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mathematics
|
A certain list consists of 21 different numbers. If n is in the list and n is 4 times the average(arithmetic mean) of the other 20 numbers in the list, then n is what fraction U of the sum of the 21 numbers in the list?
|
[
"1/20",
"1/6",
"1/5",
"4/21",
"5/21"
] |
This is how I used to calculate which I think works pretty well:
if you let the average of the 20 other numbers equal a, can you write this equation for sum of the list (S)
n + 20a = S
the question tells us that
n = 4a
plug this back into the first equation and you get that the sum is 24a
4a + 20a = 24a
therefore fraction U of n to the total would be
4a/24a or 1/6
answer B
The answer is: B
|
B
|
mathematics
|
If a trader sold two cars each at Rs. 325475 and gains 15% on the first and loses 15% on the second, then his profit or loss percent on the whole is?
|
[
"1.44%",
"1.74%",
"1.84%",
"1.97%",
"2.25%"
] |
SP of each car is Rs. 325475, he gains 15% on first car and losses 15% on second car.
In this case, there will be loss and percentage of loss is given by
= [(profit%)(loss%)]/100
= (15)(15)/100 % = 1.44%
Answer:E
The answer is: E
|
E
|
mathematics
|
Average of all prime numbers between 35 to 50
|
[
"42",
"37.8",
"39",
"39.8",
"40"
] |
Explanation:
Prime numbers between 35 and 50 are:
37, 41, 43, 47
Average of prime numbers between 35 to 50 will be
(37+41+43+47 / 4)=168 / 4=42
Option A
The answer is: A
|
A
|
mathematics
|
A tap can fill a tank in 12 hours. After half the tank is filled three more similar taps are opened. What is the total time taken to fill the tank completely?
|
[
"13 hrs 30 mins",
"14 hrs 30 mins",
"15 hrs 30 mins",
"16 hrs 30 mins",
"17 hrs 30 mins"
] |
Time taken by one tap to fill the tank = 6 hrs.
Part filled by the taps in 1 hour = 4 * 1/12 = 1/3
Remaining part = 1 - 1/2 = 1/2
1/3 : 1/2 :: 1 : x
x = 1/2 * 1 * 3 = 1.5 hrs = 1 hrs 30 min
So, total time taken = 13 hrs 30 mins
ANSWER: A
The answer is: A
|
A
|
mathematics
|
What is the least value of k. So that 123k578 is divisible by 11.
|
[
"8",
"7",
"5",
"6",
"4"
] |
Explanation:
The Difference of the sum of the digits at odd place and the sum of the digits at even place of the number, is either 0 or a number divisible by 11.
(1 + 3 + 5 + 8) - (2 + k + 7) = 17 - 9 - k = 8 - k
Therefore if k = 8, then the value become zero.
k = 8 is the least value
so that 123k578 is divisible by 11.
Answer: Option A
The answer is: A
|
A
|
mathematics
|
In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected?
|
[
"159",
"194",
"210",
"209",
"166"
] |
Out of 10 students 4 children should to be selected.
So the combination will be 10C4.
10C4=10!/6!*4!=10*9*8*7*6!/6!*(4*3*2*1)
10C4=210
There are 210 differect possible ways to select 4 children out of 10 students.
The answer is: C
|
C
|
mathematics
|
A box contains 5 red, 4 blue, and 3 white balls. In how many ways can we select 4 balls such that at least 2 are red?
|
[
"235",
"270",
"280",
"285",
"240"
] |
Explanation:
You decline to mention whether balls of the same color are identical. If they are, then you have only 99 ways to do so. Why? Two positions are dedicated to red. For the remaining two, you can have red, blue or white (all are sufficiently numerous to allow that) and so that's 3×3=93×3=9 ways.
If, on the other hand balls of the same color are non-identical, then you can select four balls of any color is (5+4+3/4)=495(5+4+34)=495 ways. No red ball is selected in (4+3/4)=35 ways. Exactly one red ball is selected in 5×(4+3/3)175 ways. Thus, you select at least two red balls in 495−(35+175)=285 ways
Answer is D
The answer is: D
|
D
|
mathematics
|
A, B and C shared profits in ratio of 5 : 3 : 8. Theypartnered for 14months, 8months and 7months respectively. What was he ratio of their investments ?
|
[
"10 : 49 : 45",
"20 : 49 : 64",
"12 : 21 : 64",
"20 : 29 : 64",
"30 : 29 : 63"
] |
Simply multiply profit sharing ratio with investment ratio to get investment amount ratio.
Let X is the total investment
⇒14 x = 5
⇒ 8 x = 3
⇒ 7x = 8
⇒ Final investment ratio = 12 : 21 : 64
C
The answer is: C
|
C
|
mathematics
|
A polygon has 230 diagonals. How many sides does it have?
Self made
|
[
"22",
"23",
"24",
"25",
"26"
] |
The best way to solve this problem is to use the formula: An n sided polygon can have n*(n - 3)/2 diagonals
n*(n - 3)/2 = 230
n*(n - 3) = 460
Substitute n from the answer choices. n = 23
Answer: B
The answer is: B
|
B
|
mathematics
|
Triangle STV has sides ST = TV = 26, and SV = 20. What is the area?
|
[
"160",
"180",
"200",
"220",
"240"
] |
Let the base B of the triangle be SV = 20. Then we need to find the height H.
H^2 = 26^2 - 10^2 = 576 and then H = 24.
The area is (1/2)*B*H = 10*24 = 240
The answer is E.
The answer is: E
|
E
|
mathematics
|
What is the probability of rolling four six-sided dice, and getting a different number on each die?
|
[
"1/12",
"1/3",
"4/9",
"5/9",
"5/13"
] |
MAGOOSHOFFICIAL SOLUTION
For the first die, we can roll any one of six numbers. For the second die, we can roll any number save for the number we rolled on the first die, giving us 5 possibilities. For the third die, we can roll four different numbers (we can’t roll the number we rolled on the first or second die.
6 x 5 x 4 x 3 = 360 possibilities out of 216 total possibilities. (For total possibilities we get 6 x 6 x 6x6 = 1296).
360/1296 = 5/13
Answer: E.
The answer is: E
|
E
|
mathematics
|
Worldwide production of motor vehicles was 3.9 million vehicles in 1946 and 65.4 million in 1987. Of the following, which is closest to the average (arithmetic mean) annual increase, in millions, in worldwide production of motor vehicles during this period?
|
[
"0.08",
"1.0",
"1.1",
"1.5",
"41.8"
] |
Change in production of motor vehicles = 65.4 - 3.9 = 61.5 million in 41 years (1987 - 1946)
average increase per year = 61.5/41 = 1.5 million (apporx.)
Answer (D)
The answer is: D
|
D
|
mathematics
|
If the average (arithmetic mean) of a and b is 45 and the average of b and c is 80, what is the value of c − a?
|
[
"25",
"70",
"90",
"140",
"It cannot be determined from the information given"
] |
the arithmetic mean of a and b =(a+b)/2=45 -- a+b=90 --1
similarly for b+c=160 --2
subtracting 1 from 2 we have
c-a=70;
ANSWER:B
The answer is: B
|
B
|
mathematics
|
At what time between 4 and 5 o’clock the hands are in opposite direction?
|
[
"3 2/11 minutes past 4 o’clock",
"3 5/11 minutes past 4 o’clock",
"10 10/11 minutes past 4 o’clock",
"10 2/11 minutes past 4 o’clock",
"54 6/11 mintues past 4'0 clock"
] |
To be in opposite directions, they must be 30 min. spaces apart.
Minute hand will have to gain 50 min. spaces.
55 min. spaces are gained in 60 min.
50 min. spaces are gained in 60/55 x 50 min. or 54 6/11 min. Required time = 54 6/11 min. past 4 o’clock
ANSWER:E
The answer is: E
|
E
|
mathematics
|
In 19 years time the combined ages of my three brothers will be 94. What will it be in nine years time?
|
[
"45",
"62",
"82",
"97",
"56"
] |
C
82
Combined age in 9 years time will 94 – (3 x (13 – 9))
94 – 12 = 82.
The answer is: C
|
C
|
mathematics
|
If 213 × 16 = 3408, then 1.6 × 213.0 is equal to :
|
[
"0.3408",
"3.408",
"34.08",
"340.8",
"None of these"
] |
Solution
1.6 × 21.3 = (16/10x 213)= (16x 213/10) = 3408/10 = 340.8. Answer D
The answer is: D
|
D
|
mathematics
|
If 21520 books need to be placed in boxes and each box can contain at most 9 books. How many books will be in the last unfilled box?
|
[
"9 books",
"8 books",
"1 book",
"4 books",
"5 books"
] |
The number of books that can be placed in boxes of 9 books is the first number that is divisible by 9 that occurs before 21520.
In order to divide the sum in 9 parts, the amount must be divisible by 9
Divisibility rule of 9: The sum of the digits must be divisible by 9
Sum of digits of 21520 = 10 and 9 is divisible by 9.
Hence, we need to remove 1 to this number for it to be divisible by 9
Correct Option: C
The answer is: C
|
C
|
mathematics
|
If x 2 – y 2 = 101, find the value of x 2 + y 2 ,
given that x and y are natural numbers.
|
[
"5100",
"5101",
"5102",
"5103",
"5104"
] |
x^2 – y^2 = 101
=> (x+y)*(x-y) = 101*1
x+y = 101
x-y = 1
so, x = 51, y = 50
(x^2 + y^2) = 51^2 + 50^2 = 5101
ANSWER:B
The answer is: B
|
B
|
mathematics
|
A man buys oranges at Rs 5 a dozen and an equal number at Rs 4 a dozen. He sells them at Rs 5.50 a dozen and makes a profit of Rs 50. How many oranges does he buy?
|
[
"30 dozens",
"40 dozens",
"50 dozens",
"60 dozens",
"70 dozens"
] |
Explanation:
Cost Price of 2 dozen oranges Rs. (5 + 4) = Rs. 9.
Sell price of 2 dozen oranges = Rs. 11.
If profit is Rs 2, oranges bought = 2 dozen.
If profit is Rs. 50, oranges bought = (2/2) * 50 dozens = 50 dozens. Answer: C
The answer is: C
|
C
|
mathematics
|
What is the CP of Rs 100 stock at 7 discount, with 1/5% brokerage?
|
[
"93.9",
"96.3",
"93.2",
"96.7",
"96.21"
] |
Explanation:
Use the formula,
CP= 100 – discount + brokerage%
CP= 100-7+1/5
93.2
Thus the CP is Rs 93.2.
ANSWER: C
The answer is: C
|
C
|
mathematics
|
A factory produces x widgets per day. The factory's fixed costs are $8000 per day. The price per widget is $80 and the variable costs are $20 per widget. How many widgets need to be produced for profits of $5000 a day?
|
[
"42.33",
"90.33",
"168",
"216.67",
"400"
] |
profits=5000=60x-8000 --> x=216.67
Answer D.
The answer is: D
|
D
|
mathematics
|
The length and breadth of a rectangle is increased by 11% and 22% respectively. What is the increase in the area?
|
[
"35.22",
"33.52",
"35.42",
"36.22",
"38.42"
] |
100*100=10000
111*122=13542
------------
3542
10000-------3542
100----------35.42
Answer C
The answer is: C
|
C
|
mathematics
|
The present population of a town is 4320. Population increase rate is 20% p.a. Find the population of town before 2 years?
|
[
"2500",
"2100",
"3500",
"3000",
"2050"
] |
P = 4320
R = 20%
Required population of town = P/(1 + R/100)^T
= 4320/(1 + 20/100)^2
= 4320/(6/5)^2
= 3000(approximately)
Answer is D
The answer is: D
|
D
|
mathematics
|
A wheel that has 6 cogs is meshed with a larger wheel of 14 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions mad by the larger wheel is:
|
[
"4",
"9",
"12",
"21",
"35"
] |
More cogs less revolution,..
so
6:14::x:21
(21*6)/14=9
ANSWER:B
The answer is: B
|
B
|
mathematics
|
If $20,000 interest is invested in x percent simple annual interest for n years, which of the following represents the total amount of interest, in dollars, that will be earned by this investment in the n years?
|
[
"10,000(x^n)",
"20,000n(x/100)",
"20,000(x/100)^n",
"10,000(1 + x/100)^n",
"10,000n(1 + x/100)"
] |
Principal * no.of years * percentage of interest
Answer : B
The answer is: B
|
B
|
mathematics
|
two friends deepak and rajeev have agreed to meet at a definite spot on a particular day between 9pm and 10pm. the first person to come waits for some time and leaves.If the other one does not turn up by that time.If Deepak comes first,he waits for 45minutes and if Rajeev comes first,he waits for 15minutes.What is the probability of meeting between Deepak and rajeev if their arrival times are independent of eachother and each person arrives during the indicated period at random?
|
[
"3/4",
"11/16",
"7/8",
"3/16",
"3/15"
] |
deepak : 45/60 = 3/4
rajeev : 15/60= 1/4
as these are independent events
total probability = (3/4)*(1/4)
= 3/16
ANSWER:D
The answer is: D
|
D
|
mathematics
|
Find the area, diameter = 10m.
|
[
"78.24 square meter",
"78.57 square meter",
"78.26 square meter",
"24.24 square meter",
"24.43 square meter"
] |
Diameter = 10 meter.
Radius = diameter/2.
= 10/2.
= 5 meter.
Area of a circle = πr2.
Here, pi (Ï€) = 3.14 meter, radius (r) = 5.
Area of a circle = 3.14 × 5 × 5..
= 3.14 × 25.
= 78.57 square meter ANSWER : B
The answer is: B
|
B
|
mathematics
|
The smallest number when increased by " 1 " is exactly divisible by 6,18,36,48, 60 is:
|
[
"724",
"721",
"720",
"719",
"700"
] |
LCM = 720
720 - 1 = 719
ANSWER:D
The answer is: D
|
D
|
mathematics
|
If 3g + 1 < 2g < 9 - g, which of the following must be true?
I. -1 < g < 3
II. g < -1
III. g < 3
|
[
"II only",
"III only",
"I and II only",
"II and III only",
"I, II and III"
] |
Just try plugging g in a number like 0 or 1, and you'll quickly find that the inequality doesn't hold.
So you can immediately cross out any answers with I or III, leaving just (A) II only.
The answer is: A
|
A
|
mathematics
|
By investing Rs. 1620 in 8% stock, Michael earns Rs. 135. The stock is then quoted at:
|
[
"Rs 96",
"Rs 100",
"Rs 150",
"Rs 160",
"Rs 200"
] |
to earn Rs 135 investment = Rs 1620
to earn Rs 8 investment =>1620/135*8=96
ANSWER A
The answer is: A
|
A
|
mathematics
|
If integers w and b are distinct factors of 30, which of the following CANNOT be a factor of 30?
I. wb + b^2
II. (w+ b)^2
III. w + b
|
[
"I only",
"II only",
"III only",
"I and II only",
"I, II, and III"
] |
Factors of 30 are: 1, 2, 3, 5, 6, 10, 15, and 30.
I. wb + b^2 --> if w=1 and b=2 then wb + b^2=6, which is a factor of 30. OK;
II. (w + b)^2 --> (w + b)^2 is a perfect square, no perfect square (but 1) is a factor of 30. DISCARD;
III. w + b --> if w=1 and b=2 then w + b=3, which is a factor of 30. OK.
Answer: B.
The answer is: B
|
B
|
mathematics
|
A sum of Rs. 1360 has been divided among A, B and C such that A gets of what B gets and B gets of what C gets. B’s share is:
|
[
"Rs. 120",
"Rs. 160",
"Rs. 240",
"Rs. 300",
"None"
] |
EXPLANATION
Let C’s share = Rs. x
Then, B’s share = Rs. x/4 , A’s share = Rs. (2/3 x x/4 ) = Rs. x/6
=x/6 + x/4 + x = 13660
=> 17x/12 = 13660
=> 13660 x 12/ 17 = Rs.960
Hence, B’s share = Rs. (960/4) = Rs. 240.
Answer C
The answer is: C
|
C
|
mathematics
|
At Jefferson Elementary School, the number of teachers and students (kindergarten through sixth grade) totals 510. The ratio of students to teachers is 16 to 1. Kindergarten students make up 1/10 of the student population and fifth and sixth graders account for 1/3 of the remainder. Students in first and second grades account for 1/4 of all the students. If there are an equal number of students in the third and fourth grades, then the number of students in third grade is how many greater or fewer than the number of students in kindergarten?
|
[
"20 greater",
"17 fewer",
"28 fewer",
"36 fewer",
"44 fewer"
] |
Soln>> from the given ratio of 16:1 u can derive that ter are 480 students
KG= 1/10 * 480 =48
5th and 6th graders = 1/3 * 384= 128 (1/3 of remainder)
1st and 2nd grade = 1/4 * 480 =120 ( 1/4 of all students)
equal number of students in 3rd and 4th => 480 - 344= 136 and 136/2=68 each since equal number
(344 is the sum of remaining students)
thus 48-68 =20>>> therfore answer is 20 greater
A
The answer is: A
|
A
|
mathematics
|
There are 81 people in a certain community who belong to the local golf club, tennis club or both clubs. If twice as many people belong to the tennis club as belong to the golf club, what could be the number of people who belong to both clubs?
|
[
"4",
"7",
"27",
"21",
"37"
] |
let's find the range of Both and hence the range of x. Minimum value of Both: Say there is no overlap in the two sets. 81 = x + 2x
x = 27
In this case Both = 0 Maximum value of Both: Say there is maximum overlap between the two sets. One set has x so it could be a subset of the set 2x.
81 = 2x
But x cannot be a decimal so (x-1) could be the overlap (= Both) and there could be 1 in only the Golf club.
81 = 2 x + x - (x - 1)
x = 40
In this case Both = 40 - 1 = 39 So Both lies between 0 and 39 Only option (E) satisfies this condition. ANSWER:E
The answer is: E
|
E
|
mathematics
|
The present worth of a sum due sometime hence is Rs. 576 and the banker’s gain is Rs. 16. The true discount is :
|
[
"36",
"52",
"66",
"96",
"None"
] |
Sol.
T.D. = √P.W. * B.G. = √576 * 16 = 96.
Answer D
The answer is: D
|
D
|
mathematics
|
The Royals softball team played 75 games and won 55 of them. What percent of the games did they lose? (round to the nearest tenth)
|
[
"26.7% games lost",
"27.7% games lost",
"25.7% games lost",
"20.7% games lost",
"22.7% games lost"
] |
Total 100%=75
Won=55
Lost=20
75-55
=20
x/100=20/75
Multiply the opposites:
100 x 20 = 2000
Divide by the remaining number:
26.667/2000.000
75
26.7% games lost (rounded to tenth)
correct answer A
The answer is: A
|
A
|
mathematics
|
In Company B, the total monthly payroll for the 20 factory workers is $36,000 and the total monthly payroll for the 50 office workers is $110,000. By how much does the average (arithmetic mean) monthly salary of an office worker exceed that of a factory worker in this company?
|
[
"$400",
"$450",
"$500",
"$550",
"$600"
] |
The average monthly salary of a factory worker is: $36,000 / 20 = $1800.
The average monthly salary of an office worker is: $110,000 / 50 = $2200.
The difference in average salary is: $2200 - $1800 = $400.
The answer is A.
The answer is: A
|
A
|
mathematics
|
A seller of used cars has 12 cars to sell and each of his clients selected 4 cars that he liked most. If each car was selected exactly thrice, how many clients visited the garage?
|
[
"9",
"10",
"12",
"14",
"16"
] |
IfNo caris selected more than once then the number of clients = 12/4 = 3
But since every car is being selected three times so No. of Clients must be thrice as well =3*3 = 9
Answer: option A
The answer is: A
|
A
|
mathematics
|
The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is:
|
[
"200 m",
"225 m",
"245 m",
"250 m",
"350 m"
] |
Explanation:
Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30 = 25/2 => 2(130 + x) = 750 => x = 245 m.
ANSWER IS C
The answer is: C
|
C
|
mathematics
|
Peter invests $100,000 in an account that pays 10% annual interest: the interest is paid once, at the end of the year. Martha invests $100,000 in an account that pays 10% annual interest, compounding monthly at the end of each month. At the end of one full year, compared to Peter's account, approximately how much more does Martha’s account have?
|
[
"$471.31",
"$4713.10",
"$47.13",
"$4.71",
"Zero"
] |
Peters interest= $100,000*0.10 = $10,000 or $833.33 each month.
Martha’s interest, 10%/12 = 0.833% each month:
For the 1st month = $100,000*0.00833 = $833.33;
For the 2nd month = $833.33 + 0.833% of 833.33 = ~$840, so we would have interest earned on interest (very small amount);
For the 3rd month = $840 + 0.833% of 840 = ~$847;
For the 4th month = $847 + 0.833% of 847 = ~$854;
...
For the 12th month = $905 + 0.833% of 905 = ~$912.
The difference between Peters interest and Martha’s interest = ~(7 + 14 + ... + 77) = $462.
Answer: A.
The answer is: A
|
A
|
mathematics
|
Of the 800 employees of Company X, 90 percent have been with the company for at least ten years. If y of theselong-termmembers were to retire and no other employee changes were to occur, what value of y would reduce the percent oflong-termemployees in the company to 60 percent ?
|
[
"200",
"160",
"112",
"80",
"600"
] |
The # oflong-termemployees is 90%*800=720.
After y of them retire new # oflong-termemployees would become 720-y.
Total # of employees would become 800-y.
We want 720-y to be 60% of 800-y --> 720-y=(800 -y)*60% --> y = 600.
Answer: E.
The answer is: E
|
E
|
mathematics
|
A, B and C started a business A's investment is 2 times of B's investment is 5 times of C's investment. Find the profit of B in the total profit of Rs. 1600.
|
[
"Rs. 25600",
"Rs. 8500",
"Rs. 7200",
"Rs. 500",
"None of these"
] |
Explanation:
A = 2B and B = 5C
=> A : B = 2:1 and B : C = 5 : 1
=> A : B : C = 10 : 5 : 1
Ratio of capitals of A, B and C = 10 : 5 : 1
B's share = Rs.[(5/16) × 1600] = Rs. 500
Answer: Option D
The answer is: D
|
D
|
mathematics
|
A starts business with Rs.3500 and after 9 months, B joins with A as his partner. After a year, the profit is divided in the ratio 2 : 3. What is B’s contribution in the Capital ?
|
[
"24887",
"20778",
"23788",
"21000",
"2811"
] |
Explanation:
A invested Rs.3500 for 12 months.
Let B joined with investment x. And he invested for 12 - 9 = 3 months.
So there profit ratio = (3500 × 12) : (3x) = 2 : 3
⇒ x = 21000
Answer: D
The answer is: D
|
D
|
mathematics
|
For what range of values of 'x' will the inequality 15x - 2/x > 1?
|
[
"x > 0.4",
"x < 1/3",
"-1/3 < x < 0.4, x > 15/2",
"-1/3 < x and x< 0, x > 2/5",
"x < -1/3 and x > 2/5"
] |
In Case 1 where x > 0, I agree. I calculated x > (-1/3) and x > 2/5, and because x > 0, it must be x > 2/5.
In Case 2 where x < 0, I don't understand why you say that the range must be x > -1/3 and x < 0, since the values that satisfy the inequality 15x^2 - x - 2 < 0show that x < -1/3 and x < 2/5.
I have the same doubt. Shouldn't the answer be D?
____________
The answer IS D.
The answer is: D
|
D
|
mathematics
|
A train 300 m long can cross an electric pole in 30 sec and then find the speed of the train?
|
[
"76 Kmph",
"54 Kmph",
"72 Kmph",
"36 Kmph",
"91 Kmph"
] |
Length = Speed * time
Speed = L/T
S = 300/30
S = 10 M/Sec
Speed= 10*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 36 Kmph
Answer: D
The answer is: D
|
D
|
mathematics
|
The sum of all the integers a such that -26 < a < 24 is
|
[
"0",
"-2",
"-25",
"-49",
"-51"
] |
Easy one -
-25, -24, -23,-22,...... -1,0, 1, 2...., 22, 23
Cancel everyhitng and we're left with - -25 and -24 a = -49.
D is the answer.
The answer is: D
|
D
|
mathematics
|
A polling company surveyed a certain country, and it found that 35% of that country’s registered voters had an unfavorable impression of both of that state’s major political parties and that 20% had a favorable impression only of Party R. If one registered voter has a favorable impression of both parties for every two registered voters who have a favorable impression only of Party B, then what percentage of the country’s registered voters have a favorable impression of both parties (assuming that respondents to the poll were given a choice between favorable and unfavorable impressions only)?
|
[
"15",
"20",
"30",
"35",
"45"
] |
S=100
not( R and B ) =35
only R=20
(R and B)/B=1/2
let ( R and B ) =x
only B =2x
so now, 20+35+x+2x=100
x= 15
A ans
The answer is: A
|
A
|
mathematics
|
I chose a number and divide it by 9. Then I subtracted 100 from the result and got 10. What was the number I chose?
|
[
"600",
"700",
"990",
"900",
"None"
] |
Solution:
Let x be the number I chose, then
x/9−100=10
x/9=110
x=990
Answer C
The answer is: C
|
C
|
mathematics
|
If grapes are 92% water and raisins are 20% water, then how much did a quantity of raisins, which currently weighs 13 pounds, weigh when all the raisins were grapes? (Assume that the only difference between their raisin-weight and their grape-weight is water that evaporated during their transformation.)
|
[
"25 pounds",
"46 pounds",
"92 pounds",
"130 pounds",
"146 pounds"
] |
Since only water evaporates, then the weight of pulp (non-water) in grapes and raisins is the same. Thus 0.08*{weight of grapes}=0.8*{weight of raisins} --> 0.08x = 0.8*13 --> x = 130.
Answer: D.
The answer is: D
|
D
|
mathematics
|
A man can row his boat with the stream at 26 km/h and against the stream in 4 km/h. The man's rate is?
|
[
"1 kmph",
"7 kmph",
"98 kmph",
"11 kmph",
"4 kmph"
] |
DS = 26
US = 4
S = ?
S = (26 - 4)/2 = 11 kmph
Answer: D
The answer is: D
|
D
|
mathematics
|
Sheila works 8 hours per day on Monday, Wednesday and Friday, and 6 hours per day on Tuesday and Thursday. She does not work on Saturday and Sunday. She earns $360 per week. How much does she earn in dollars per hour?
|
[
"11",
"10",
"9",
"8",
"7"
] |
Let Sheila earn x dollars per hour
So, on Monday, Wednesday and Friday , she earns 8x each
And, on Tuesday and Thursday, she earns 6x each
In total , over the week she should earn, 3(8x) + 2(6x) = 36x
She earns $360 per week
36x =360
x =10
Correct Option : B
The answer is: B
|
B
|
mathematics
|
4, 12, 48, (...)
|
[
"7620",
"10080",
"6200",
"10020",
"240"
] |
Explanation :
Go on multiplying the given numbers by 3, 4, 5, 6, 7
Answer : Option E
The answer is: E
|
E
|
mathematics
|
What will come in place of the x in the following Number series? 73205, 6655, 605, 55, x
|
[
"32564",
"73205",
"62343",
"54756",
"78564"
] |
(B)
5 x 11 = 55, 55 x 11 = 605, 605 x 11 = 6655, 6655 x 11 = 73205
The answer is: B
|
B
|
mathematics
|
1 blue dice and 2 red Dice are thrown....what is the probability that the no. appeared on blue dice is always greater than both the no. appeared on the 2 red dice..
|
[
"55/216",
"56/216",
"57/216",
"54/216",
"53/216"
] |
if the no. on blue dice is 2 then 2 red dice can take (1,1) value = 1^2
if the no. on blue dice is 3 then 2 red dice can take (1,1)(1,2)(2,1)(2,2) = 2^2
if the no. on blue dice is 4 then 2 red dice can take (1,1)(1,2)(2,1)(2,2)(1,3)(2,3)(3,2)(3,1)(3,3) = 3^2
Similarly, if the no. on blue dice is 5 then 2 red dice can take = 4^2
and if the no. on blue dice is 6 then 2 red dice can take = 5^2
therefor, probability = total no. of favourable outcome/total no. of possible outcome
= 1^2+2^2+3^2+4^2+5^2 / 216
= 55/216
ANSWER:A
The answer is: A
|
A
|
mathematics
|
Benny goes to the market for buying some apples to be distributed between her nine kids equally.She takes 420 dollars with her .The cost of each apple is 4 dollars .How many apples does she buy to share them equally between her five kids?
|
[
"8",
"9",
"3",
"21",
"10"
] |
cost of each apple = 4 dollars
Apples that Benny can buy with the amount she has=420/4 = 90.
Apples that each kid gets evenly = 105/5 =21 Apples.
So the answer is D=21
The answer is: D
|
D
|
mathematics
|
A money lender lent a total of $1700 to two of his customers. He charged at the rate of 5%p.a. to one of them and 6% p.a. to the other. If he earned an average of 5.67% on $1700, how much did he lend to each of the two customers?
|
[
"700; 1100",
"1139; 561",
"1000; 800",
"1200; 800",
"None of the above"
] |
The method given above is the one given in the book.
However the method I used was
(1*x*5)/100 + (1700-x)*6/100 = 1700*5.67/100
Simplifying we get x=561
B
The answer is: B
|
B
|
mathematics
|
On a certain transatlantic crossing, 25 percent of a ship's passengers held round-trip tickets and also took their cars aboard the ship. If 60 percent of the passengers with round-trip tickets did not take their cars aboard the ship, what percent of the ship's passengers held round-trip tickets?
|
[
"33 1/3%",
"40%",
"50%",
"62.5%",
"66 2/3%"
] |
On a certain transatlantic crossing, 20 percent of a ship’s passengers held round-trip tickets and also took their cars abroad the ship. If 60 percent of the passengers with round-trip tickets did not take their cars abroad the ship, what percent of the ship’s passengers held round-trip tickets?
Solution: Let total number of passengers be 100
According to Q stem 40% of passengers who had round-trip tics have taken cars - let number of passengers with round trip be X then
40% of X = 25 => X= 62.5.
Answer D
The answer is: D
|
D
|
mathematics
|
What is the units' digit of the following expression (11)^5*(1)^3*(21)^5?
|
[
"0",
"1",
"3",
"5",
"9"
] |
We do not have to do any calculations or find units digit of remaining numbers...
all three terms - 11,1,21 - are ODD and since the PRODUCT contains 1, the units digit of the product will remain 1
B
The answer is: B
|
B
|
mathematics
|
There are 5 bags three of which each contains 5 white and 2 black balls, and remaining 2 bags each contains 1 white and 4 black ball; a white ball has been drawn, find the chance that it came from second group.
|
[
"2/7",
"6/35",
"8/25",
"14/89",
"3/5"
] |
Chances of selecting a white ball from group 1: 2/7----------------------Chances of selecting a white ball from group 2: 4/5
Thus combined probability of section of white ball from group 1:
3/5 x 5/7 = 3/7
Thus combined probability of section of white ball from group 2:
2/5 x 1/5 = 2/25
Out of these chances, chance of occurrence of first case : (2/25) / (3/7 + 2/25) = 14/89
D
The answer is: D
|
D
|
mathematics
|
If a, b and c are even integers, which of the following could be the value of a^2 + b^2 + c^2?
|
[
"a)36",
"b)38",
"c)42",
"d)46",
"e)50"
] |
a, b and c are even integers which means that, supposing that x, y and z are integers, then a=2x, b=2y and c=2z
Therefore we have: a^2+b^2+c^2=2^2*x^2+2^2*y+2^2*z=4x^2+4y^2+4z^2=4(x^2+y^2+z^2).
Which means that the total a^2+b^2+c^2 must be divisible by 4.
The only choice which is divisible by 4 is: A)
36=4^2+4^2+2^2
Answer: A.
The answer is: A
|
A
|
mathematics
|
In honor of the year 2012, a donor has purchased 2016 books to be distributed evenly among the elementary schools in a certain school district. If each school must receive the same number of books, and there are to be no books remaining, which of the following is NOT a number of books that each school could receive?
|
[
"18",
"36",
"42",
"51",
"56"
] |
All options other than 'D' are factors of 2012. Hence, 'D' is the answer
The answer is: D
|
D
|
mathematics
|
The side of a cube is 8 m, Find the voiume?
|
[
"515",
"509",
"502",
"508",
"512"
] |
Cube Volume = a(power)3
a(power)3 = 8(power)3
= 512 m(power)3.
Answer is E.
The answer is: E
|
E
|
mathematics
|
Of the 200 employees in a certain company, 30 percent will be relocated to City X and the remaining 70 percent will be relocated to City Y. However, 40 percent of the employees prefer City Y and 60 percent prefer City X. What is the highest possible number of employees who will be relocated to the city they prefer?
|
[
"115",
"120",
"140",
"152",
"165"
] |
120 prefer X (Group 1);
80 prefer Y (Group 2).
City Y needs 140 people: letall 80 who prefer Y (entire Group 2) be relocated there, the rest 60 will be those who prefer X from Group 1;
City X needs 60 people: 120-60=60 from Group 1 will be relocated to X, which they prefer.
So, the highest possible number of employees who will be relocated to the city they prefer is 80+60=140.
Answer: C.
The answer is: C
|
C
|
mathematics
|
Statement: Put thechild in school at the age of 5. Assumptions: At that age the child reaches appropriate level of development and is ready to learn. The schools do not admit children after 6years of age.
|
[
"Only assumption I is implicit",
"Only assumption II is implicit",
"Either I or II is implicit",
"Neither I nor II is implicit",
"Both I and II are implicit"
] |
Since the statement talks of putting the child in school at the age of 5, it means that the child is mentally prepared for the same at this age. So, I is implicit. But nothing about admission after 6 years of age is mentioned in the statement. So, II is not implicit.
A
The answer is: A
|
A
|
mathematics
|
The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 4 per square feet if there is one door of dimensions 6 feet * 3 feet and three WINDOWS of dimensions 4 feet * 3 feet each?
|
[
"4000",
"3624",
"5673",
"4530",
"4566"
] |
Area of the four walls = 2h(l + b)
Since there are doors and WINDOWS, area of the walls = 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft.
Total cost = 906 * 4 = Rs. 3624
Answer: Option B
The answer is: B
|
B
|
mathematics
|
On the number line, if x is halfway between -6 and 4, and if y is halfway between -2 and 6, what number is halfway between x and y?
|
[
"-2.5",
"-1.5",
"-0.5",
"0.5",
"1.5"
] |
x= -1 and y = 2.
The answer is D.
The answer is: D
|
D
|
mathematics
|
A certain number when divided by 80 leaves a remainder 25, what is the remainder if the same no.be divided by 15?
|
[
"4",
"5",
"6",
"7",
"9"
] |
Explanation:
80 + 25 = 105/15 = 7 (Remainder)
D
The answer is: D
|
D
|
mathematics
|
John works at a science lab that conducts experiments on bacteria. The population of the bacteria multiplies at a constant rate, and his job is to notate the population of a certain group of bacteria each hour. At 1 p.m. on a certain day, he noted that the population was 1,000 and then he left the lab. He returned in time to take a reading at 4 p.m., by which point the population had grown to 216,000. Now he has to fill in the missing data for 2 p.m. and 3 p.m. What was the population at 3 p.m.?
|
[
"72,000",
"48,000",
"50,000",
"36,000",
"40,000"
] |
let the rate be x, then population of the bacteria after each hour can be given as 1000, 1000x, 1000(x^2), 1000(x^3)
now population at 4pm =216,000
thus we have 1000(x^3) = 216,000 =216
thus x=6
therefore population at 3pm = 1000(36) = 36,000
Answer : D
The answer is: D
|
D
|
mathematics
|
An amount of money is to be divided between P, Q and R in the ratio of 3:7:12. If the difference between the shares of P and Q is Rs.2800, what will be the difference between Q and R's share?
|
[
"2788",
"3500",
"7282",
"2782",
"2729"
] |
4 --- 2800
5 --- ? => 3500
Answer:B
The answer is: B
|
B
|
mathematics
|
For a party 240 guests were invited.Contracted have gained 12.5% profit but 30 guest were absent.He charged same cost , lost 100 rs. what is the meal cost?
|
[
"20/3",
"80/3",
"10/3",
"40/3",
"50/3"
] |
Let Cost of one meal be x.
Hence, C.P. of 240 meals = 240 x.
Since contractor gains 12.5 % profit therefore
total selling price = 240x + 240*12.5/100 x
= 270x.
Now 30 guest were absent.
Therefore C.P will remain same = 240x
And new S.P for 210 guest = (270/240 ) *
210 x
In this case he incurrs a loss of Rs 100.
240x - (9/8) x * 210 = 100
x=80/3.
So, cost of one meal is Rs. 80/3.
ANSWER:B
The answer is: B
|
B
|
mathematics
|
If log 27 = 1.437, then the value of log 9 is:
|
[
"0.934",
"0.945",
"0.954",
"0.958",
"0.998"
] |
log 27 = 1.437
log (3cube ) = 1.437
3 log 3 = 1.437
log 3 = 0.479
log 9 = log(3square ) = 2 log 3 = (2 x 0.479) = 0.958.
Answer: Option D
The answer is: D
|
D
|
mathematics
|
How many numbers between 0 and 1670 have a prime tens digit and a prime units digit?
|
[
"268",
"272",
"202",
"112",
"262"
] |
There are 4 single digit prime numbers: 2, 3, 5 and 7. Hence, last two digits (tens and units) can take 4*4=16 different values: 22, 23, ..., 77.
So, in each hundred there are 16 such numbers. In 17 hundreds there will be 17*16=272 such numbers, but 4 out of them will be more than 1670, namely: 1672, 1673, 1675 and 1677. Which means that there are 272-4=268 numbers between 0 and 1670 which have a prime tens digit and a prime units digit.
Answer: A.
The answer is: A
|
A
|
mathematics
|
Ram and Shakil run a race of 2000m. First Ram gives Shakil a start of 200m and beats him by 1 minute.Next Ram gives shakil a start of 6 min and is beaten by 1000 meters . Find the time in minutes in which Ram and Shakil can run the race seperately.
|
[
"12 , 18",
"8 , 10",
"18 , 20",
"20 , 25",
"None of these"
] |
Explanation :
Let speed of ram and shakil be x and y resp.
Case 1 : Ram gives a start of 200m and beats Shakil by 1 minute.
2000/x - 1800/y= -60
2000/x= 1800/y -60---------------------(1)
Case2: Ram gives Shakil a start of 6 min and is beaten by 1000 meters
distance travelled by shakil in 6 minutes= (6*60*y) meters = 360y meters
1000/x = (2000- 360y)/y------------------(2)
Solve equation 1 and 2 to obtain x and y
Answer is x = 8 minutes, y = 10 minutes
Hence (B) is the corret answer.
Answer : B
The answer is: B
|
B
|
mathematics
|
If a*b denotes the greatest common divisor of a and b, then ((16*20)*(18*24)) = ?
|
[
"24",
"12",
"6",
"4",
"2"
] |
The greatest common divisor of 16 and 20 is 4. Hence 16*20 = 4 (note that * here denotes the function not multiplication).
The greatest common divisor of 18 and 24 is 6. Hence 18*24 = 6.
Hence ((16*20)*(18*24)) = 4*6.
The greatest common divisor of 4 and 6 is 2.
Answer; E.
The answer is: E
|
E
|
mathematics
|
The number of sequences in which 7 players can throw a ball, so that the youngest player may not be the last is -.
|
[
"1879",
"7899",
"4320",
"1680",
"1692"
] |
x Not younger_______ ↑
The last ball can be thrown by any of the remaining 6 players. The first 6 players can throw the ball in ⁶P₆ ways.
The required number of ways = 6(6!)
= 4320
Answer:C
The answer is: C
|
C
|
mathematics
|
E is the set of the first n positive odd numbers, where n is a positive integer. Given that n > k, where k is also a positive integer, x is the maximum value of the sum of k distinct members of E, and y is the minimum value of the sum of k distinct members of E, what is x + y?
|
[
"kn",
"kn + k^2",
"kn + 2k^2",
"2kn – k^2",
"2kn"
] |
Probably the easiest way to solve this question would be to assume some values for n and k.
Say n=3, so E, the set of the first n positive odd numbers would be: E={1, 3, 5};
Say k=1, so E, the maximum value of the sum of K distinct members of Z would simply be 5. Similarly, Y, the minimum value of the sum of K distinct members of E would simply be 1.
X+Y=5+1=6.
Now, substitute n=3 and k=1 in the options provided to see which one yields 6. Only asnwer choice E fits: 2kn=2*3*1=6.
Answer: E.
The answer is: E
|
E
|
mathematics
|
Dawson got a weekly raise of $160. If he gets paid every other week, write an integer describing how the raise will affect his paycheck.
|
[
"150",
"160",
"170",
"180",
"190"
] |
Let the 1st paycheck be x (integer).
Dawson got a weekly raise of $ 160.
So after completing the 1st week she will get $ (x+160).
Similarly after completing the 2nd week she will get $ (x + 160) + $ 160.
= $ (x + 160 + 160)
= $ (x + 320)
So in this way end of every week her salary will increase by (B)$ 160.
The answer is: B
|
B
|
mathematics
|
Let x be a positive integer, what is the remainder when 2^(3x+3)+3 is divided by 3?
|
[
"0",
"1",
"2",
"3",
"4"
] |
For: (2^(3x+3)+3)/3
Let n = 3x + 3
2^n
2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 16
2^5 = 32, last digit pattern repeats 2, 4, 8, 6, 2, ....
Rule: x^(m+n) = (x^m)(x^n)
(2^(3x))(2^3)
Rule: x^(mn) = (x^m)^n
((2^3)^x)(8) => Now, (8)(8) + 3 = (64) + 3 => and, 4 + 2 + 1 => Finally, (6 + 1)/3, and remainder is 1.
Answer: B
The answer is: B
|
B
|
mathematics
|
A straight fence is to be constructed from posts 6 inches wide and separated by lengths of chain 7 feet long. If a certain fence begins and ends with a post, which of the following could not be the length of the fence in feet? (12 inches = 1 foot)
|
[
"18",
"23",
"38",
"53",
"68"
] |
There is one post for each length of chain, plus one final post at the end.
The length of the fence in feet is 7.5x + 0.5, where each is the number of chain lengths.
The length of the fence is an integer when x = 1,3,5,7,...
The length of the fence could be 8, 23, 38, 53, 68,...
The answer is A.
The answer is: A
|
A
|
mathematics
|
In the xy-plane the point (-2 -3) is the centre of a circle, the point (-2, 1) lies inside the circle and the point (4, -3) lies outside the circle. If the radius r of the circle r is an integer then diameter ?
|
[
"6",
"10",
"4",
"3",
"2"
] |
Can be solved without much calculations.
You are given that (-2,-3) is the center of the circle. Point (4,-3) lies inside the circle ---> the radius is lesser than distance of (-2,-3) from (4,-3) ---> lesser than 6 units but the radius will also be greater than the distance of (-2,-3) from (-2,1) ----> greater than 4 units.
Thus the radius is >4 but <6 and as it is an integer, the only possible value of radius = 5 units.
Diameter =2r= 10
B is the correct answer.
The answer is: B
|
B
|
mathematics
|
If a: b = 3:4, b:c = 7:9, c:d = 5:7, find a:d?
|
[
"5:12",
"7:12",
"3:11",
"5:11",
"7:11"
] |
Explanation:
a/d = (3/4)*(7/9)*(5/7) => 5/12
ANSWER IS A
The answer is: A
|
A
|
mathematics
|
The amount of an investment will double in approximately 70/ p years, where p is the percent interest, compounded annually. If Thelma invests $ 40,000 in a long-term CD that pays 5 percent interest, compounded annually, what will be the approximate total value of the investment when Thelma is ready to retire 56 years later?
|
[
"$ 280,000",
"$ 320,000",
"$ 360,000",
"$ 450,000",
"$ 640,000"
] |
The amount of an investment will double in approximately 70/ p years, where p is the percent interest, compounded annually. If Thelma invests $ 40,000 in a long-term CD that pays 5 percent interest, compounded annually, what will be the approximate total value of the investment when Thelma is ready to retire 42 years later?
The investment gets doubled in 70/p years. Therefore, the investment gets doubled in 70/5= every 14 years. After 56 years, the investment will get doubled 56/14= 4 times.
So the amount invested will get doubled thrice.
So, 40000 *2^4 = 640000
Hence, the answer is E.
The answer is: E
|
E
|
mathematics
|
12 men take 18 days to complete a job whereas 12 women in 18 days can complete 5/6 of the same job. How many days will 10 men and 8 women together take to complete the same job?
|
[
"6",
"13 1â„2",
"13",
"Data inadequate",
"None of these"
] |
12 M × 18 = 12 W × 18 × 6/5
\ w = 5/6 M
10M + 8W = 10M + 8 × 5/6M = 16 2/3 M
\16 2/3men can complete the same work
in 12×18/16 2/3=13 days
Answer C
The answer is: C
|
C
|
mathematics
|
A train running at the speed of 6 km/hr crosses a pole in 2 seconds. Find the length of the train?
|
[
"150",
"872",
"3.33",
"3.21",
"30.1"
] |
Speed = 6*(5/18) m/sec = 5/3 m/sec
Length of Train (Distance) = Speed * Time
5/3) * 2 = 3.33 meter
Answer:C
The answer is: C
|
C
|
mathematics
|
A credit card company has a cash back option for their customers which is based on the annual amount that they charge on their credit cards. The customer receives 1.5% cash on their first $5000 of purchase, 2.5% on the next $5000 of purchase and a 3% on cash back on portion that exceeds $10,000. If a customer receives a cash back of 2.5% on their total annual charges made on the credit card, then what was the customer's annual charge?
|
[
"$17,500",
"$20,000",
"$22,500",
"$25,000",
"$27,500"
] |
The customer receives $75 for the first $5000.
The customer receives $125 for the next $5000.
Let x be the total amount of the customer's annual charge.
$200 + 0.03(x-10,000)=0.025x
0.005x=100
x=20,000
The answer is B.
The answer is: B
|
B
|
mathematics
|
A bowl contains equal numbers of red, orange, green, blue, and yellow candies. Kaz eats all of the green candies and half of the orange ones. Next, he eats half of the remaining pieces of each color. Finally, he eats red and yellow candies in equal proportions until the total number of remaining candies of all colors equals 30% of the original number. What percent of the red candies remain?
|
[
"22.5%",
"31.5%",
"37.5%",
"42.5%",
"46.5%"
] |
Let x be the original number of each color so there are a total of 5x candies.
Kaz eats all of the green candies and half of the orange ones.
There are 0 green candies and 0.5x orange candies remaining.
He eats half of the remaining pieces of each color.
There are 0.25x orange candies, and 0.5x each of red, yellow, and blue candies.
He eats red and yellow candies in equal proportions.
orange+blue+red+yellow = 0.75x + red + yellow = 1.5x
red + yellow = 0.75x
red = 0.375x, since red = yellow.
The answer is C.
The answer is: C
|
C
|
mathematics
|
On the xy-coordinate plane, point A lies on the y-axis and point B lies on the x-axis. Points A, B, and C form a right triangle with a 90-degree angle at point C and the triangle has an area of 20. If AC is parallel to the x-axis, and BC is parallel to the y-axis, which of the following could be the coordinates of point C?
|
[
"(3, 7)",
"(-8, 4)",
"(5, -8)",
"(-2, 10)",
"(-5, -5)"
] |
The area of the triangle formed will be:
1/2 * base * height =
1/2 * |(X-coordinate of point C)| * |(Y-coordinate of point C)| = 20
Thus |product of coordinates of point C| = 40
The answer is C.
The answer is: C
|
C
|
mathematics
|
The red triangle is equilateral with a side of 23 centimetres. Its perimeter is
|
[
"68 cm",
"69 cm",
"70 cm",
"71 cm",
"None"
] |
Solution:
All three sides of an equilateral triangle are equal. Thus, its perimeter will be 23 × 3 = 69 cm
Answer B
The answer is: B
|
B
|
mathematics
|
Two persons , Ram & Lakshman , who are at a distance of 100 km from each other, move towards each other from two places P and Q at speeds of 20 kmph and 25 kmph respectively. Lakshman reaches P, returns immediately and meets Ram at R, who started on the return journey to P immediately after reaching Q. What is the distance between Q and R?
|
[
"33 1/3 km",
"25 km",
"30km",
"27 1/3 km",
"None of these"
] |
Ram takes 100/20 = 5 hours to cover the distance from P to Q. By that time Lakshman covers
covers 5 *25 = 125 km
Lakshman covers 25 km more than the distance PQ . Now the distance between them = 75 km
Time taken by them to meet = Distance/ Relative speed = 75/(20+25) = 75/45 = 5/3 hrs.
Distance between Q and R is nothing but the distance covered by Ram in 5/3 hours = 20 *5/3 = 100/3 km or 33 1/3 km
Answer: A
The answer is: A
|
A
|
mathematics
|
Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is?
|
[
"60 gallons",
"100 gallons",
"120 gallons",
"180 gallons",
"130 gallons"
] |
Work done by the waste pipe in 1 minute = 1/15 - (1/20 + 1/24) = - 1/40
Volume of 1/40 part = 3 gallons\
Volume of whole = 3 * 40 = 120 gallons.
ANSWER:C
The answer is: C
|
C
|
mathematics
|
A certain company consists of 7 managers and 8 non-managers. How many different teams of 3 employees can be formed in which at least one member of the team is a manager and at least one member of the team is not a manager? (Two groups are considered different if at least one group member is different)
|
[
"84",
"108",
"135",
"270",
"364"
] |
Total # of teams of 3 possible is 15C3=455
# of teams with only managers or only non-managers is: 7C3+8C3=35+56=91;
# of teams of 3 with at least one manager or at least one non-manager is: 455-91=364.
ANSWER:E
The answer is: E
|
E
|
mathematics
|
The owner of a furniture shop charges his customer 20% more than the cost price. If a customer paid Rs. 3000 for a computer table, then what was the cost price of the computer table?
|
[
"2500",
"2772",
"1991",
"6725",
"2099"
] |
CP = SP * (100/(100 + profit%))
= 3000(100/120) = Rs. 2500.
Answer: A
The answer is: A
|
A
|
mathematics
|
A six-sided die is rolled once. What is the probability that the number rolled is an even number greater than 2?
|
[
"1/4",
"2/4",
"1/2",
"1/3",
"2/3"
] |
Out of the 6 possible numbers that may rolled, 3 are even: 2, 4 and 6 BUT only 4 and 6 are greater than 2. Hence the probability that the number rolled is an even number greater than 2 is given by
(number of even numbers greater than 2) / 6 = 2 / 6 = 1 / 3
correct answer D
The answer is: D
|
D
|
mathematics
|
The owner of a furniture shop charges his customer 32% more than the cost price. If a customer paid Rs. 5400 for a computer table, then what was the cost price of the computer table?
|
[
"Rs.4090",
"Rs.4067",
"Rs.6290",
"Rs.6725",
"Rs.6708"
] |
CP = SP * (100/(100 + profit%))
= 5400(100/132) = Rs.4090.
Answer: A
The answer is: A
|
A
|
mathematics
|
A bullet train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the bullet train is 54 km/hr, what is the length of the platform?
|
[
"210 cm",
"120 cm",
"340 cm",
"240 cm",
"330 cm"
] |
D
240 cm
The answer is: D
|
D
|
mathematics
|
Two stations P and Q are 155 km apart on a straight track. One train starts from P at 7 a.m. and travels towards Q at 20 kmph. Another train starts from Q at 8 a.m. and travels towards P at a speed of 25 kmph. At what time will they meet?
|
[
"10 am",
"12 am",
"10.30 am",
"12.30 am",
"11 am"
] |
Assume both trains meet after x hours after 7 am
Distance covered by train starting from P in x hours = 20x km
Distance covered by train starting from Q in (x-1) hours = 25(x-1)
Total distance = 155
=> 20x + 25(x-1) = 155
=> 45x = 180
=> x= 4
Means, they meet after 3 hours after 7 am, ie, they meet at 11 am
Answer is E.
The answer is: E
|
E
|
mathematics
|
The cross-section of a cannel is a trapezium in shape. If the cannel is 8 m wide at the top and 6 m wide at the bottom and the area of cross-section is 700 sq m, the depth of cannel is?
|
[
"76",
"100",
"27",
"80",
"25"
] |
1/2 * d (8+ 6) = 700
d = 100
Answer: B
The answer is: B
|
B
|
mathematics
|
Let Q represent a set of three distinct prime numbers. If the sum of the numbers in Q is even and x is a member of Q, then what is the least possible value that x can be?
|
[
"1",
"2",
"3",
"5",
"7"
] |
Q = p1+p2+p3= even (and all primes are distinct)
if the least prime is 2 then we have sum of Q = even.
Ans. B. 2
The answer is: B
|
B
|
mathematics
|
A corporation triples its annual bonus to 50 of its employees. What percent W of the employees’ new bonus is the increase?
|
[
"50%",
"662⁄3%",
"100%",
"200%",
"300%"
] |
W of the employees’ new bonus is the increase Hence B.
The answer is: B
|
B
|
mathematics
|
Cara leaves her home and walks toward Don's house. Two hours later, Don leaves his home and walks toward Cara's house. The distance between their homes is 45 kilometers, Cara's walking speed is 6 km/h, and Don's walking speed is 5 km/h. How many kilometers will Cara walk before she meets Don?
|
[
"26",
"27",
"28",
"29",
"30"
] |
Cara walks 12 km in the first two hours so there are 33 km remaining.
When Don starts walking, they complete a total of 11 km per hour.
They will meet three hours after Don starts walking.
Since Cara walks for 5 hours, she walks 30 km.
The answer is E.
The answer is: E
|
E
|
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