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mathematics | The price of a T.V. set worth Rs. 40000 is to be paid in 20 installments of Rs. 1000 each. If the rate of interest be 6% per annum, and the first installment be paid at the time of purchase, then the value of the last installment covering the interest as well will be? | [
"22678",
"26699",
"26788",
"19000",
"39000"
]
| Money paid in cash = Rs. 1000
Balance payment = (40000 - 1000) = Rs. 39000
Answer: E
The answer is: E | E |
mathematics | The parameter of a square is equal to the perimeter of a rectangle of length 16 cm and breadth 14 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places)? | [
"23.58",
"23.56",
"23.54",
"23.57",
"23.51"
]
| Let the side of the square be a cm.
Parameter of the rectangle = 2(16 + 14) = 60 cm Parameter of the square = 60 cm
i.e. 4a = 60
A = 15
Diameter of the semicircle = 15 cm
Circimference of the semicircle
= 1/2(β)(15)
= 1/2(22/7)(15) = 330/14 = 23.57 cm to two decimal places
Answer:D
The answer is: D | D |
mathematics | A certain car averages 25 miles per gallon of gasoline when driven in the city and 45 miles per gallon when driving on the highway. According to these rates, which of the following is closest to the number of miles per gallon that the car averages when it is driven 10 miles in the city and then 50 miles on the highway? | [
"28",
"30",
"33",
"36",
"40"
]
| 10*1/25 gpm+50*1/45 gpm=1.6=1.5 total gallons
60 total miles/1.5 total gallons=40 average mpg
E. 40
The answer is: E | E |
mathematics | A car covers a distance of 624 km in 6 Β½ hours. Find its speed? | [
"104 kmph",
"187 kmph",
"164 kmph",
"175 kmph",
"106 kmph"
]
| 624/6
= 104 kmph
Answer: A
The answer is: A | A |
mathematics | If x is an integer and 2.134 Γ 10^x is less than 21000, what is the greatest possible value for x? | [
"7",
"6",
"5",
"4",
"3"
]
| If x=4
2.134 Γ 10^4 = 21340 > 21000
So, x = 3
Answer : E
The answer is: E | E |
mathematics | To mail a package, the rate is 20 cents for the first pound and 5 cents for each additional pound. Two packages weighing 5 pounds and 10 pounds, respectively can be mailed seperately or combined as one package. Which method is cheaper and how much money is saved? | [
"Combined, with a saving of 10 cents",
"Separately, with a saving of 10 cents",
"Combined, with a saving of 15 cents",
"Separately, with a saving of 15 cents",
"Combined, with a saving of 5 cents"
]
| 5 pounds = 1*20+4*5 = 40
10 pounds = 1*20+9*5 =65
total = 105
15 pound = 1*20+14*5 = 90
dif. 15
Answer : C
The answer is: C | C |
mathematics | |9 - 4| - |12 - 14| = ? | [
"3",
"2",
"1",
"0",
"4"
]
| |9 - 4| - |12 - 14| = | 5 | - | -2 | = 5 - 2 = 3
correct answer A
The answer is: A | A |
mathematics | Evaluate :
28% of 400 + 45 % of 250 | [
"220.3",
"224.5",
"190.3",
"150",
"None of these"
]
| Explanation:
28% of 400 + 45 % of 250
= (28/100 *400 + 45/100 * 250)
= (112 + 112.5)
= 224.5
ANSWER B
The answer is: B | B |
mathematics | Meg and Bob are among the 4 participants in a cycling race. If each participant finishes the race and no two participants finish at the same time, in how many different possible orders can the participants finish the race so that Meg finishes ahead of Bob? | [
"24",
"30",
"12",
"90",
"120"
]
| Total # of ways the race can be finished is 4!. In half of the cases Meg finishes ahead of Bob and in other half Bob finishes ahead of Meg. So, ways Meg to finish ahead of Bob is 4!/2=12.
Answer: C.
The answer is: C | C |
mathematics | A batsman scored 120 runs whichincluded 3 boundaries and 8sixes. What % of his total score did he make by running between the wickets | [
"40%",
"50%",
"65%",
"70%",
"75%"
]
| Number of runs made by running = 110 - (3 x 4 + 8 x 6)
= 120 - (60)
= 60
Now, we need to calculate 60 is what percent of 120.
=> 60/120 * 100 = 50 %
B
The answer is: B | B |
mathematics | The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot @Rs.26.50 per metre is Rs.5300, what is the length of the plot in metres? | [
"55",
"60",
"65",
"70",
"75"
]
| Length of the fence =530026.50=200 m
β 2(length + breadth)=200 m
β 2(breadth + 20 + breadth)=200 m (β΅ length = breadth+20)
β breadth + 20 + breadth =100 m
β breadth =40 m
length =40+20=60 m
Answer is B.
The answer is: B | B |
mathematics | A person covered one-fourth of the total distance at 26 kmph and remaining distance at 24 kmph. What is the average speed for the total distance? | [
"27 (1/3)kmph",
"21 (1/3)kmph",
"21 (1/7)kmph",
"26 (1/3)kmph",
"31 (1/3)kmph"
]
| Let the total distance be x km
total time taken = (x/4)/16 + (3x/4)/24 = x/64 + x/32 = 3x/64
Average speed = x/(3x/64) = 64/3kmph = 21 (1/3)kmph.
Answer:B
The answer is: B | B |
mathematics | An empty wooden vessel weighs 20% of its total weight when filled with paint. If the weight of a partially filled vessel is one half that of a completely filled vessel, what fraction of the vessel is filled. | [
"3/5",
"5/9",
"1/24",
"9/19",
"2/5"
]
| An empty wooden vessel weighs 20% of its total weight when filled with paint:
Vessel = 0.2(Vessel + Paint);
20V = V + P (so the weight of completely filled vessel is 10V)
P = 19V (so the weight of the paint when the vessels is completely filled is 19V).
The weight of a partially filled vessel is one half that of a completely filled vessel:
V + P' = 1/2*20V;
P' = 9V (so the weight of the paint when the vessels is partially filled is 9V).
What fraction of the vessel is filled?
So, we need to find the ratio of the weight of the paint when the vessel iscompletely filledto the weight of the paint when the vessel ispartially filled:
P'/P = 9V/19V = 9/19.
Answer: D.
The answer is: D | D |
mathematics | Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30Β° and 45Β° respectively. If the lighthouse is 100 m high, the distance between the two ships is: | [
"173 m",
"200 m",
"273 m",
"300 m",
"373 m"
]
| Let AB be the lighthouse and C and D be the positions of the ships.
Then, AB = 100 m, ACB = 30Β° and ADB = 45Β°.
AB = tan 30Β° = 1 AC = AB x 3 = 1003 m.
AC 3
AB = tan 45Β° = 1 AD = AB = 100 m.
AD
CD = (AC + AD) = (1003 + 100) m
= 100(3 + 1)
= (100 x 2.73) m
= 273 m.
Answer = C
The answer is: C | C |
mathematics | If S is the sum of the reciprocals of the consecutive integers from 81 to 90, inclusive, which of the following is less than S?
I. 1/8
II. 1/9
III. 1/10
IV. 1/5
V. 1/8>S >1/9 | [
"V",
"I",
"II",
"III",
"IV"
]
| Since we summarize the reciprocals from 90 to 81, we can say also that we add ten numbers who are all (with one exception 1/90) greater than 1/90, so that the sum must be greater than 1/9.
On the other side we can say that we add the reciprocals from 91 to 100, so that the sum has to be less than the sum of ten times 1/91.
sum has to be greater than 1/9 and less than 1/8
A
The answer is: A | A |
mathematics | 2 + 2^2 + 2^3 + ... + 2^8 = ? | [
"510",
"310",
"210",
"410",
"None of them"
]
| Given series is a G.P. with a = 2, r = 2 and n = 8.
sum = a(r^n-1)/(r-1) = 2 x (2^8 β1)/(2-1)= (2 x 255) =510
Answer is A.
The answer is: A | A |
mathematics | A certain sum is invested at simple interest at 18% p.a. for two years instead of investing at 12% p.a. for the same time period. Therefore the interest received is more by Rs. 300. Find the sum? | [
"7000",
"2500",
"2778",
"2800",
"2791"
]
| Let the sum be Rs. x.
(x * 18 * 2)/100 - (x * 12 * 2)/100 = 300 => 36x/100 - 24x/100 =300
=> 12x/100 = 300 => x = 2500.Answer:B
The answer is: B | B |
mathematics | If Q is a negative integer, which of the following must be a negative integer? | [
"Q + 1",
"Q/2+3",
"Q^4",
"Q β y",
"Q^11"
]
| We need to check each option here:
A. Q + 1
This will depend on the value of Q. Nothing can be said
B. Q/2+3
This will depend on the value of Q. Nothing can be said
C. Q^4
This will always be positive. Even powers of negative numbers are positive and odd powers are negative
D. Q β y
This will depend on the value of Q. Nothing can be said
E. Q^11
This will always be negative. Even powers of negative numbers are positive and odd powers are negative
Correct Option: E
The answer is: E | E |
mathematics | For a certain set, the value range of its members is 108.4. A new set is created from the members of the old set as follows: 12 is subtracted from a member of the old set, and the result is divided by 4. The resulting value is a member of the new set. If this operation is done for each member of the old set, what is the range of values of the members of the new set? | [
"24.1",
"27.1",
"54.4",
"98.4",
"108.4"
]
| Let x and z be the smallest and largest of the original set, respectively.
z - x = 108.4
The smallest and largest members of the new set will be (x-12) / 4 and (z-12) / 4.
Then the range is (z-12) / 4 - (x-12) / 4 = (z-x) / 4 = 108.4 / 4 = 27.1
The answer is B.
The answer is: B | B |
mathematics | By selling 8 pencils for a rupee a man loses 60%. How many for a rupee should he sell in order to gain 60%? | [
"8",
"9",
"2",
"6",
"4"
]
| 40% --- 8
160% --- ?
40/160 * 12 = 2
Answer: C
The answer is: C | C |
mathematics | The area of a circular field is 17.56 hectares. Find the cost of fencing it at the rate of Rs. 5 per metre approximately | [
"4457",
"4567",
"4235",
"4547",
"7429"
]
| Explanation:
Area = (17.56 x 10000) m2= 175600 m2.
Ξ R2 = 175600 β (R)2 = (175600 x (7/22)) β R = 236.37 m.
Circumference = 2Ξ R = (2 x (22/7) x 236.37) m =1485.78 m.
Cost of fencing = Rs. (1485.78 x 5) = Rs. 7429.
Answer: Option E
The answer is: E | E |
mathematics | A certain telescope increases the visual range at a particular location from 50 kilometers to 150 kilometers. By what percent is the visual range increased by using the telescope ? | [
"30%",
"33 1/2%",
"40%",
"60%",
"200%"
]
| Original visual range = 50 km
New visual range = 150 km
Percent increase in the visual range by using the telescope
= (150-50)/50 * 100%
= 2 * 100%
= 200 %
Answer E
The answer is: E | E |
mathematics | A box has 12 shapes; 3 circles, 5 squares, and 4 triangles. How many groups of 3 shapes can be made with at least 1 triangle? | [
"46",
"64",
"164",
"146",
"56"
]
| The problem asks for a combination, since order doesn't matter. Now, selecting r items from a set of n gives the Combination Formula: nCr= n!/r!(n-r)!
n = 12
r = 3
So, total groups is 12C3 = 12!/(3!(12 - 3)!) = 220, and
n = 12 - 4 = 8
r = 3
for groups without a triangle is 8C3 = 8!/(3!(8 - 3)!) = 56,
so, groups with at least 1 triangle = 220 - 56 = 164
Answer: C
The answer is: C | C |
mathematics | There are two examinations rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is: | [
"20",
"80",
"100",
"200",
"None"
]
| EXPLANATION
Let the number of students in rooms A and B be x and y respectively.
Then, x β 10 = y + 10 x β y = 20 β¦. (i)
and x + 20 = 2(y β 20) x β 2y = -60 β¦. (ii)
Solving (i) and (ii) we get: x = 100 , y = 80.
The required answer A = 100.
Answer C
The answer is: C | C |
mathematics | In an election between two candidates, the winner has a margin of 10% of the votes polled. If 4000 people change their mind and vote for the loser, the loser would have won by a margin of 10% of the votes polled. Find the total number of votes polled in the election? | [
"16000",
"10000",
"40000",
"12000",
"5000"
]
| Winner - Looser
55% - 45%
If 4000 people change their mind and vote for the loser:
Winner - Looser
45% - 55%
Thus 4,000 people compose 25% of all voters, which means that the total number of votes is
40,000
Answer: C
The answer is: C | C |
mathematics | A boat goes 100 km downstream in 10 hours, and 75 m upstream in 15 hours. The speed of the stream is? | [
"22 1/7",
"22 1/4",
"22 1/2",
"22 1/1",
"22 1/3"
]
| 100 --- 10 DS = 10
? ---- 1
75 ---- 15 US = 5
? ----- 1 S = (10 - 5)/2
= 22 1/2 kmp Answer: C
The answer is: C | C |
mathematics | which of the following inequalities indicates the set of all values of d for which the lengths R of the three sides of a triangle can be 3,4, and d? | [
"0<d<1",
"0<d<5",
"0<d<7",
"1<d<5",
"1<d<7"
]
| This question is a good way to apply one of the most basic relation between the 3 sides of a triangle. In a triangle (ANY TRIANGLE), any side MUST be greater than the positive difference of the other two sides and less than than the sum of the other 2 sides. Let the sides of a triangle be a,b,c .
Thus,
|a-b| < c < a+b
|b-c| < a < b+c
|c-a| < b < a+c
Thus, if the sides of the triangle are 3,4 and d,
4-3<d<4+3 ---> 1<d<7. Thus E is the correct answer.
The answer is: E | E |
mathematics | Listed below are the mean temperatures measured in the Tokharian desert in a certain month. What is the median temperature E in that particular month?
Mean Temp (CΒ°) No. of days
29 --------------------> 5
30 --------------------> 11
31 --------------------> 8
32 --------------------> 6 | [
"29",
"30",
"30.5",
"31",
"32"
]
| to find out median===>they must be arranged in ascending order.
29 29 29...(5 times)30 30 30 30.....(11 times)31 31 31.....(8 times)32 32 32 .....(6 times)
total days=5+11+8+6=30
therefore 30 numbers ...median E will be==>mean of 15 and 16 th place temperature===>(30+30)/2=30
hence B
The answer is: B | B |
mathematics | A and B began business with Rs.7000 and Rs.15000 after 6 months, A advances Rs.3000 and B withdraws Rs.5000. At the end of the year, their profits amounted to Rs.2940 find the share of A and B respectively. | [
"1100, 1750",
"1140, 1800",
"940, 2000",
"1190, 1750",
"1000: 1690"
]
| 7*6 + 10*6):(15*6 + 10*6) =102 : 150 = 51 : 75 = 17 : 25
17 : 25
A's Share = 17/42 * 2940 = 1190.
B's Share = 25/42 * 2940 = 1750.
A and B shares respectively 1190 and 1750 . Answer: D
The answer is: D | D |
mathematics | A person earns 15% on investment but loses 10% on another investment. If the ratio of the two investments be 3:5, what is the gain or loss on the two investments taken together? | [
"0.63 %",
"0.64 %",
"0.65 %",
"0.66 %",
"None"
]
| Sol.
Suppose he invested 300 & 500 respectively profit : 15% of 300 = 45 loss =
500 *10 = 50 net loss = - 5 5/800 *100 = 0.63 %
Answer A
The answer is: A | A |
mathematics | N and M are each 3-digit integers. Each of the numbers 1, 2, 3,4,5 and 6 is a digit of either N or M. What is the smallest possible positive difference between N and M? | [
"59",
"49",
"58",
"113",
"131"
]
| You have 6 digits: 1,2, 3, 4, 5, 6
Each digit needs to be used to make two 3 digit numbers. This means that we will use each of the digits only once and in only one of the numbers. The numbers need to be as close to each other as possible. The numbers cannot be equal so the greater number needs to be as small as possible and the smaller number needs to be as large as possible to be close to each other.
The first digit (hundreds digit) of both numbers should be consecutive integers
Now let's think about the next digit (the tens digit). To minimize the difference between the numbers, the tens digit of the greater number should be as small as possible and the tens digit of the smaller number should be as large as possible . So let's not use 1 and 6 in the hundreds places and reserve them for the tens places Now what are the options?
Try and make a pair with (2** and 3**). Make the 2** number as large as possible and make the 3** number as small as possible.
265 and 314 (difference is 49) or
Try and make a pair with (4** and 5**). Make the 4** number as large as possible and make the 5** number as small as possible. We get 463 and 512 (difference is 49)
B
The answer is: B | B |
mathematics | The ratio of the length and the breadth of a rectangle is 4 : 3 and the area of the rectangle is 6912 sq cm. Find the ratio of the breadth and the area of the rectangle? | [
"1 : 96",
"1 : 97",
"1 : 98",
"1 : 99",
"1 : 93"
]
| Let the length and the breadth of the rectangle be 4x cm and 3x respectively.
(4x)(3x) = 6912
12x2 = 6912
x2 = 576 = 4 * 144 = 22 * 122 (x > 0)
=> x = 2 * 12 = 24
Ratio of the breadth and the areas = 3x : 12x2 = 1 : 4x = 1: 96.
Answer: Option A
The answer is: A | A |
mathematics | On a baseball team, 4 players including Alice want to play 1st base, 2nd base, or 3rd base. Before every game, the coach chooses a name randomly from a bag and this person plays 1st base. Then the coach chooses the next name randomly and this person plays 2nd base. The coach then chooses a third name randomly and this person plays 3rd base. What is the probability that Alice plays 1st, 2nd, or 3rd base? | [
"3/4",
"5/6",
"7/8",
"9/16",
"11/16"
]
| The total number of ways to choose three players is 4C3=4.
Excluding Alice, the number of ways to choose three players is 3C3=1.
P(Alice is not chosen)=1/4.
P(Alice is chosen)=1 - 1/4 = 3/4.
The answer is A.
The answer is: A | A |
mathematics | Use distributive property to solve the problem below:
Maria bought 15 notebooks and 6 pens costing 2 dollars each.How much did Maria pay? | [
"30 dollars",
"40 dollars",
"50 dollars",
"42 dollars",
"70 dollars"
]
| Solution
2 Γ (15 + 6) = 2 Γ 15 + 2 Γ 6 = 30 + 12 = 42 dollars
Answer D
The answer is: D | D |
mathematics | If log1087.5 = 2.9421, then the number of digits in (875)10 is? | [
"30",
"28",
"27",
"26",
"40"
]
| X = (875)10 = (87.5 x 10)10
Therefore, log10X = 10(log2087.5 + 1)
= 10(2.9421 + 1)
= 10(3.9421) = 39.421
X = antilog(39.421)
Therefore, number of digits in X = 40.
ANSWER:E
The answer is: E | E |
mathematics | Rice weighing 25/4 pounds was divided equally and placed in 4 containers. How many ounces of rice were in each container? (Note that 1 pound = 16 ounces) | [
"22",
"25",
"28",
"31",
"34"
]
| 25/4 Γ· 4 = 25/16 pounds in each container
25/16 pounds * 16 ounces / pound = 25 ounces in each container
The answer is B.
The answer is: B | B |
mathematics | There was two trains from calcutta to kanyakumari one train is fast service travels with a speed 75km per hour another travels with a speed of 44km per hour the time taken to reach from calcutta to kanyakumari is 4hours less than the first train...find the distance b/w calcatta to kanyakumari | [
"415.8 km",
"425.8 km",
"435.8 km",
"445.8 km",
"455.8 km"
]
| let distance b/w calcutta to kanyakumari is = x km
then eqn is
x/44 - x/75 = 4
=> x*(75-44)=4*75*44
=> x = 425.8 km
ANSWER:B
The answer is: B | B |
mathematics | A began business with 12500 and is joined afterwards by B with 25000. When did B join, if the profits at the end of the year are divided equally? | [
"8 months",
"9 months",
"6 months",
"5 months",
"None of these"
]
| Let B join after x months of the start of the business so that Bβs money is invested for (12 β x) months.
β΄ Profit ratio is 12 Γ 12500 : (12 β x) Γ 25000
or 12 : 2(12 β x)
Since profit is equally divided so
12 = 2(12 β x) or x = 6. Thus B joined after 8 months.
Answer C
The answer is: C | C |
mathematics | The ratio of two quantities is 2 to 5. If each of the quantities is increased by 7, what is the ratio of these two new quantities? | [
"2/5",
"5/8",
"7/13",
"22/25",
"It cannot be determined from the information given."
]
| Correct Answer: E
Let x and y be the two quantities such that x/y = 2/5. There is no algebraic operation that can be used to increase x and y each by 3 and determine what happens to the ratio 2/5.
For example, if x = 2 and y = 5, then (x+7)/(y+7) = (2+7)/(5+7) = 9/12 =3/4. However, if x = 4 and y = 10 (which would still set x/y = 2/5), then (x+3)/(y+3) = (4+7)/(10+7) = 11/17. The ratio of the two new quantities cannot be uniquely determined from the information given, and the correct answer is (E).
The answer is: E | E |
mathematics | Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. If the faster train passes the slower train in 36 seconds,what is the length of each train? | [
"50 m",
"80 m",
"76 m",
"58 m",
"90 m"
]
| let length of each train = x m
total distance while passing the slower train = (x+x) = 2x m
relative speed = (46-36) = 10 km/hr
=10*5/18 = 50/18 m/s
time = 36 sec
2x/36 = 50/18 => x=50
ANSWER A
The answer is: A | A |
mathematics | In Kaya's teacher's desk there are 4 pink highlighters, 2 yellow highlighters, and 5 blue highlighters. How many highlighters are there in all? | [
"11",
"22",
"77",
"33",
"88"
]
| Add the numbers of highlighters.
4 + 2 + 5 =11.
Answer is A.
The answer is: A | A |
mathematics | What no. should be subtracted from x^3+4x^2β7x+12x^3+4x^2β7x+12, if it is to be perfectly divisible by x+3x+3? | [
"40",
"42",
"44",
"48",
"52"
]
| According to remainder theorem when dfracf(x)x+adfracf(x)x+a, then the remainder is f(βa)f(βa).
In this case, as x+3x+3 divides x3+4x2β7x+12βkx3+4x2β7x+12βk perfectly (kk being the number to be subtracted), the remainder is 0 when the value of xx is substituted by -3.
i.e., (β3)3+4(β3)2β7(β3)+12βk=0(β3)3+4(β3)2β7(β3)+12βk=0
or β27+36+21+12=kβ27+36+21+12=k
or k=k= 42
B
The answer is: B | B |
mathematics | Eighteen years ago, a father was three times as old as his son. Now the father is only twice as old his son. Then the sum of the present ages of the son and the father is: | [
"54",
"72",
"105",
"108",
"51"
]
| Answer: Option D
Let the present ages of the father and son be 2x and x years respectively.
Then, (2x - 18) = 3(x - 18) => x = 36
Required sum = (2x + x) = 108 years.
The answer is: D | D |
mathematics | At a meeting of 5 Chiefs of Staff, the Chief of Naval Operations does not want to sit next to the Chief of the National Guard Bureau. How many ways can the Chiefs of Staff be seated around a circular table? | [
"9",
"12",
"15",
"18",
"21"
]
| 5 people can be arranged around a table in 4! ways.
Consider the two chiefs who will not sit together as a single unit.
The number of ways to arrange 4 units around a table is 3!
We need to multiply this by 2 as the two people can be switched in each arrangement.
The total number of ways to arrange the chiefs is 4! - 2*3! = 2*3! = 12
The answer is B.
The answer is: B | B |
mathematics | What is the HCF of 2/3, 4/9 and 6/18 | [
"7/45",
"2/45",
"1/9",
"8/45",
"9/45"
]
| Explanation:
HCF of Fractions = HCF of Numerators/LCM of Denominators
= (HCF of 2, 4, 6)/(LCM of 3, 9, 18) = 2/18 = 1/9
Answer: Option C
The answer is: C | C |
mathematics | How many 7-letter words can be formed using the letters of the English alphabet that contain 3 different vowels and 4 different consonants? | [
"5!*5c2 *21c2",
"4!*5c2 *21c2",
"4!*5c3 *21c2",
"6!*5c3 *21c2",
"7!*5c3 *21c4"
]
| combination for 3 vowels out of 5 = 5c3 ways
combination for 4 consonants of 21 = 21c4 ways
Additionally the arrangement can be = 7!
total arrangements =7!*5c3 *21c4
E
The answer is: E | E |
mathematics | The price of a certain product increased by the same percent from 1960 to 1970 as from 1970 to 1980. If its price of $1.60 in 1970 was 150 percent of its price in 1960, what was its price in 1980? | [
"a) $ 1.80",
"b) $ 2.00",
"c) $ 2.40",
"d) $ 2.70",
"e) $ 3.00"
]
| The price in 1970 was 150 percent of its price in 1960, means that the percent increase was 50% from 1960 to 1970 (and from 1970 to 1980).
Therefore the price in 1980 = $1.6*1.5 = $2.4.
Answer: C.
The answer is: C | C |
mathematics | A parking space have 10 different slots. 10 cars has to arrange in 8 slots. But there are exactly 4 cars between 6 specified cars. In how many ways cars can be arranged? | [
"17280",
"65000",
"1500",
"1640",
"1440"
]
| we arranged 2 specified cars in 4 slots = 4!
remaining 6 cars in 6 slots = 6!
number of ways = 4!*6! = 17280
correct option is A
The answer is: A | A |
mathematics | A train covers a distance of 11 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is? | [
"m",
"m",
"m",
"m",
"m"
]
| Speed = (11/10 * 60) km/hr
= (66 * 5/18) m/sec = 55/3 m/sec.
Length of the train = 55/3 * 6
= 110 m.
Answer:C
The answer is: C | C |
mathematics | A train of length 560 metres takes 90 seconds to cross a tunnel of length 340 metres. What is the speed of the train in km/hr? | [
"36 km/hr.",
"46 km/hr.",
"30 km/hr.",
"48 km/hr.",
"None"
]
| Sol.
Speed = [560+340 / 90] m/sec = [900 / 90 * 18/5] km/hr = 36km/hr.
Answer A
The answer is: A | A |
mathematics | A person borrows Rs. 5000 for 2 years at 4% p.a. simple interest. He immediately lends it to another person at 6 p.a for 2 years. Find his gain in the transaction per year. | [
"100 rs",
"150 rs",
"160 rs",
"180 rs",
"200 rs"
]
| Gain in 2 years =
[(5000*6*2)/100]-[(5000*4*2)/100]
600-400=200
Gain in 1 year =(200/2)=100 rs
ANSWER:A
The answer is: A | A |
mathematics | 3889 + 12.952 - ? = 3854.002 | [
"47.95",
"49.75",
"45.97",
"47.59",
"45.79"
]
| Let 3889 + 12.952 - x = 3854.002.
Then x = (3889 + 12.952) - 3854.002
= 3901.952 - 3854.002
= 47.95.
Answer is A
The answer is: A | A |
mathematics | A person is 24 years older than his daughter. In 2 years, the personβs age will be 2 times the age of his daughter. Then, the current age of the daughter is: | [
"22",
"42",
"32",
"41",
"56"
]
| Let the daughterβs current age be A years. Then, the personβs current age = (A +24) years.
(A + 24) + 2 = 2 (A + 2)
A + 26 = 2A + 4
A = 22
The answer is: A | A |
mathematics | Reena took a loan of 1000 with simple interest for as many years as the rate of interest. If she paid 40 as interest at the end of the loan period, what was the rate of interest? | [
"3.8",
"2",
"6",
"Cannot be determined",
"None"
]
| Explanation: Let rate = R% and time = R years.
Then, (1000 x R x R)/100 = 40
10RΓΒ² = 40
RΓΒ² = 4
R = 2.
Answer: Option B
The answer is: B | B |
mathematics | Given the following factorials (x+3)!, (x-2)!, and (x+4)! what is the value of x if the greatest common divisor is 720? | [
"8",
"9",
"7",
"6",
"10"
]
| GCD of (x+3)!, (x-2)!, and (x+4)! is 720. Find x.
Best way to find n is substitute each of the answer and find out the correct one.
I started with A.
Try 8 and find GCD or 11!, 6! and 12!. 6! itself is 720 and 6! which is contained in the other two factorials. This satisfies the condition, hence answer is 7. Also, we can eliminate all other answers as they are less than 7 and n-2 turns out to be less than 5! and hence cannot have a divisor of 120.
Answer is A.
The answer is: A | A |
mathematics | A train 125 m long passes a man, running at 7 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is? | [
"52 km/hr",
"17 km/hr",
"76 km/hr",
"50 km/hr",
"15 km/hr"
]
| Speed of the train relative to man = 125/10 = 25/2 m/sec.
= 25/2 * 18/5 = 45 km/hr
Let the speed of the train be x km/hr. Then, relative speed = (x - 7) km/hr.
x - 7 = 45 => x = 52 km/hr.
Answer: A
The answer is: A | A |
mathematics | P and Q invested in a business. They earned some profit which they divided in the ratio of 2:3. If P invested Rs.50, 000, the amount invested by Q is: | [
"Rs. 65,000",
"Rs. 70,000",
"Rs. 75,000",
"Rs. 90,000",
"Rs. 60,000"
]
| Q invested = 50000/2*3 = 75000
Answer : C
The answer is: C | C |
mathematics | Two trains start from A & B and travel towards each other at
speed of 50kmph and 60kmph resp. At the time of the meeting the
second train has traveled 100km more than the first.the distance
between them. | [
"800 km",
"900 km",
"1000 km",
"1100 km",
"1200 km"
]
| Let the distance traveled by the first train be x km
then distance covered by the second train is x + 100km
x/50 = x+100 / 60
x= 500
so the distance between A & B is x + x + 100 = 1100 km
Answer is D.
The answer is: D | D |
mathematics | 16 meters of wire is available to fence off a flower bed in the form of a circular sector. What must the radius of the circle in meters be, if we wish to have a flower bed with the greatest possible surface area? | [
"2β2",
"4",
"5",
"4β2",
"none of these"
]
| Area of Sector, A = x/360*pi*r^2
Circumference of the sector = 16
=> x/360*2*pi*r +2r= 16
=> 2A/r+2r=16
=> A=(r16- 2r^2)/2
= r8-r^2
We will now max using derivations
Max value of A will found at A=0
i.e 8-2r=0
r=4
B
The answer is: B | B |
mathematics | If (5^13)(9^7)=3(15^x), what is the value of x? | [
"7",
"9",
"11",
"13",
"15"
]
| (5^13)(9^7)=3(15^x)
=> 5^13 * 3^14 = 3 * 3^x * 5^x
=> 5^13 * 3^14 = 3^(x+1) * 5^x
Value of x = 13
Answer D
The answer is: D | D |
mathematics | If 1/2 of a pencil is blue, 1/8 of the remaining is red and the remaining 3/8 is white, what is the total length of the pencil? | [
"5",
"3",
"1",
"4",
"2"
]
| Blue is 1/2 but can also be written as 4/8
Red is 1/8
White is 3/8
4/8+1/8+3/8= 8/8=1
Answer is C) 1
The answer is: C | C |
mathematics | In what time will a train 320 m long cross an electric pole, it its speed be 144 km/hr? | [
"2.5 sec",
"8.0 sec",
"3.5 sec",
"2.9 sec",
"9.5 sec"
]
| Speed = 144 * 5/18 = 40 m/sec
Time taken = 320/40
= 8.0 sec.
Answer: B
The answer is: B | B |
mathematics | The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 400 resolutions? | [
"563.2 m",
"704 m",
"287 m",
"278 m",
"927 m"
]
| In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 400 resolutions.
= 400 * 2 * 22/7 * 22.4 = 56320 cm
= 563.2 m
Answer:A
The answer is: A | A |
mathematics | Consider the sets Tn = {n, n + 1, n + 2, n + 3, n + 4}, where n = 1, 2, 3,...., 120. How many of these sets contain 6 or any integral multiple thereof (i.e., any one of the numbers 6, 12, 18, ...)? | [
"(a)100",
"(b) 81",
"(c) 82",
"(d) 83",
"(e) 84"
]
| T1: 1,2,3,4,5
T2: 2,3,4,5,6
T3: 3,4,5,6,7
etc.
means that every multiple of 6 will be involved in 5 sets. We have (120-6)/6+1=20 such multiples.
So, final number of sets is 20*5=100
Answer: A
The answer is: A | A |
mathematics | 20 men can dig a tunnel in 30 days. If after 10 days, 20 more men are deployed to dig the tunnel, how many more days it will take to dig the whole tunnel? | [
"10",
"15",
"20",
"25",
"30"
]
| A
Remaining work can be completed by 20 men in 30-10 = 20 days.
If 20 men can do X work in 20 days, and let us say 40 men take N days to do the same work.
Now, more men, less number of days (inversely proportion)
20 : 40 :: N : 20
N = 20 X 20 / 40 = 10 days.
The answer is: A | A |
mathematics | A dishonest milkman professes to sell his milk at cost price but he mixes it with water and thereby gains 25%. The percentage of water in the mixture is: | [
"4%",
"61/4%",
"20%",
"25%",
"30%"
]
| Let C.P. of 1 litre milk be Re. 1
Then, S.P. of 1 litre of mixture = Re. 1, Gain = 25%.
CP of 1 lr = 100/125*1 = 4/5
Ratio of milk to water = 4/5:1/5 = 4:1
=20%
ANSWER C
The answer is: C | C |
mathematics | Abby and Bobby type at constant rates of 80 words per minute and 60 words per minute, respectively. Bobby begins typing before Abby and has typed 600 words when Abby begins typing at 1:30 pm. If they continue typing at their respective rates, at what time will Abby have typed exactly 400 more words than Bobby? | [
"1:40 PM",
"1:50 PM",
"2:00 PM",
"2:10 PM",
"2:20 PM"
]
| Say time needed for Abby to type 200 more words than Bobby is t. In that time she would type 80t words and Bobby would type 60t words.
Now, total words typed by Bobby would be 600+60t and we want that number to be 200 less than 80t: 600+60t=80t-400 --> t=50.
1:30 PM + 50 minutes = 2:20 PM.
Answer: E.
The answer is: E | E |
mathematics | What is the total cost of 2 sandwiches at $2.49 each and 4 sodas at $1.87 each? | [
"$3.36",
"$6.85",
"$8.46",
"$10.08",
"$12.46"
]
| Answer = E
2 * 2.49 + 4 * 1.87
= 2 (2.50 - 0.01) + 4 (2.00 - 0.13)
= 5 + 8 - 0.02 - 0.52
= 13 - 0.54
= 12.46
The answer is: E | E |
mathematics | If six machines working at the same rate can do 3/4 of a job in 30 minutes, how many minutes would it take two machines working at the same rate to do 3/5 of the job? | [
"45",
"60",
"72",
"80",
"100"
]
| using the std formula
m1d1h1/w1=m2d2h2/w2
substituting the values we have
6*1/2*4/3=2*5/3*x (converted 30 min into hours =1/2)
4=10/3*x
x=6/5 hour
so 72 minutes
ANSWER:C
The answer is: C | C |
mathematics | The average of seven numbers is 4. The average of first three numbers is 2 and the average of last three numbers is 6. What is the middle number? | [
"3",
"4",
"6",
"7",
"8"
]
| The total of seven numbers = 7X4 = 28
The total of first 3 and last 3 numbers is = 3 X 2+3 X 6 = 24
So, the middle number is (28 - 24 ) = 4
B
The answer is: B | B |
mathematics | A certain animal in the zoo has consumed 39 pounds of food in six days. If it continues to eat at the same rate, in how many more days will its total consumption be 156 pounds? | [
"18",
"7",
"12",
"9",
"none of the above"
]
| Ans is A:
39 pounds --> 6 days
91 pounds --> x days
x = 156*6/39 = 24
the animal has already consumed food in 6 days so the the number of
days for it's total consumption be 156 pounds is 24-6 = 18
The answer is: A | A |
mathematics | When a train travels at a speed of 80kmph,it reaches the destination on time.when the same train travels at a speed of 50kmph,it reaches its destination 15min late.what is the length of journey? | [
"25km",
"50km",
"60km",
"85km",
"95km"
]
| Let x be the time reached with the speed 80km/h
50km/h ----> x+15
Distance is equal so
80(km/h)Γ xhr = 50(km/h) Γ (x+15) hr
So
80 x = 50x + 750
So the would be in km
And x = 25
ANSWER:A
The answer is: A | A |
mathematics | In what ratio must a grocer mix two varieties of pulses costing Rs. 15 and Rs. 20 per kg respectively so as to get a mixture worth Rs. 16.50 kg? | [
"4:7",
"3:7",
"4:3",
"7:3",
"2:3"
]
| Cost of 1 kg pulses of 1st kind=Rs. 15
Cost of 1 kg pulses of 2nd kind=Rs. 20
Mean Price=Rs. 16.50
Cost of 1 kg pulses of 1st kind - Mean Price=15-16.50=Rs 1.50
Cost of 1 kg pulses of 2nd kind - Mean Price=20-16.50=Rs 3.50
Required rate = 3.50 : 1.50 = 7 : 3.
Answer:D
The answer is: D | D |
mathematics | A man can row downstream at the rate of 45 Kmph and upstream at 23 Kmph. Find the manβs rate in still water and rate of current? | [
"8.5",
"10.0",
"12.5",
"11.0",
"8.25"
]
| Rate of still water = 1/2 (down stream + upstream)
= 1/2 (45 + 23) = 34 Kmph
rate of current = 1/2 (down stream - upstream)
= 1/2 (45 - 23)
= 1/2 (22)
= 11 kmph
Answer is D.
The answer is: D | D |
mathematics | Rs 50000 is divided into two parts One part is given to a person with 10% interest and another part is given to a person with 20 % interest. At the end of first year he gets profit 8000 Find money given by 10%? | [
"20000",
"40000",
"50000",
"60000",
"70000"
]
| let first parrt is x and second part is y then x+y=50000----------eq1
total profit=profit on x +profit on y
8000=(x*10*1)/100 + (y*20*1)/100
80000=x+2y-----------------------------------eq2
80000=50000+y
so y=30000 then x =50000-30000=20000
first part =20000
ANSWER:A
The answer is: A | A |
mathematics | How much tea worth $0.93 per pound must be mixed with tea worth $0.75 per pound to produce 10 pounds worth $0.85 per pound? | [
"2 2β9",
"3 1β2",
"4 4β9",
"5 5β9",
"9 1β2"
]
| Let weight of tea worth .75 $ = w1
and weight of tea worth .93 $ = w2
w1 + w2 = 10 --- equation 1
.85 = ( w1*.75 + w2* .93 )/(w1+ w2 )
=> .85 w1 + .85 w2 = .75 w1 + .93 w2
=> .10 w1 -.08 w2 = 0
=> 10 w1 - 8 w2 = 0 --- equation 2
From 1 ,
8 w1 + 8 w2 = 80 --- equation 3
From equations 2 and 3 , we get
18 w1 = 80
=> w1 = 40/9
and w2 = 50/9
Answer D
The answer is: D | D |
mathematics | A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train? | [
"145",
"180",
"181",
"184",
"150"
]
| Length of the train be βXβ
X + 120/15 = X + 180/18
6X + 720 = 5X + 900
X = 180m
Answer: Option B
The answer is: B | B |
mathematics | If 20 % of certain quantity of work is done by A and the rest 80% by B, the work is completed in 20 days. If 80% of the work is done by A and the remaining 20% by B, then the work is completed in 30 days. How many days are required to complete the work , if A and B work together. | [
"11 1/9",
"10 1/9",
"12",
"15",
"Source: TIME material."
]
| Use algebra :
0.2/A + 0.8/B = 20
1/A + 4/B = 100
0.8/A + 0.2/B = 30
4/A+ 1/B = 150
15/B = 250
B = 3/50 work per day
A = 3/100 work per day
Combined rate = 3/40 + 3/100 = 9/100
Time taken when working together = 100/9 = 11(1/9) days
Answer (A)
The answer is: A | A |
mathematics | If a car went the first third of the distance at 80 kmh, the second third at 18 kmh, and the last third at 48 kmh, what was the average speed of the car for the entire trip? | [
"34 kmh",
"40 kmh",
"42 kmh",
"44 kmh",
"50 kmh"
]
| Assume D/3 = 720 (this number is convenient because it is divisible by 80, 18 and 48)
So:
720 = 80*T1 = 9 hrs
720 = 18*T2 = 40 hrs
720 = 48*T3 = 15 hrs
T = T1 + T2 + T3 = 64 hrs
D = RT
(720*3) = R*64
R = 33.75
ANSWER: A
The answer is: A | A |
mathematics | An error 2% in excess is made while measuring the side of a square. What is the percentage of error in the calculated area of the square? | [
"4.04",
"4.02",
"4.01",
"4.05",
"4.06"
]
| Formula for Calculation of Percentage error is:
=(xβyβ(xy)/100)%
=(2+2+(2Γ2)/100)%=4.04%
Answer is A.
The answer is: A | A |
mathematics | If 2^k = 4, then 2^(2K+2) = | [
"29",
"45",
"81",
"64",
"18"
]
| 2^k=4
2^2k=4^2
2^2k=16
2^(2k+2)
=2^2k*2^2
=16*4
=64
Answer: D
The answer is: D | D |
mathematics | A photograph measuring 2 1''β2 Γ 1 7''β8 is to be enlarged so that the length will be 4β. How many inches will the enlarged breadth be? | [
"1 1β2",
"2 1β8",
"3",
"3 3β8",
"None of these"
]
| Let enlarged breadth be x inches. Then,
5β2 : 4 :: 15β8 : x
β 5β2x = 4 Γ 15β8 β x = 3 inches.
Answer C
The answer is: C | C |
mathematics | Salesperson A's compensation for any week is $350 plus 6 percent of the portion of A's total sales above $1,000 for that week. Salesperson B's compensation for any week is 8 percent of A's total sales for that week. For what amount of total weekly sales would both salepeople earn the same compensation? | [
"$21,000",
"$18,000",
"$15,000",
"$ 14,500",
"$4,000"
]
| sometime, setting up an equation is an easy way to go with:
350 + 0.06 (x - 1000) = 0.08 x
x = 14,500
Ans : D
The answer is: D | D |
mathematics | There are 7 players in a bowling team with an average weight of 85 Kg. If two new players join the team, one weighs 110 Kg and the second weighs 60 Kg, what will be the new average weight?
. | [
"75 Kg",
"80 Kg",
"85 Kg.",
"90 Kg",
"92 Kg"
]
| New average weight= 110+60/2= 85 kgs
Since avg weight of 85 is added to avg weight of 85, the average will remain the same, i.e 85
C is the answer
The answer is: C | C |
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 black ball has been drawn, find the chance that it came from second group. | [
"2/7",
"6/35",
"8/25",
"28/43",
"3/5"
]
| Please go through my solution and suggest any mistake.
Chances of selecting a black ball from group 1: 2/7----------------------Chances of selecting a black ball from group 2: 4/5
Thus combined probability of section of black ball from group 1:
3/5 x 2/7 = 6/35
Thus combined probability of section of black ball from group 2:
2/5 x 4/5 = 8/25
Out of these chances, chance of occurrence of first case : (8/25) / (6/35 + 8/25) = 28/43
D
The answer is: D | D |
mathematics | A man complete a journey in 10 hrs. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km? | [
"271 km",
"224 km",
"243 km",
"222 km",
"215 km"
]
| B
224 km
Let the total distance be x km.
Then, [(1/2 x) / 21 + (1/2 x) / 24] = 10
15x = 168 * 20 => x = 224 km.
The answer is: B | B |
mathematics | If goods be purchased for Rs.840 and one-fourth be sold at a loss of 20% at what gain percent should the remainder be sold so as to gain 20% on the whole transaction? | [
"33 1/7%",
"33 6/3%",
"33 1/3%",
"39 1/3%",
"33 1/4%"
]
| 1/4 CP = 210 SP = 21*(80/100) = 168
SP = 840*(120/100) = 1008
1008 - 168 = 840
3/4 SP = 630
Gain = 210
630 --- 210
100 --- ? => 33 1/3%
Answer:C
The answer is: C | C |
mathematics | The length of a rectangle is halved, while its breadth is tripled. Watis the % change in area? | [
"30%",
"40%",
"50%",
"60%",
"65%"
]
| Let original length = x and original breadth = y.
Original area = xy.
New length = x .
2
New breadth = 3y.
New area = x x 3y = 3 xy.
2 2
Increase % = 1 xy x 1 x 100 % = 50%.
2 xy
C
The answer is: C | C |
mathematics | Mike and Fritz ran a 30-mile Marathon. Mike ran 10 miles at 10 miles per hour and then ran at 5 miles per hour for the remaining 20 miles.Fritz ran the first one-third (by time) of the run at 10 miles per hour and the remaining two-thirds of the run at 5 miles per hour. How much time in hours did Fritz take to complete the Marathon? | [
"3",
"3.5",
"4",
"4.5",
"5"
]
| Let total time= t
F travelled at rate 10mph for t/3 time and 5mph for 2t/3 time
d= s1t1+s2t2
30= 10*t/3 + 5*2t/3
30= 20t/3
t= 4.5
D is the answer
The answer is: D | D |
mathematics | Three-fourth of two-third of three-seventh of a number is 27. what is 10% of that number? | [
"12.6%",
"6.3%",
"27%",
"25.2%",
"None of these"
]
| Explanation :
Solution: Assume the number be x. then, 3/4 of 2/3 of 3/7 of x = 27.
x = 27 * 7/3 *3/2 * 4/3.
x = 126
.'. 10% of 126 = 10/100 * 126 = 12.6
Answer : A
The answer is: A | A |
mathematics | A, B, C subscribe Rs. 50,000 for a business. A subscribes Rs. 4000 more than B and B Rs. 5000 more than C. Out of a total profit of Rs. 35,000, B receives: | [
"s. 11,000",
"s. 11,300",
"s. 11,500",
"s. 11,700",
"s. 11,900"
]
| Let C = x.
Then, B = x + 5000 and A = x + 5000 + 4000 = x + 9000.
So, x + x + 5000 + x + 9000 = 50000
3x = 36000
x = 12000
A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12.
B's share = Rs. (35000 x 17/50) = Rs. 11,900.
E
The answer is: E | E |
mathematics | There are k-2 members in a certain band, including Jim and Ellen. Two members are to be selected to attend the Grammy awards ceremony. If there are 15 possible combinations in which Jim and Ellen are not selected, what is the value of k? | [
"8",
"9",
"10",
"11",
"12"
]
| There are k-2 members in the band, and k-4 members without Jim and Ellen.
(k-4)C2 = 15
(k-4)(k-5)/2 = 15
(k-4)(k-5) = 30 = 6*5
k = 10
The answer is C.
The answer is: C | C |
mathematics | The average of any 5 consecutive odd natural numbers is k . If two more such numbers , just next to the previous 5 numbers are added , the new average becomes | [
"k+8",
"k+1",
"k+9",
"k+2",
"k+4"
]
| Explanation:
The 5 consecutive odd numbers whose average is k are (k-4), (k-2), k, (k+2), (k+4)
Again the average of (k-4), (k-2), k, (k+2), (k+4), (k+6), (k+8) is (k+2)
Answer: D
The answer is: D | D |
mathematics | A man invests some money partly in 9% stock at 96 and partly in 12% stock at 120. To obtain equal dividends from both, he must invest the money in the ratio: | [
"16:15",
"15:16",
"12:11",
"11:13",
"13:18"
]
| Let the Face Value of Stock giving dividend 9% be Rs. x, whose Market Value is Rs.96.
Let the Face Value of Stock giving dividend 12% be Rs. y, whose Market Value is Rs.120.
By given formula,
Face Value * Dividend % / Market Value = Annual income.
Annual Income from 1st Stock = 9x/96.
Annual Income from 2nd Stock = 12y/120.
To obtain equal dividends from both,
Annual Income from 1st Stock = Annual Income from 2nd Stock.
= 9x/96 = 12y/120.
= x/y = 96/90.
We find GCD of 96, 90 = 6.
= x/y = 16*6 / 15*6.
= Required ratio = x:y = 16:15.
answer : A
The answer is: A | A |
mathematics | Sophia finished 2/3 of a book. She calculated that she finished 90 more pages than she has yet to read. How long is her book? | [
"270",
"150",
"130",
"90",
"210"
]
| Let x be the total number of pages in the book, then she finished 2/3*x pages.
Then she has xβ2/3*x=1/3*x pages left.
2/3*xβ1/3*x=90
1/3*x=90
x=270
So the book is 270 pages long.
Answer is A.
The answer is: A | A |
mathematics | In a class, the number of girls is 20% more than that of the boys. The strength of the class is 66. If 4 more girls are admitted to the class, the ratio of the number of boys to that of the girls is | [
"1:2",
"3:4",
"1:4",
"3:5",
"None"
]
| Solution: Girls:boys = 6:5;
Hence, girls = 6*66/11 = 36;
Boys = 30;
New ratio, 30:(36+4) = 3:4.
Answer: Option B
The answer is: B | B |
mathematics | A boat goes 100 km downstream in 10 hours, and 75 m upstream in 15 hours. The speed of the stream is? | [
"2 (1/9) km/h",
"2 (1/5) km/h",
"2 (3/2) km/h",
"2 (1/2) km/h",
"2 (1/1) km/h"
]
| :100 --- 10 DS = 10
? ---- 1
75 ---- 15 US = 5
? ----- 1 S = (10 - 5)/2
= 2 2 Β½ kmph
Answer: D
The answer is: D | D |
mathematics | What is the difference between the place values of two sevens in the numeral 54707429 ? | [
"699990",
"693000",
"99980",
"699930",
"None of these"
]
| Explanation:
Required Difference
= 700000 - 7000 = 693000
Answer is B
The answer is: B | B |
mathematics | How many of the positive factors of 85 , 105 and how many common factors are there in numbers? | [
"5",
"4",
"2",
"3",
"1"
]
| factors of 85 - 1, 5, 17, 85
factors of 105 - 1, 3, 5, 7, 15, 21, 35, 105
Comparing both, we have two common factors of 85 and 105- 1,5
Answer(C)
The answer is: C | C |
mathematics | 120 +520 Γ· 5.00 = ? | [
"100",
"150",
"120",
"520",
"None"
]
| Answer
Given expression = 120 +520 Γ· 5.00
= 120 + 104
= 224
Correct Option: E
The answer is: E | E |
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