58.
ANSWER: B
The answer is: B | B |
mathematics | In a recent head-to-head run-off election, 15,000 absentee ballets were cast. 1/5 of the absentee ballets were thrown out and 1/4 of the remaining absentee ballets were cast for Candidate A. How many absentee votes did Candidate B receive? | [
"2,000",
"3,000",
"6,000",
"8,000",
"9,000"
]
| 4/5 * 3/4 (total absentee votes) = 3/5 (total votes)=3/5*15000=9000
Answer is E
The answer is: E | E |
mathematics | Two pipes P and Q can fill a cistern in 12 and 15 minutes respectively. Both are opened together, but at the end of 3 minutes the first is turned off. How much longer will the cistern take to fill? | [
"11 1/5",
"11 1/4",
"11 1/5",
"11 1/3",
"11 2/3"
]
| 3/12 + x/15 = 1
x= 11 1/4
Answer: B
The answer is: B | B |
mathematics | Currently guavas cost 30 cents/pound. Due to a disease affecting the guava trees it is expected that next month guavas will cost 50% more than they do currently. How much are guavas expected to cost next month? | [
"50 cents /pound",
"45 cents /pound",
"55 cents /pound",
"60 cents /pound",
"65 cents /pound"
]
| If a new cost is p percent greater than the old cost, then (new cost) = (old cost) + (p/100)(old cost).
In this case, (new cost) = 30 cents/pound + (50/100)(30 cents/pound)
= 30 cents/pound + 15 cents/pound
= 45 cents /pound
Answer : B
The answer is: B | B |
mathematics | A train 100 m long can cross an electric pole in 20 sec and then find the speed of the train? | [
"19 Kmph",
"18 Kmph",
"72 Kmph",
"17 Kmph",
"91 Kmph"
]
| Length = Speed * time
Speed = L/T
S = 100/20
S = 5 M/Sec
Speed= 5*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 18 Kmph
Answer: B
The answer is: B | B |
mathematics | In a stream running at 2 Kmph, a motor boat goes 10 Km upstream and back again to the starting point in 55 minutes. Find the speed of motor boat in still water? | [
"11",
"15",
"22",
"18",
"25"
]
| Let the speed of motor boat instill water be X kmph
Then, speed in downstream = (X + 2) km
and. speed in upstream = (X - 2) kmph
Time taken to row 10km & back = (10/X+2,10/X-2)
10/X+2 + 10/X-2 = 55/60
11X2 - 240X - 44 = 0
(X - 22)(11x + 2) = 0
X = 22 or X = -2/11
Then X = 22 kmph
Answer is C.
The answer is: C | C |
mathematics | X, Y, and Z are consecutive numbers and X > Y > Z. Also, X + 3Y + 3Z = 5Y + 6. What is the value of Z? | [
"2",
"3",
"4",
"5",
"6"
]
| If X, Y, and Z are consecutive numbers and X > Y > Z, then Y = Z+1 and X = Z+2.
X + 3Y + 3Z = 5Y + 6
Z+2+3Z+3+3Z = 5Z+5+6
2Z = 6
Z = 3
The answer is B.
The answer is: B | B |
mathematics | A certain company reported that the revenue on sales increased 60 % from 2000 to 2003, and increased 80 % from 2000 to 2005. What was the approximate percent increase in revenue for this store from 2003 to 2005? | [
"50 %",
"40 %",
"35 %",
"32 %",
"13 %"
]
| Assume the revenue in 2000 to be 100. Then in 2003 it would be 160 and and in 2005 180, so from 2003 to 2005 it increased by (180-160)/160=20/160=13%
Answer: E.
The answer is: E | E |
mathematics | If x inches are cut from the length, l, of a rectangle and y inches are cut from the width, w, of the same rectangle, then which of the following correctly expresses the amount of the area of the original rectangle that was removed in terms of l, w, x, and y? | [
"xy",
"lw – yx",
"ly + wx – xy",
"lx + wy – xy",
"xy – lw – wy"
]
| Initial Area = l*w
Area after cutting rectangle = (l-x)*(w-y)
Area removed = Initial Area - Final Area = l*w - (l-x)*(w-y) = l*w - [l*w-x*w-l*y+x*y) = x*w+l*y-x*y
Answer: Option C
The answer is: C | C |
mathematics | A man spends 1/5 of his salary on food, 1/10 of his salary on house rent and 3/5 of his salary on clothes. He still has $18000 left with him. Find his salary. | [
"$100000",
"$200000",
"$140000",
"$180000",
"$250000"
]
| The expenditure incurred on each item is expressed as part of the total amount (salary), so it is an independent activity.
In general for independent activities
[1 – (x1/y1 + x2/y2 + x3/y3)] × Total amount = Balance amount
[1 – (1/5 + 1/10 + 3/5)] × Total salary = $18000
[1 – 9/10] × Total salary = $18000
Therefore total salary = $18000 × 10 = $180000
The answer is: D | D |
mathematics | What is the greatest value of x such that 4^x is a factor of 21! ? | [
"5",
"6",
"3",
"2",
"4"
]
| Pretty simple, really.
If m = 6, then 4m = 24, which is 12x2, both of which are included in 21!
Since 6 is the largest number here, its the answer.
Answer is B
The answer is: B | B |
mathematics | Find the amount on Rs.5000 in 2 years, the rate of interest being 4% per first year and 5% for the second year? | [
"2328",
"2798",
"5460",
"2799",
"2771"
]
| 5000 * 104/100 * 105/100 => 5460.Answer: C
The answer is: C | C |
mathematics | If n and k are integers whose product is 2500, which of the following statements must be true? | [
"n+k>0",
"n does not equal k",
"Either n or k is a multiple of 10",
"If n is even, then k is odd",
"If n is odd, then k is even"
]
| If n is odd and k is odd, then the product is odd.
The answer is E.
The answer is: E | E |
mathematics | A rectangular-shaped carpet that measures x feet by y feet is priced at $24. What is the cost of the carpet, in dollars per square yard? (1 square yard = 9 square feet) | [
"180xy",
"216/(xy)",
"20xy",
"20xy/9",
"xy/180"
]
| The area of the carpet in feet is xy.
The area in square yards is xy / 9.
The price per square yard is 24 / (xy/9) = 216/(xy).
The answer is B.
The answer is: B | B |
mathematics | I am an odd number; take away an alphabet and I become even. What number am I? | [
"6",
"8",
"9",
"3",
"7"
]
| E
7 (SEVEN-S=EVEN)
The answer is: E | E |
mathematics | If a number p is prime, and 2p+1 = q, where q is also prime, then the decimal expansion of 1/q will produce a decimal with q-1 digits. If this method produces a decimal with 166 digits, what is the units digit of the product of p and q | [
"1",
"3",
"5",
"7",
"9"
]
| 3/7 = 0.428571... (a repeating pattern one digit long)
B
The answer is: B | B |
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