subject
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mathematics | Two pipes A and B can separately fill a tank in 2 minutes and 15 minutes respectively. Both the pipes are opened together but 4 minutes after the start the pipe A is turned off. How much time will it take to fill the tank? | [
"11",
"10",
"17",
"16",
"18"
]
| 4/12 + x/15 = 1
x = 10
Answer:B
The answer is: B | B |
mathematics | If the charge of staying in a student youth hostel $18.00/day for the first week, and $14.00/day for each additional week, How much does it cost to stay for 23 days? | [
"$160",
"$350",
"$282",
"$274",
"$286"
]
| Total number of days of stay = 23
Charge of staying in first week = 18*7 = 126 $
Charge of staying for additional days =(23-7)*14 = 16*14 = 224 $
Total charge =126 +224 = 350$
Answer B
The answer is: B | B |
mathematics | A big beautiful cube is formed by rearranging the 160 coloured and 56 non-coloured similar cubes in such a way that the exposure of the coloured cubes to the outside is minimum. The percentage of exposed area to the coloured is : | [
"25.9%",
"44.44%",
"35%",
"61%",
"None of these"
]
| Well the big cube which has the side built with 6 little cubes (6^3) will haveinsidethe cube which has the side built with 4 little cubes (6-2 edges), so 4^3. .. Similarly, the cube which has the side built with 4 little cubes (4^3) will haveinsidethe cube which has the side built with 2 little cubes, (4-2 edges), so 2^3... answer is B
The answer is: B | B |
mathematics | At a loading dock, each worker on the night crew loaded 3/4 as many boxes as each worker on the day crew. If the night crew has 5/6 as many workers as the day crew, what fraction of all the boxes loaded by the two crews did the day crew load? | [
"4/7",
"5/9",
"6/11",
"7/12",
"8/13"
]
| Let x be the number of workers on the day crew.
Let y be the number of boxes loaded by each member of the day crew.
Then the number of boxes loaded by the day crew is xy.
The number of boxes loaded by the night crew is (5x/6)(3y/4) = 5xy/8
The total number of boxes is xy + 5xy/8 = 13xy/8
The fraction loaded by the day crew is xy / (13xy/8) = 8/13
The answer is E.
The answer is: E | E |
mathematics | Arrange the following in descending order :
A) 111(4),
B) 110 x 109 x 108 x 107,
C)109 x 110 x 112 x 113 | [
"all are equal",
"B,A.C",
"A,B,C",
"A,C,B",
"None"
]
| Explanation :
if you see option B...you can easily say it is the lowest value. Now about A and C you can see the sum of the values on both side is equal on this type of cases the side which as more number of values closer than other side and to the maximum value among given numbers will be the biggest value..If you couldn't understand the explanation take two sample and compare
Answer : D
The answer is: D | D |
mathematics | Rahul is 30 years older than his daughter Mary. In 20 years Rahul will be twice as old as Mary. What is Mary current age. | [
"12",
"14",
"10",
"16",
"18"
]
| Now: Mary = x, Rahul =x+30
In 20 years Mary = x+20, Rahul= x+30+20 or 2(x+20)
x+30+20= 2(x+20)
x+50=2x+40
50-40=2x-x
x= 10
Mary is 10 years old
Answer : C
The answer is: C | C |
mathematics | If 2^4, 3^3, and 10^3 are factors of the product of 1,452 and w, where w is a positive integer, what is the smallest possible value of w? | [
"198",
"288",
"360",
"396",
"484"
]
| I will go with C (pending elements to match is 2^2*3^2*10^1 = 360
The answer is: C | C |
mathematics | The speeds of three asteroids were compared. Asteroids X-13 and Y-14 were observed for identical durations, while asteroid Z-15 was observed for 2 seconds longer. During its period of observation, asteroid Y-14 traveled three times the distance X-13 traveled, and therefore Y-14 was found to be faster than X-13 by 2500 kilometers per second. Asteroid Z-15 had an identical speed as that of X-13, but because Z-15 was observed for a longer period, it traveled five times the distance X-13 traveled during X-13's inspection. Asteroid X-13 traveled how many kilometers during its observation? | [
"500",
"625",
"1,000",
"1,500",
"2,500"
]
| X13: (t, d, s)
Y14: (t, 3d, s+2500mi/hour)
Z15: (t+2 seconds, s, 5d)
d=?
Distance = Speed*Time
x13: d = s*t
x14: 3d = (s+2500)*t ===> 3d = ts+2500t
z15: 5d = s*(t+2t) ===> 5d = st+2st ===> 5d - 2st = st
3d = 5d - 2st + 2500t
-2d = -2st + 2500t
2d = 2st - 2500t
d = st - 1250t
x13: d = s*t
st - 1250t = s*t
s - 1250 = s
-625 = s
I got to this point and couldn't go any further. This seems like a problem where I can set up individual d=r*t formulas and solve but it appears that's not the case. For future reference how would I know not to waste my time setting up this problem in the aforementioned way? Thanks!!!
The distance of Z15 is equal to five times the distance of X13 (we established that x13 is the baseline and thus, it's measurements are d, s, t)
S(T+2) = 5(S*T)What clues would I have to know to set up the equation in this fashion? Is it because I am better off setting two identical distances together?
ST+2S = 5ST
T+2 = 5T
2=4T
t= 1/2
We are looking for distance (d=s*t) so we need to solve for speed now that we have time.
Speed y14 - speed x13
Speed = d/t
3d/t - d/t = 2500 (remember, t is the same because both asteroids were observed for the same amount of time)
2d = 2500
2 = 1250
d=s*t
d=1250*(1/2)
d=625
ANSWER: B
The answer is: B | B |
mathematics | A sum of money amounts to 9800 after 5 years and 12005 after 8 years at the same rate of simple interest. The rate of interest per annum is: | [
"10",
"18",
"11",
"12",
"15"
]
| D
12
S.I. for 3 years = (12005 - 9800) = 2205.
S.I. for 5 years = (2205/3)x 5 = 3675
Principal = (9800 - 3675) = 6125.
Hence, rate = (100 x 3675)/(6125x5)% = 12%
The answer is: D | D |
mathematics | A person travels equal distances with speeds of 50km/hr,100km/hr and 120km/hr and takes a total time of 23 minutes. The total distance is? | [
"15km",
"30km",
"45km",
"50km",
"60km"
]
| Let the total distance be 3x km
x/50 + x/100 + x/120 = 23/60
23x/600 = 23/60
23x = 230
x = 10km
Total distance = 3x = 30km
Answer is B
The answer is: B | B |
mathematics | How many integers are between 9 and 67/5, inclusive? | [
"5",
"7",
"9",
"10",
"11"
]
| 67/5 = 13.xx
We are not concerned about the exact value of 67/5 as we just need the integers.
Since the values are small, we can write down the integers.
The different integers between 9 and 67/5 would be 9, 10, 11, 12,13
Total number of integers = 5
Option A
The answer is: A | A |
mathematics | The sum of 4 hours 45 minutes and 5 hours 55 minutes is approximately what percent of a day? | [
"32%",
"36%",
"40%",
"44%",
"48%"
]
| Since the question is asking for an approximate percentage
4:45+5:55 ~ 11 hours
% of day = 11*100/24 ~ 11*100/25= 44%
Answer is D.
The answer is: D | D |
mathematics | The different of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and 15 as remainder.What is the smaller number ? | [
"360",
"320",
"290",
"240",
"270"
]
| Let the smaller number be x.Then larger number =(x+1365).
x+1365=6x+15
5x=1350
x=270
smaller number =270.
Answer is E
The answer is: E | E |
mathematics | Riya and Priya set on a journey. Riya moves eastward at a speed of 21kmph and Priya moves westward at a speed of 22 kmph.How far will be priya from Riya after 60 minutes | [
"43kms",
"45kms",
"50kms",
"30kms",
"40kms"
]
| total eastward distance= 21kmph*1hr=21 km
total westward distance= 22kmph*1hr=22 km
total distn betn them= 21+22=43km
ans 43km
ANSWER:A
The answer is: A | A |
mathematics | A certain artist is selling five paintings for the following prices: $7,000, $8,000, $9,000, $23,000, and $25,000. If the price of the most expensive painting is increased $3,000, which of the following statements best describes the change in the mean and the median of the paintings? | [
"The mean and the median will remain unchanged.",
"The mean will remain unchanged but the median will increase.",
"The mean will increase but the median will remain unchanged.",
"The mean and the median will increase by the same amount.",
"The mean and the median will increase by different amounts."
]
| Old set = {7000, 8000, 9000, 23000, 25000}.
New set = {7000, 8000, 9000, 23000, 28000} --> the median (middle term) will remain the same and the mean will increase.
Answer: C.
The answer is: C | C |
mathematics | What is the % change in the area of a rectangle when its length increases by 20% and its width decreases by 20%? | [
"0%",
"20% increase",
"20% decrease",
"4% decrease",
"Insufficient data"
]
| (12/10)*(8/10) = 96/100 of original area
96/100 is a 4% decrease from 100/100 ->D
The answer is: D | D |
mathematics | Q' = 3Q - 3, what is the value of (4')' ? | [
"48",
"57",
"66",
"72",
"81"
]
| (4')'=(3*4-3)'=9'=9*9-9=72
Answer D
The answer is: D | D |
mathematics | Three friends are buying a gift for a friend. Declan contributes 3 dollars more than 1/4 the cost of the gift, Ed contributes 1 dollar less than 1/3 the cost of the gift, and Frank contributes the remaining 22 dollars. What is the cost of the gift? | [
"48",
"57.6",
"60",
"66",
"72"
]
| Declan = D, Ed = E, Frank = F
t = total
D + E + F = t
(t/4 + 3) + (t/3 - 1) + 22 = t
t = 24 + (7t/12)
12t = 24(12) + 7t
5t = 24(12)
t = 57.6
The correct answer is B.
The answer is: B | B |
mathematics | A can do a job in 10 days and B can do it in 30 days. A and B working together will finish twice the amount of work in ------- days? | [
"14 days",
"15 days",
"22 days",
"11 days",
"19 days"
]
| B
1/10 + 1/30 = 2/15
15/2 *2 = 15 days
The answer is: B | B |
mathematics | Solution for 2.01+.3+.34 | [
"2.91",
"2.65",
"2.938",
"2.986",
"2.999"
]
| 2.01+.3+.34=0
0=0-2.01-0.3-0.34
0=-2.65
answer :B
The answer is: B | B |
mathematics | The operation T is defined by x T y=1/x+1/y for all nonzero numbers x and y. If z is a number greater than 1, which of the following must be true.
I. x T (-z)=0
II. 2/z T 2/z=z
III. z T z/z-1=1 | [
"a.) I",
"b.) I and II only",
"c) I and III only",
"d) II and III only",
"e) I, II and III only"
]
| Statement I is TRUE
Statement II is TRUE
Statement III is not TRUE
Answer : B
The answer is: B | B |
mathematics | A dog takes 4 leaps for every 5 leaps of a hare but 3 leaps of a dog are equal to 4 leaps of the hare. Compare their speeds? | [
"4:5",
"16:15",
"9:13",
"5:15",
"9:17"
]
| Let the distance covered in 1 leap of the dog be x and that covered in 1 leap of the hare be y
Then 3x = 4y
x = 4/3 y
4x = 16/3 y
Ratio of speeds of dog and hare = Ratio of distances covered by them in the same time
= 4x:5y = 16/3 y : 5 = 16:15
Answer is B
The answer is: B | B |
mathematics | If all the 6 are replaced by 9, then the algebraic sum of all the numbers from 1 to 100(both inclusive) varies by | [
"330",
"340",
"350",
"360",
"370"
]
| 1 11 21 .......91
2 12 22........92
3 13 23........93
. . . .. . .. . .
. . .. .. . .. .
. . .. . . .. . ...
there are total 20 occurrence of 6. once place at 6 th row in every column and tens place in 6 th column
and diff of 6 and 9 is 3 so
3*1*10+3*10*10 = 330
ANSWER:A
The answer is: A | A |
mathematics | A,B and C started a business by investing Rs.2000/- , Rs.3000/- and Rs.4000/- respectively. Total profit is Rs.4500/-. Find the A’s share? | [
"Rs.1000/-",
"Rs.1500/-",
"Rs.2000/-",
"Rs.3000/-",
"Rs.3400/-"
]
| A = Rs.2000/- , that is 2 parts
B = Rs.3000/- , that is 3 parts
C = Rs.4000/- , that is 4 parts
Total 9 parts -------> profit (4500/-)
----->1 part -------->Rs.500/-
then A's share 2 parts -----> Rs.1000/-
A
The answer is: A | A |
mathematics | Seats for Maths, Physics and Biology are in the ratio of 7 : 7 : 8 respectively. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the respective ratio of increased seats? | [
"14 : 15 : 20",
"6 : 7 : 8",
"6 : 8 : 9",
"Cannot be determined",
"None of these"
]
| Reqd ratio 7 × 140â„100 : 7 × 150â„100 : 8 × 175â„100
= 7 × 140 : 7 × 150 : 8 × 175 = 14 : 15 : 20
Answer A
The answer is: A | A |
mathematics | The rate of a certain chemical reaction is directly proportional to the square of the concentration of chemical A present and inversely proportional to the concentration of chemical B present. If the concentration of chemical B is increased by 100%, which of the following is closest to the percent change in the concentration of chemical A required to keep the reaction rate unchanged? | [
"100% decrease",
"50% decrease",
"40% decrease",
"40% increase",
"50% increase"
]
| CA: Concentration A
CB: Concentration B
R: Reaction rate
Formula for reaction rate:
R = (CA^2) / CB
Thus if CB is increased by 100% >> means concentration doubles >> 2xCB
Thus, for R to remain the same (CA^2) also has to double.
>> 2 x (CA^2) >> to see what happens to CA, take the 2 into the bracket by taking its root
>> (SQRT 2 CA)^2
SQRT 2 is roughly 40% >> answer D
The answer is: D | D |
mathematics | If you divide 7^115 by 5, which remainder do you get? | [
"0",
"1",
"2",
"3",
"4"
]
| The units digit of 7^1 is 7.
The units digit of 7^2 is 9.
The units digit of 7^3 is 3.
The units digit of 7^4 is 1.
The units digit of 7^5 is 7.
etc...
The units digit of 7^n repeats in blocks of 4: {7, 9, 3, 1}
The remainder of 115/4 is 3.
So the units digit of 7^115 is 3.
The remainder of 7^115 / 5 is 3.
The answer is D.
The answer is: D | D |
mathematics | The average weight of a class is x pounds. When a new student weighing 90 pounds joins the class, the average decreases by 1 pound. In a few months the student’s weight increases to 110 pounds and the average weight of the class becomes x + 4 pounds. None of the other students’ weights changed. What is the value of x? | [
"85",
"86",
"88",
"90",
"99"
]
| When the student weighs 90 pounds the average weight is x - 1 pounds;
When the student weighs 110 pounds the average weight is x + 4 pounds.
So, the increase in total weight of 110 - 90 = 20 pounds corresponds to the increase in average weight of (x + 4) - (x - 1) =5 pounds, which means that there are 20/5 = 4 students (including the new one). So, initially there were 5 student.
Total weight = 5x + 90 = 6(x-1) --> x = 96 pounds.
Answer: E.
The answer is: E | E |
mathematics | When a merchant imported a certain item, she paid a 7 percent import tax on the portion of the total value of the item in excess of $1,000. If the amount of the import tax that the merchant paid was $111.30, what was the total value of the item? | [
"$2380",
"$2590",
"$2760",
"$2940",
"$3150"
]
| Let x be the value of the item.
0.07*(x-1000) = 111.30
x = 2590
The answer is B.
The answer is: B | B |
mathematics | One quantity of wheat at Rs 9.30 per Kg is mixed with another quality at a certain rate in the ratio 8:7. If the mixture so formed be worth Rs 10 per Kg, what is the rate per Kg of the second quality of wheat? | [
"Rs 12.47",
"Rs 10.80",
"Rs 10.80",
"Rs 47.66",
"None of these"
]
| Explanation :
Let the rate of second quality be Rs x per Kg.
C.P of 1Kg wheat of 1st kind = Rs 9.30
C.P of 1 Kg wheat of 2nd kind = Rs. x.
Mean price = Rs 10.
The given ratio is 8 : 7.
Rs 9.30 Rs x
\ /
(Mean Price)
Rs 10
/ \
x-10 : 0.7
8 : 7
Then, the ratio is :-
=>(x-10) : 0.7 = 8 : 7.
=>7x -70=5.6.
=>x=75.6/7.
Hence, the required amount is 10.80 per Kg.
Answer : B
The answer is: B | B |
mathematics | A and B starts a business with Rs.8000 each, and after 4 months, B withdraws half of his capital . How should they share the profits at the end of the 16 months? | [
"18:11",
"16:11",
"18:19",
"18:121",
"18:112"
]
| A invests Rs.8000 for 16 months, but B invests Rs.8000 for the first 4 months and then withdraws Rs.4000. So, the investment of B for remaining 14 months is Rs.4000 only.
A : B
8000*16 : (8000*4) + (4000*14)
128000 : 88000
A:B = 16:11.Answer:B
The answer is: B | B |
mathematics | Walking at 75% of his usual speed a man takes 24 minutes more to cover a distance. What is his usual time to cover this distance? | [
"30",
"36",
"42",
"48",
"72"
]
| speed is inversly proprtional to time
walking at 75% of speed meand 3/4s takes 4/3t.
It takes 24 minutes extra to cover the distance. then
4/3t=t+24
4t=3t+72
t=72
Option E is correct
The answer is: E | E |
mathematics | Two musicians, Maria and Perry, work at independent constant rates to tune a warehouse full of instruments. If both musicians start at the same time and work at their normal rates, they will complete the job in 45 minutes. However, if Perry were to work at thrice Maria’s rate, they would take only 20 minutes. How long would it take Perry, working alone at his normal rate, to tune the warehouse full of instruments? | [
"1 hr 20 min",
"1 hr 7 min",
"2 hr",
"2 hr 20 min",
"3 hr"
]
| Sol:
Lets Perry Rate be P and Rate of Maria be M
(rate)*(time)= Work or rate = work/time
first equation=> P+M = 1/45
converting it to hrs P+M= 1/(45/60) => 1/(3/4) =>4/3
second equation => M+3M =>1/20
converting it to hrs 4M=1/(20/60) =>1/(1/3) =>3
therefore M= 3/4 and P=7/12
Rate of Perry = 7/12
time= work/rate (work = 1 job)
Time= 1 hrs 7 mins
Answer : B
The answer is: B | B |
mathematics | The simple interest on Rs.12000 at a certain rate of interest in five years is Rs.7200. Find the compound interest on the same amount for five years at the same rate of interest? | [
"3052.83",
"3052.22",
"3052.08",
"3052.8",
"3052.13"
]
| R = 100 I / PT
=> R = (100 * 7200)/ (12000 * 5) = 12%
CI = P{ [1 + R /100]n - 1}
= 12000 { [ 1 + 12 / 100]2 - 1}
= Rs.3052.80
Answer: D
The answer is: D | D |
mathematics | A circular rim 28 inches in diameter rotates the same number of inches per second as a circular rim 42 inches in diameter. If the smaller rim makes x revolutions per second, how many revolutions per minute does the larger rim makes in terms of x ? | [
"40x",
"75x",
"48x",
"24x",
"x/75"
]
| The larger rim must circulate for the same number of inches the smaller rim does.
C = (pi)d
C(small): (pi)*28
C(large): (pi)*42
Lets say the time horizon is 60 seconds, so during that time the smaller rim covers a distance of (pi)*28*60 = (pi)*(1680) inches
(pi)*(1680) = (pi)*(42)(x)
pi*(40) = pi*(x)
40=x
Answer: A. 40x
The answer is: A | A |
mathematics | In 1982 and 1983, Company B’s operating expenses were $12.0 million and $14.0 million, respectively, and its revenues were $15.6 million and $18.8 million, respectively. What was the percent increase in Company B’s profit (revenues minus operating expenses) from 1982 to 1983 ? | [
"3%",
"16 2/3%",
"25%",
"33 1/3%",
"60%"
]
| Profit in 1982=15.6-12.0=3.6
profit in 1983=18.8-14.0=4.8
increase in profit=4.8-3.6=1.2
percentage increase
12*100/36 =33.33 ; ANSWER:D
The answer is: D | D |
mathematics | Two pipes can fill the cistern in 10hr and 12 hr respectively, while the third empty it in 20hr.
If all pipes are opened simultaneously, then the cistern will be filled in | [
"10.5",
"8",
"6",
"7.5",
"8.5"
]
| First pipe fills cistern in 10 hours.
So, in 1 hour, pipe fills 1/10 of the cistern capacity
2nd pipe fills cistern in 12 hours.
So, in 1 hour, 2nd pipe fills 1/12 of the cistern capacity
3rd pipe empties cistern in 20 hours
So, in 1 hour, 3rd pipe empties 1/20 of the cistern capacity
Net volume added to cistern per hour = Volume filled by 1st pipe per hour + Volume filled by 2nd pipe per hour - Volume emptied by 3rd pipe per hour
= 1/10 + 1/12 - 1/20
=(6 + 5 - 3) / 60 = 8/60
=> Net volume added to cistern per hour = 2/15
So, Cistern will be fill in 15/2 hours = 7.5 hours
So, answer is D
The answer is: D | D |
mathematics | A ship sails out to a mark at the rate of 22 kmph. and sails back at the rate of 12 kmph. The average rate of sailing is ? | [
"5 km/hr",
"12 km/hr",
"16 km/hr",
"25 km/hr",
"None"
]
| Answer
Average = ( 2uv / u +v ) km/hr
= ( 2 x 22 x 12 ) / (22 +12 ) km/hr.
= 16 km/hr.
Correct Option: C
The answer is: C | C |
mathematics | What distance will be covered by a bus moving at 126 kmph in 10 seconds? | [
"287",
"600",
"350",
"276",
"207"
]
| 126 kmph = 126 * 5/18
= 35 mps
D = Speed * time = 35 * 10
= 350 m.
Answer:C
The answer is: C | C |
mathematics | A cistern can be filled by a tap in 3 hours while it can be emptied by another tap in 6 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled? | [
"5.2 hrs",
"2.9 hrs",
"1.9 hrs",
"6 hrs",
"5 hrs"
]
| Net part filled in 1 hour = (1/3 - 1/6) = 1/6
The cistern will be filled in 6/1 hrs i.e., 6 hrs.
Answer:D
The answer is: D | D |
mathematics | If x is 12 percent greater than 80, then x = | [
"89.6",
"91.0",
"88.0",
"70.9",
"71.2"
]
| 12% of 80 = (80*0.12) = 9.6
12% greater than 80 = 80 + 9.6 = 89.6
Answer is clearly A.
The answer is: A | A |
mathematics | If CRY is coded as MRYC then how will GET be coded? | [
"MTEG",
"MGET",
"MEGT",
"METG",
"METC"
]
| CRY=M+RYC
GET=M+ETG
METG
ANSWER:D
The answer is: D | D |
mathematics | Joe invested a certain sum of money in a simple interest bond whose value grew to $260 at the end of 3 years and to $360 at the end of another 5 years. What was the rate of interest in which he invested his sum? | [
"6%",
"8%",
"10%",
"12%",
"15%"
]
| In 5 years, the value grew $100, so the simple interest was $20 per year.
In 3 years, the total interest was 3*$20 = $60
The principal is $260 - $60 = 200.
The interest rate is $20/$200 = 10%
The answer is C.
The answer is: C | C |
mathematics | If a - b = 3 and a(power 2) + b(power 2) = 27, find the value of ab. | [
"5",
"9",
"4",
"10",
"3"
]
| 2ab = (a(power 2) + b(power 2) - (a - b)(power 2)
= 27 - 9 = 18
ab = 9.
Answer is B.
The answer is: B | B |
mathematics | A man whose speed is 8 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 3 kmph, find his average speed for the total journey ? | [
"1 kmph",
"5 kmph",
"6 kmph",
"4 kmph",
"6.8 kmph"
]
| Explanation:
Speed of Man = 8 kmph
Speed of stream = 3 kmph
Speed in DownStream = 11 kmph
Speed in UpStream = 5 kmph
Average Speed = (2 x 11 x 5)/16 = 6.8 kmph.
Answer: E
The answer is: E | E |
mathematics | If 7 boys meet at a reunion and each boy shakes hands exactly once with each of the others, then what is the total number of handshakes | [
"21",
"42",
"43",
"44",
"45"
]
| n(n-1)/2 =7*6/2
=21
ANSWER:A
The answer is: A | A |
mathematics | Every letter in the alphabet has a number value that is equal to its place in the alphabet. Thus, the letter A has a value of 1, the letter B has a value of 2, the letter C has a value of 3, etc... The number value of a word is obtained by adding up the value of the letters in the word and then multiplying that sum by the length of the word. What is the number value of the word "HEN"? | [
"69",
"72",
"75",
"78",
"81"
]
| "HEN" = (8+5+14)*3=81.
The answer is E.
The answer is: E | E |
mathematics | The radius of a semi circle is 35 cm then its perimeter is? | [
"32.8",
"180",
"32.1",
"32.2",
"32.9"
]
| Diameter 70 cm
1/2 * 22/7 * 70 +70 = 180
Answer : B
The answer is: B | B |
mathematics | Number of ways in which the letters of word PARDENS can be arranged with vowels in alphabetical order, is | [
"360",
"240",
"2520",
"480",
"None of these"
]
| Solution
Order of vowels of fixed
∴ required number of ways are 7!/2!.
Answer C
The answer is: C | C |
mathematics | Solving a linear equation with several occurrences of the variable, solve for w. Simplify answer as much as possible.
(7w + 6)/6 + (9w +8)/2 = 22 | [
"1",
"2",
"3",
"4",
"5"
]
| (7w + 6)/6 + (9w +8)/2 = 22
or, [7w + 6 + 3(9w + 8)]/6 = 22
or, 7w + 6 + 27w + 24 = 132
or, 34w + 30 = 132
or, 34w = 132 - 30
or, 34w = 102
or, w = 102/34
Therefore, w = 3
Answer: C
The answer is: C | C |
mathematics | Find √? /13 = 4 ? | [
"76",
"5776",
"304",
"2704",
"None"
]
| Answer
Let √N/13= 4
Then √N = 13 x 4 = 52
∴ N = 52 x 52 = 2704.
Correct Option: D
The answer is: D | D |
mathematics | A box contains eight bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that exactly three bulbs are good? | [
"10/35",
"11/35",
"9/35",
"8/35",
"6/35"
]
| Required probability = (4C3 . 4C1)/8C4 = (4 * 4)/70
= 8/35
Answer:D
The answer is: D | D |
mathematics | The length of a rectangle is increased by 25% and its breadth is decreased by 20%. What is the effect on its area? | [
"Remains same",
"5% decrease",
"7% decrease",
"2% decrease",
"3% decrease"
]
| 100 * 100 = 10000
125 * 80 = 10000
No change
A
The answer is: A | A |
mathematics | One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill tank in 36 min, then the slower pipe alone will be able to fill the tank in? | [
"81 min",
"108 min",
"144 min",
"192 min",
"120 min"
]
| 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 = 1/36
4/x = 1/36 => x = 144 min.
ANSWER:C
The answer is: C | C |
mathematics | Cecilia, Robbie, and Briony all bought stamps. The number of stamps Cecilia purchased was equal to a single digit. The number of stamps only one of them purchased was divisible by 7. The number of stamps one of them bought was an even number. Which of the following could represent the numbers of stamps each purchased? | [
"3, 8, 24",
"7, 9, 17",
"6, 9, 12",
"5, 15, 18",
"9, 10, 13"
]
| I didnt get your point on eliminating D.
The number of stamps only one purchased was divisible by 7.Could that not be Cecilia with 9 stamps.
I choose this and marked D.
The answer is: D | D |
mathematics | Suganya and Suriya are partners in a business. Suganya invests Rs. 35,000 for 8 months and Suriya invests Rs.42,000 for 10 months. Out of a profit of Rs.30,570. Suganya's share is | [
"Rs.9471",
"Rs.12,628",
"Rs.262.8",
"Rs.241.7",
"None"
]
| Solution
Ratio of their shares =(35000×8):(42000×10)
= 128 : 125
Suganya's share = Rs.(30570 ×2/253)
= Rs.241.7.
Answer D
The answer is: D | D |
mathematics | Find the number of different 4-letter words with or without meaning that can be formed from the letters of the word " NUMBER" | [
"340",
"360",
"320",
"420",
"440"
]
| There are 6 letters in the word "NUMBER". So the number of 4-letter words 6P4 =360 Answer : B
The answer is: B | B |
mathematics | In a certain pond, 40 fish were caught, tagged, and returned to the pond. A few days later, 40 fish were caught again, of which 2 were found to have been tagged. If the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, what`s the approximate number of fish in the pond? | [
"400",
"625",
"1250",
"2500",
"1000"
]
| If x is total number of fish in the pond :
4 = 40/x * 100
=> x = 1000
So answer is E
The answer is: E | E |
mathematics | In a certain game of dice, the player’s score is determined as a sum of three throws of a single die. The player with the highest score wins the round. If more than one player has the highest score, the winnings of the round are divided equally among these players. If Jim plays this game against 24 other players, what is the probability of the minimum score that will guarantee Jim some monetary payoff? | [
"1/216",
"1/221",
"1/212",
"1/84",
"1/42"
]
| Toguaranteethat Jim will get some monetary payoff he must score the maximum score of 6+6+6=18, because if he gets even one less than that so 17, someone can get 18 and Jim will get nothing.
P(18)=1/6^3=1/216.
Answer: A.
The answer is: A | A |
mathematics | If (2^13)(25^S) = 5(10^m) what is the value of m ? | [
"7",
"13",
"15",
"16",
"23"
]
| given
2^13 * 25^s = 5 * 10^2
=> 2^13 * 5^(2s) = 2^m * 5^(m+1)
Ans B
on comparing the power of 2 => m=13
The answer is: B | B |
mathematics | Working alone at its constant rate, pump F pumped out ¼ of the water in a tank in 2 hours. Then pumps G and H started working and the three pumps, working simultaneously at their respective constant rates, pumped out the rest of the water in 3 hours. If pump G, working alone at its constant rate, would have taken 18 hours to pump out the rest of the water, how many hours would it have taken pump H, working alone at its constant rate, to pump out all of the water that was pumped out of the tank? | [
"6",
"12",
"15",
"18",
"24"
]
| Rate of pump F = 1/8
3 hours are required to pump out the remaining (3/4)ths of tank --> 1 hr to pump out 1/4
Rate of F + Rate of G + Rate of H = 1/4
Rate of G + Rate of H = 1/4 - 1/8 = 1/8
G takes 18 hours to pump out the remaining (3/4)ths of tank --> 6 hrs per (1/4)ths --> 24 hrs to pump out fully.
Rate of G = 1/24
1/24 + Rate of H = 1/8
Rate of H = 1/8 - 1/24 = 1/12
Time required to pump out all the water by H = 12 hrs
Answer: B
The answer is: B | B |
mathematics | 3 people are sitting in a 4 seat row watching a football game. At halftime they all get up. When they return, they each randomly sit down on one of the 4 chairs. What is the likelihood that none of the 4 end up sitting in the same chair that they sat in during the first half? | [
"1/2",
"9/24",
"15/24",
"18/24",
"21/24"
]
| Originally seated A B C D
now when after they get up and when they sit back again .
1st- A has option to sit on 3 seats ( apart from his previous seat . thus he now sits on B's seat.)
2nd- Similarly B has option to sit on 3 seats ( because A has already occupied B's previous seat, thus B sits on a's seat.)
3rd- Now C has only 1 option to sit on D's seat . and similarly D also has one option to sit on C's seat.)
hence total favourable outcomes 3*1*1=3
and total possible outcomes =3!=6
probability of the favourable outcome=1/2. A
The answer is: A | A |
mathematics | Find the average of first 20 natural numbers. | [
"A)11.5",
"B)20.5",
"C)10.5",
"D)15.5",
"E)21.9"
]
| Sum of first n natural numbers = n(n+1)/2
sum of first 20 natural numbers = 20*21/2 =210
average = 210/20 = 10.5
Answer is C
The answer is: C | C |
mathematics | Before being simplified, the instructions for computing income tax in Country R were to add 2 percent of one's annual income to the average (arithmetic mean) of 100 units of Country R's currency and 1 percent of one's annual income. Which of the following represents the simplified formula for computing the income tax, in Country R's currency, for a person in that country whose annual income is X? | [
"50X/200",
"50+3X/100",
"50+X/40",
"100+X/50",
"100+3X/100"
]
| 50+X/40=C
The answer is: C | C |
mathematics | A shipment of 1500 heads of cabbage, each of which was approximately the same size was purchased for $600.The day the shipment arrived 2/3 of the heads were sold, each at 25% above the cost per head.The following day the rest were sold at a price per head equal to 14% less than the price each head sold for the day before.what was the gross profit on this shipment? | [
"$100",
"$115",
"$125",
"$130",
"$135"
]
| Sol:
1500 heads -> $600
1 head -> $600/1500
1 head -> $(2/5)
25% more of (2/5) -> 125/100 * 2/5 = $(1/2)
He sold 2/3*1500 = 1000 heads for $(1/2) per head
Total revenue by selling 1000 heads = 1000 * 1/2 = $500
Heads left: 500
Cost per head: 86% of the previous price: 86/100 * 1/2 = $(3/7)
Total revenue by selling 500 heads = 3/7 * 500 = 215
Total revenue after selling 1500 cabbage heads - 215+500 = $715
Money spent on the purchase: $600
Profit = 715-600 = $115
Ans: B
The answer is: B | B |
mathematics | In a T.V. factory, an average of 60 TVs are produced per day for the fist 25 days of the months. A few workers fell ill for the next five days reducing the daily average for the month to 58 sets per day . The average production per day for day last 5 days is ? | [
"45",
"48",
"52",
"58",
"None"
]
| Production during these 5 days = Total production in a month - production in first 25 days.
= 30 x 58 - 25 x 60
= 240
∴ Average for last 5 days = 240 / 5
= 48
Correct Option: B
The answer is: B | B |
mathematics | Timothy leaves home for school, riding his bicycle at a rate of 9 miles per hour. Fifteen minutes after he leaves, his mother sees Timothy’s math homework lying on his bed and immediately leaves home to bring it to him. If his mother drives at 27 miles per hour, how far (in terms of miles) must she drive before she reaches Timothy?
I think is a 700 level problem but I tag it as 600/700, let me know. Either way I hope in an explanationThanks | [
"27/8",
"3",
"4",
"9",
"12"
]
| In 15 mins, Timothy travels=9/4 miles.
Now, let his mother takes x hours to reach him, traveling at 27mph.
So, 27x=9x+9/4
x=1/8 hrs.
Thus, the distance traveled by his mother to reach= 27*1/8=27/8miles. Ans A
The answer is: A | A |
mathematics | Mandrake has to choose from 4 from 18 people. There are 3 girls, 5 boys , 10 children. What is total probability that he will choose 1G , 2B , 1C? | [
"1/7",
"2/7",
"3/7",
"4/7",
"5/51"
]
| (3C1 * 5C2 * 10C1)/ 18C4 = 3*10*10/1820= 300/1820=5/51
ANSWER:E
The answer is: E | E |
mathematics | A number is 101102103104...150. As 101 102 103 103.... 150. What is reminder when divided by 3? | [
"2",
"5",
"6",
"7",
"8"
]
| Divisibility rule for 3 also same as 9. so from the above discussion sum of the digits = 380 and remainder = 380/3 = 2.
Answer:A
The answer is: A | A |
mathematics | How many positive integers between 5 and 5000(both are inclusive) are there such that they are multiples of 5? | [
"1500",
"1000",
"999",
"1001",
"1005"
]
| Multiples of 5 = 5,10,15-----,5000
Number of multiples of 5 => 5000-5/5+1= 1000
Answer is B
The answer is: B | B |
mathematics | How many positive integers less than 254 are multiple of 4 but NOT multiples of 6? | [
"20",
"31",
"42",
"43",
"64"
]
| 252/4=63
Multiples of 4 which are a multiple of 6 will be of the form 2*2*3=12n where n>0
240/12=20
63-20=43
Answer: D
The answer is: D | D |
mathematics | The difference between C.I. and S.I. on an amount of Rs. 15,000 for 2 years is Rs. 96. What is the rate of interest per annum? | [
"8",
"10",
"12",
"14",
"16"
]
| [15000 * (1 + R/100)2 - 15000] - (15000 * R * 2)/100 = 96
15000[(1 + R/100)2 - 1 - 2R/100] = 96
15000[(100 + R)2 - 10000 - 200R]/10000 = 96
R2 = (96 * 2)/3 = 64 => R = 8
Rate = 8%
ANSWER:A
The answer is: A | A |
mathematics | A factory produces 4340 toys per week. If the workers at this factory work 2 days a week and if these workers make the same number of toys everyday, how many toys are produced each day? | [
"1375 toys",
"2170 toys",
"2375 toys",
"2175 toys",
"5375 toys"
]
| To find the number of toys produced every day, we divide the total number of toys produced in one week (of 2 days) by 2.
4340 / 2 = 2170 toys
correct answer B
The answer is: B | B |
mathematics | Josh and Dan have a 12 apples each. Together they flip a coin 6 times. For every heads, Josh receives an apple from Dan, and for every tails Dan receives an apple from Josh. After the coin has been flipped 6 times, what is the probability that Josh has more than 12 apples but fewer than 18? | [
"1/64",
"15/64",
"21/64",
"21/32",
"5/6"
]
| minimum number of times to win is 4 to have more than 12 apples .
coz: if he wins 3 times => he gets 3 apples and give 3 apples ; no change
so he needs to win 4 times OR 5 times
Not 6 times because ,
if he wins 6 times => he gets 6 apples and he will have 18 apples
Now number of ways to win 4 times out of 6 times 6C4
Now number of ways to win 5 times out of 6 times 6C5
Total number of ways 2626 ways
Probability =(6C4) + (6C5)/2^6
=21/64
Answer :C
The answer is: C | C |
mathematics | Round trip time of 110 meters in a river is 16 min. the velocity of stream is 3m/min. what is the velocity of the person in the still water? | [
"6",
"7",
"8",
"9",
"10"
]
| let speed of boat be x.hence upstream=x-3 and downstream=x+3..so we have
55/x+3 + 55/x-3 = 16...solving we get x=8
ANSWER:C
The answer is: C | C |
mathematics | How many digits are in (8×10^12)(10×10^9)? | [
"20",
"23",
"26",
"27",
"28"
]
| The question simplfies to (8×10^12)(10^10)
=> 8*10^22
=> Will contain 22 zeros +1 digit 8
=>23
Ans B
The answer is: B | B |
mathematics | There is a group of persons each of whom can completea piece of work in 16 days, when they are working individually. On the 1st day 1 person works, on the second day another person joins him, on the third day one more person joins them & this process continues till the work is completed. How many days are needed to complete the work? | [
"5 1⁄2 days",
"5 1⁄3 days",
"5 1⁄6 days",
"6 1⁄6 days",
"7 1⁄6 days"
]
| Work completed in 1st day = 1/16
Work completed in 2nd day = (1/16) + (1/16) = 2/16
Work completed in 3rd day = (1/16) + (1/16) + (1/16) = 3/16
…
An easy way to attack such problems is from the choices. You can see the choices are
very close to each other. So just see one by one.
For instance, The first choice given in 3 1⁄4
The work done in 3 days = 1/16 + 2/16 + 3/16 = (1+2+3)/16 = 6/16
The work done in 4 days = (1+2+3+4)/16 = 10/16
The work done in 5 days = (1+2+3+4+5)/16 = 15/16, almost close, isn't it?
The work done in 6 days = (1+2+3+4+5+6)/16 > 1
Hence the answer is less than 6, but greater than 5. Hence the answer is 5 1⁄6 days.
(Just for your reference, work done in 5 days = 15/16.
Pending work in 6th day = 1 – 15/16 = 1/16.
In 6th day, 6 people are working and work done = 6/16.
To complete the work 1/16, time required = (1/16) / (6/16) = 1/6 days.
Hence total time required = 5 + 1/6 = 5 1⁄6 days
C
The answer is: C | C |
mathematics | In the quadrilateral PQRS d=7 cm, h1=4.2 cm and
h2=2.1 cm. Find the area | [
"21",
"22",
"23",
"24",
"25"
]
| area of quad.=1/2*any diagonal*(sum of 2 perpendiculars which is drawn on that diagona)
so 1/2*7*(4.2+2.1)=22.05
ANSWER:B
The answer is: B | B |
mathematics | Two trains 140m and 160m long run at the speed of 60kmph and 40kmph in opposite directions in parallel tracks. The time which they take to cross each other is? | [
"5.6sec",
"8.9sec",
"10.8sec",
"12.6sec",
"15sec"
]
| Relative speed = 60+40 = 100kmph * 5/18 = 250/9 m/s
Distance covered in crossing each other = 140+160 = 300m
Required time = 300*9/250 = 54/5 = 10.8sec
Answer is C
The answer is: C | C |
mathematics | A envelop weight 8.5 gm,if 880 of these envelop are sent with an advertisement mail. How much wieght? | [
"6.6kg",
"6.8kg",
"7.48kg",
"6.9kg",
"7.8kg"
]
| 880*8.5
7480.0gm
7.48kg
ANSWER:C
The answer is: C | C |
mathematics | In a city the doors of buildings where numbered from 1 to 100. How many 3’s are there as the door number? | [
"10",
"20",
"30",
"40",
"50"
]
| We will have the 3’s as follows 3,13,23,30,31,32,33,34,35,36,37,38,39,43,53,63,73,83,93.
In 33 we have 2 3’s. So we get 20 3’s from 1 to 100.
Note: for any numbers from 1 to 9 we’ll get 20 as answer.
Answer B
The answer is: B | B |
mathematics | A man can row upstream at 4km/hr and down stream at 10km/hr find mans rate in still water ? | [
"4km/hr",
"5km/hr",
"5.5km/hr",
"6km/hr",
"7km/hr"
]
| given upstream(u) =4km/hr
down stream (v)= 10km/hr rate in still water =1/2(u+v)=1/2(4+10)=7km/hr Answer is (E):7
The answer is: E | E |
mathematics | Salaries of Ravi and Sumit are in the ratio 2:3. If the salary of each is increased by Rs. 4000, the new ratio becomes 40:57. What is Sumit's salary? | [
"38000",
"46800",
"36700",
"50000",
"60000"
]
| Explanation:
Let the original salaries of Ravi and Sumit be Rs. 2x and Rs. 3x respectively.
Then,
(2x+4000) / (3x+4000) = 40 / 57
⇒ 57 × (2x + 4000) = 40 × (3x+4000)
⇒ 6x = 68,000
⇒ 3x = 34,000
Sumit's present salary = (3x + 4000) = Rs.(34000 + 4000) = Rs. 38,000
Answer: A
The answer is: A | A |
mathematics | The average weight of 16 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg. Find the average weights of all the boys in the class. | [
"48.0",
"48.55",
"49.05",
"49.0",
"45.0"
]
| Average weight of 16 boys = 50.25
Total weight of 16 boys = 50.25 × 16
Average weight of remaining 8 boys = 45.15
Total weight of remaining 8 boys = 45.15 × 8
Total weight of all boys in the class = (50.25 × 16)+ (45.15 × 8)
Total boys = 16 + 8 = 24
Average weight of all the boys = ((50.25×16)+(45.15×8))/24
=(50.25×2)+(45.15×1)/3
=(16.75×2)+15.05
=33.5+15.05=48.55
Answer is B.
The answer is: B | B |
mathematics | A certain debt will be paid in 52 installments from January 1 to December 31 of a certain year. Each of the first 8 payments is to be $410; each of the remaining payments is to be $65 more than each of the first 8 payments. What is the average (arithmetic mean) payment that will be made on the debt for the year? | [
"443",
"450",
"465",
"468",
"475"
]
| Total number of installments = 52
Payment per installment for the first 8 installments = 410
Payment per installment for the remaining 32 installments = 410+65=475
Average = (8*410 + 44*475)/52 = 465
Answer C
The answer is: C | C |
mathematics | Question: A sporting good store sells one type of baseball bat and one type of baseball. The cost for 2 bats and 4 balls is $180. The cost for 1 bat and 6 balls is $170, as well. If someone were to buy an equal number of bats and balls, at most how many bats can he purchase if he has a budget of $210 for the purchase?
Options: | [
"1",
"2",
"3",
"4",
"5"
]
| IMO it should be C that is C
reason:
formed an equation... bat = b ball = c
2b+4c=180
1b+6c=170
solving both we get b that is bat = 50 and c that is ball = 20
new equation 210 to be divided in equal
3b+3c=210
3*50 + 3*20 = 210
150+60= 210
The answer is: C | C |
mathematics | A policeman noticed a criminal from a distance of 265 km. The criminal starts running and the policeman chases him. The criminal and the policeman run at the rate of 8 km and 9 km per hour respectively. What is the distance between them after 3 minutes ? | [
"100 m",
"120 m",
"130 m",
"150 m",
"None of these"
]
| Explanation :
Solution: Relative speed = (9 - 8) = 1 km/hr.
Distance covered in 3 minutes = (1 * 3/60) km = 1/20 km = 50 m.
.'. Distance between the criminal and policeman = (265 - 50) m = 215 m.
Answer : E
The answer is: E | E |
mathematics | If 4a = 16b and 8b = 13c, Find a:b:c? | [
"52:13:8",
"13:7:52",
"7:13:52",
"7:13:54",
"None of these"
]
| Explanation:
(4a = 16b ==> a/b = 16/4)
and (8b = 13c ==> b/c = 13/8)
==> a:b = 16:4 and b:c = 13:8
a:b:c = 52:13:8
Answer: Option A
The answer is: A | A |
mathematics | What is the remainder when 1273 * 1275 * 1277 *1285 is divided by 12? | [
"9",
"1",
"11",
"0",
"7"
]
| 1271*1275*1277*1285 = (1272 + 1)(1272 + 3)(1284 - 7)(1284 + 1) = (multiple of 12 - 1)(multiple of 12 + 3)(multiple of 12 - 7)(multiple of 12 + 1)
Now, if we expand this expression all terms but the last one will have a multiple of 12 in them, thus will leave no remainder upon division by 12, the last term will be (1)(3)(-7)(1) = 21. Thus the question becomes: what is the remainder upon division of 21 by 12? The answer to this question is 9.
Answer: A
The answer is: A | A |
mathematics | If 50 honey bees make 50 grams of honey in 50 days, then 1 honey bee will make 1 gram of honey in how many days? | [
"1",
"3.5",
"20",
"49",
"50"
]
| Explanation :
Let the required number days be x.
Less honey bees, More days (Indirect Proportion)
Less honey, Less days (Direct Proportion)
Honey bees 1 : 50 :: 50 : x
Honey 50 : 1
=> 1 x 50 x x = 50 x 1 x 50
=> x = 50.
Answer : E
The answer is: E | E |
mathematics | Each of the integers from 1 to 9, inclusive, is written on a separate slip of blank paper and the ten slips are dropped into hat. If the slips are then drawn one at a time without replacement, how many must be drawn to ensure that the numbers on two of the slips drawn will have a sum of 10? | [
"3",
"4",
"5",
"6",
"7"
]
| Answer is 6. In the worst case, you could end up drawing 1,2,3,4,5. 7th draw will result in either of 6,7,8,9 which would result in the numbers adding to 10.
D
The answer is: D | D |
mathematics | Two ants, Arthur and Lily, have discovered a picnic and are bringing crumbs back to the anthill. Lily makes twice as many trips and carries one and a half times as many crumbs per trip as Arthur. If Arthur carries a total of a crumbs to the anthill, how many crumbs will Lily bring to the anthill, in terms of a? | [
"a/2",
"a",
"3a/2",
"2a",
"3a"
]
| Lets do it by picking up numbers. Let Arthur carry 2 crumbs per trip, this means Lily carries 3 crumbs per trip. Also let Arthur make 2 trips and so Lily makes 4 trips.
Thus total crumbs carried by Arthur (a) = 2 x 2 = 4, total crumbs carried by Lily = 3 x 4 = 12. 12 is 3 times 4, so E
The answer is: E | E |
mathematics | Four of the following five are alike in a certain way and hence form a group. Which one does not belong to the group? | [
"70",
"80",
"52",
"48",
"68"
]
| A
All the numbers are multiple of 4, except 70.
The answer is: A | A |
mathematics | A class is 6 meters 24 centimeters in length and 4 meters 32 centimeters in width. Find the least number of square tiles of equal size required to cover the entire floor of the class room ? | [
"115",
"117",
"116",
"114",
"113"
]
| Explanation:
Length = 6 m 24 cm = 624 cm
Width = 4 m 32 cm = 432 cm
HCF of 624 and 432 = 48
Number of square tiles required = (624 x 432)/(48 x 48) = 13 x 9 = 117.
ANSWER IS B
The answer is: B | B |
mathematics | How many words of 11letters could be Formed with all the vowels present only in the even places ,and the consonants only in the odd places,using letters of english alphabet each letter may appear only once. | [
"21!",
"26!/5!",
"21! /(5! * 5! )",
"21!* 5!/15!",
"21!* 6!/5!"
]
| (21*20*19*18*17*16)*5! = 21! * 5! / 15!
ANSWER:C
The answer is: C | C |
mathematics | The ratio of the volumes of two cubes is 729 : 1331. What is the ratio of their total surface areas? | [
"81 : 121",
"81 : 128",
"81 : 120",
"81 : 125",
"81 : 122"
]
| Ratio of the sides = 3√729 : 3√1331 = 9 : 11
Ratio of surface areas = 92 : 112 = 81 : 121
Answer: A
The answer is: A | A |
mathematics | The ratio of buses to cars on River Road is 1 to 17. If there are 80 fewer buses than cars on River Road, how many cars are on River Road? | [
"40",
"85",
"60",
"30",
"20"
]
| B/C=1/17
C-B=80.........> B=C-80
(C-80)/C=1/17
Testing answers. Clearly Eliminate ACDE
Put C=85.........> (85-80)/85=5/85=1/17
Answer: B
The answer is: B | B |
mathematics | The average age of a class of 22 students is 21 years. The average increased by 1 when the teacher's age also included. What is the age of the teacher? | [
"44",
"48",
"45",
"43",
"50"
]
| Total age = 22 * 21
tot age of all stu + age of the teacher = 23*22
age of the teacher = 23*22-22*21 = 44
ANSWER A
The answer is: A | A |
mathematics | John makes $60 a week from his job. He earns a raise and now makes $80 a week. What is the % increase? | [
"16%",
"16.66%",
"18%",
"21%",
"33.33%"
]
| Increase = (20/60)*100 = 33.33%.
E
The answer is: E | E |
mathematics | Selling an kite for Rs. 30, a shop keeper gains 30%. During a clearance sale, the shopkeeper allows a discount of 10% on the marked price. His gain percent during the sale is? | [
"8%",
"10%",
"11%",
"17%",
"20%"
]
| Explanation:
Marked price = Rs. 30
C.P. = 100/130 * 30 = Rs. 23.07
Sale price = 90% of Rs. 30 = Rs. 27
Required gain % = 3.92/23.07 * 100 = 17%.
Answer: D
The answer is: D | D |
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