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mathematics | A person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 20%? | [
"600",
"882",
"772",
"652",
"271"
]
| Cost price = Rs.500
profit = 20% of 500 = Rs.100
Selling price = Cost price + Profit
= 500 + 100 = 600
Answer:A
The answer is: A | A |
mathematics | Two coins are tossed, find the probability that two Tails are obtained | [
"1/3",
"1/4",
"1/5",
"1/7",
"2/3"
]
| The sample space S is given by.
S = {(H,T),(H,H),(T,H),(T,T)}
Let E be the event "two heads are obtained".
E = {(T,T)}
P(E) = n(E) / n(S) = 1/4
B
The answer is: B | B |
mathematics | The average of numbers 0.34204, 0.34203, 0.34202 and 0.34201 is ? | [
"0.34202",
"0.34204",
"0.342022",
"0.342025",
"None"
]
| Answer
Average = (0.34204 + 0.34203 + 0.34202 + 0.34201)/ 4
=1.3681/ 4
=0.342025
Correct Option: D
The answer is: D | D |
mathematics | 12 points lie on a circle. How many cyclic quadrilaterals can be drawn by using these points? | [
"990",
"495",
"1980",
"none",
"Cannot be determined"
]
| Explanation :
For any set of 4 points we get a cyclic quadrilateral. Number of ways of choosing 4 points out of 12 points is 12C4=495Therefore, we can draw 495 quadrilaterals.
Answer : B
The answer is: B | B |
mathematics | Find the area of trapezium whose parallel sides are 10 cm and 18 cm long, and the distance between them is 15 cm. | [
"287 cm2",
"785 cm2",
"285 cm2",
"785 cm2",
"210 cm2"
]
| Explanation:
Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them) = 1/2 (10 + 18) * (15) = 210 cm2
Answer: Option E
The answer is: E | E |
mathematics | Working together, Wayne and his son can shovel the entire driveway in three hours. If Wayne can shovel five times as fast as his son can, how many hours would it take for his son to shovel the entire driveway on his own? | [
"4",
"6",
"8",
"9",
"12"
]
| W: the time for Wyane to do the job
S: the time for his son to do the job
We have 1/W + 1/S = 1/5 and W = 5S
Then we have 1/(5*S) + 1/S = 1/5<=> 6/(5*S) = 1/5 <=> S = 6
ANS: B
The answer is: B | B |
mathematics | A book club rented the party room of a local restaurant to meet and discuss its current novel over dinner. The total charge, including food and service, was $ 900. If each member of the club paid at least $ 40, then what is the greatest possible number of members in the club? | [
"19",
"20",
"21",
"23",
"25"
]
| Given: Each person spends $40
By looking at the options, we see that if there were 20 members, each person will spend atleast $40
Hence the greatest number of members = 22.5 Option D
The answer is: D | D |
mathematics | The decimal d is formed by writing in succession all the positive integers in descending order after the decimal point; that is d = 0.15141312111098765
What is the 19th and 20th digits of d to the right of decimal point? | [
"32",
"43",
"54",
"12",
"21"
]
| The descending order of numbers begins with 15.
0.15141312111098765
So, 15, 14, 13, 12, 11, 10, ...,(first 12 digits are 2 digit numbers).
Then, 9, 8, 7, 6, 5, ...,(next 5 digits are single digit numbers).
It follows that 4, 3, and 2 are the next digits, thus 3 and 2 are the 19th and 20th digits, respectively.
Answer: A
The answer is: A | A |
mathematics | A number is four less than two times the other number. If their difference is 21, what is the greater number? | [
"50",
"46",
"31",
"21",
"15"
]
| A = one number
B = other number
A = -4 + 2B
A - B = 21
solve for A by adding B to each side
A = B + 21
Substitute (B + 21) for A in A = -4 + 2B
(B + 21) = -4 + 2B
add -B to each side
21 = -4 + B
add 4 to each side
25 = B
Since A = B + 21 , A = 25 + 21 , A = 46
ANSWER:B
The answer is: B | B |
mathematics | A garrison of 2000 men has provisions for 54 days. At the end of 15 days, a reinforcement arrives, and it is now found that the provisions will last only for 20 days more. What is the reinforcement? | [
"1778",
"1682",
"9178",
"1900",
"1782"
]
| 2000 ---- 54
2000 ---- 39
x ----- 20
x*20 = 2000*39
x = 3900
2000
-------
1900
Answer: D
The answer is: D | D |
mathematics | I purchases perfume from a store and gave him a thousand rupee note.
The perfume cost Rs.300.
Since the store person have no change, he gets the change from next shop and return me 800 rupees.
After a while, the next shopkeeper comes and told the 1st shopkeeper that the note is a fraud and takes his money back.
How much loss does the 1st shopkeeper have to bear ? | [
"2004",
"2011",
"5000",
"5400",
"1000"
]
| E
Rupees 1000
The answer is: E | E |
mathematics | A cistern can be filled by a tap in 3 hours while it can be emptied by another tap in 5 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",
"7.5 hrs",
"1.4 hrs"
]
| Net part filled in 1 hour = (1/3 - 1/5) = 2/15
The cistern will be filled in 15/2 hrs i.e., 7.5 hrs.
Answer:D
The answer is: D | D |
mathematics | 2400÷20÷10=? | [
"43",
"12",
"15",
"20",
"24"
]
| 2400 ÷ 20 = 120
120 ÷ 10 = 12
Answer is B
The answer is: B | B |
mathematics | The average earning of a mechanic for the first 4days of a week is Rs.18 and for the last four days is Rs.22. If he earns Rs.20 on the fourth day, his average earning forthe whole week is? | [
"Rs. 10",
"Rs. 20",
"Rs. 30",
"Rs. 40",
"Rs. 50"
]
| Total earning for the week = Sum of earning of first four days + Sum of earning of last four days - Earning of 4th day
= 4 x18 + 4 x 22 -20
= Rs. 140
∴ Average earning = 140 / 7
= Rs. 20
B
The answer is: B | B |
mathematics | At what price must an article costing Rs.150 be marked in order that after deducting 10% from the list price. It may be sold at a profit of 30% on the cost price? | [
"62.5",
"62.0",
"62.6",
"216.67",
"62.2"
]
| CP = 150
SP = 150*(130/100) = 195
MP*(90/100) = 195
MP = 216.67
Answer: D
The answer is: D | D |
mathematics | If x, y, and z are consecutive odd integers, with x < y < z, then which of the following must be true?
I. x + y + z is odd
II. (x+z)/y is not an integer
III. xy/2 is not an integer | [
"I only",
"II only",
"III only",
"I and II only",
"I, II, and III"
]
| consecutive odds are:
2x+1, 2x+3, 2x+5
I. 2x+1+2x+3+2x+5=6x+9=3(2x+3), 2x+3 is not divisible by 2 hence odd, odd * odd = odd Hence I is odd - TRUE
II. 2x+1+2x+5=4x+6/2x+3=2(2x+3)/2x+3=2, so integer - TRUE
III. (2x+1)*(2x+3)=4x^2+6x+2x+3=4x^2+8x+3=(4x(x+2)+3)/2 is not integer, so TRUE
ANSWER: E
The answer is: E | E |
mathematics | Which of the following values is the greatest | [
"a) 11% of 89",
"b) 22% of 78",
"c) 33% of 67",
"d) 55% of 56",
"e) 55% of 45"
]
| Are you sure that you checked the answer key correctly? I just signed up forVeritas(haven't started yet, not until March) but I have access to the materials and the answer key I'm looking at says D
The answer is: D | D |
mathematics | Find the odd man out
36, 315, 612, 810, 966, 1362 | [
"966",
"612",
"315",
"36",
"1362"
]
| 315is divisible by 3 which is odd number where as all others are even numbers divisible by 3.
ANSWER:C
The answer is: C | C |
mathematics | In a camp, there is a meal for 120 men or 200 children. If 170 children have taken the meal, how many men will be catered to with remaining meal? | [
"30",
"20",
"18",
"57",
"63"
]
| There is a meal for 200 children.
170 children have taken the meal.
Remaining meal is to be catered to 30 children.
Now, 200 children 120 men.
30 children = (120/200)x 30 = 18 men.
C
The answer is: C | C |
mathematics | In a city 100% votes are registered, in which 60% vote for congress and 40% vote for BJP. There is a person A, who gets 75% of congress votes and 8% of BJP votes. How many votes got by A? | [
"48.9 %",
"78.2 %",
"48.2 %",
"48.7 %",
"48.6 %"
]
| Assume total votes are 100. So A got
75% of 60 = 45
8% of 40 = 3.2
A total of 48.2 %
Answer:B
The answer is: B | B |
mathematics | On Saturday morning, John will begin a camping vacation and he will return home at the end of the first day on which it rains. If on the first three days of the vacation the probability of rain on each day is 0.2, what is the probability that Malachi will return home at the end of the day on the following Monday? | [
"0.008",
"0.125",
"0.128",
"0.512",
"0.64"
]
| Re-phrasing the question:
What is the probability of: Saturday: No rain, Sunday: No rain, Monday: Rain
Probability of rain = 0.2
Therefore, probability of no rain = 0.8
0.8*0.8*0.2 = 0.128
Hence C
The answer is: C | C |
mathematics | In the sequence 1, 2, 4, 8, 16, 32, …, each term after the first is twice the previous term. What is the sum of the 16th, 17th terms in the sequence? | [
"2^18",
"3(2^17)",
"7(2^16)",
"3(2^15)",
"7(2^15)"
]
| the sequence comes out to be 2^0,2^1,2^2,2^3 and so on...
so 16th term will be 2^15
17th term 2^16
adding all three
we get
2^15+(2^15)*2
so answer is 2^15(1+2)=>3(2^15)
answer D
The answer is: D | D |
mathematics | Simplify
16−[5−(6+2(7−8−5¯¯¯¯¯¯¯¯¯¯¯))] | [
"23",
"25",
"28",
"30",
"32"
]
| Explanation:
=16−[5−(6+2(7−8+5))]
(Please check due to overline, sign has been changed)
=16−[5−(6+2×4))]
=16−[−9]=16+9=25
Option B
The answer is: B | B |
mathematics | If the cost price of 12 pens is equal to the selling price of 8 pens, the gain percent is: | [
"80%",
"90%",
"50%",
"40%",
"10%"
]
| Explanation:
Let C.P. of each pen be Re. 1.
Then, C.P. of 8 pens = Rs. 8; S.P. of 8 pens = Rs. 12.
Gain % = 4/8 * 100 = 50%
Answer:C
The answer is: C | C |
mathematics | A factory produces x widgets per day. The factory's fixed costs are $7000 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 $6200 a day? | [
"42.33",
"90.33",
"168",
"220",
"400"
]
| profits=6200=60x-8000 --> x=220
Answer D.
The answer is: D | D |
mathematics | If a man buys 1 liter of milk for 12 rs. and mixes it with 20% water and sells it for 15 rs then what is the %age of gain... | [
"30",
"40",
"50",
"60",
"70"
]
| Quantity after adding 20% water=1.2 liter
SP of 1.2 lit.@15 Rs./liter=15*1.2=18 Rs
CP=12 Rs/lit.
% profit=100*(18-12)/12=50
ANSWER:C
The answer is: C | C |
mathematics | Simplify 3/4 of 6 0 – 8/5 of 60 + ? = 12 | [
"48",
"24",
"56",
"63",
"14"
]
| 60 × 3/4 = 45, 60 × 8/5 = 96
45 – 96 + ? = 12 => 96 + 12 = 108 – 45 = 63
[63 + 45 = 108 – 96 = 12]
Option D
The answer is: D | D |
mathematics | If in a certain sequence of consecutive multiples of 50, the median is 825, and the greatest term is 1050, how many terms that are smaller than 825 are there in the sequence? | [
"6",
"5",
"8",
"12",
"13"
]
| Since the median is 825 we know there must be a even number of integers because 50 is not a multiple of 825.
So the list around 625 must go. 750 800 (825) 850 900 950 1000 1050
Since we know there are 5 numbers greater than 825 then there must be 5 numbers less then 825.
answer:B
The answer is: B | B |
mathematics | 50 is what percent of 125? | [
"35%",
"40%",
"45%",
"50%",
"55%"
]
| 50/125×100=50% ANSWER : B
The answer is: B | B |
mathematics | Each of the 50 members in a high school class is required to sign up for a minimum of one and a maximum of three academic clubs. The three clubs to choose from are the poetry club, the history club, and the writing club. A total of 17 students sign up for the poetry club, 24 students for the history club, and 22 students for the writing club. If 3 students sign up for exactly two clubs, how many students sign up for all three clubs? | [
"5",
"6",
"7",
"8",
"9"
]
| The total number in the three clubs is 17+24+22=63.
All 50 students signed up for at least one club.
3 of those students signed up for exactly one more club.
63 - 53 = 10 so 5 students must have signed up for exactly three clubs.
The answer is A.
The answer is: A | A |
mathematics | If 7<x<9<y<15, then what is the greatest possible positive integer difference of x and y? | [
"7",
"4",
"5",
"6",
"3"
]
| Let x=7.1 and y=14.1
Greatest possible difference=14.1-7.1=7
Answer A
The answer is: A | A |
mathematics | If log303 = a, log305 = b, then log308 =? | [
"3(1 - a - b)",
"(a - b + 1)",
"(1 - a - b)",
"(a - b + 1)",
"none of these"
]
| a + b = log3015 = log30(30/2) = 1- log302
=> log302 = (1 - a - b)
Therefore, log308 = 3(1 - a - b).
ANSWER:A
The answer is: A | A |
mathematics | A Man can row upstream at 85kmph and downward stream at 47 kmph. Find Man's rate of the current | [
"19km/hr",
"20km/hr",
"65km/hr",
"2.8km/hr",
"4.4km/hr"
]
| Rate of the current=1/2(85-47)km/hr
=19km/hr
correct option is :A
The answer is: A | A |
mathematics | A company seeks to hire a sales manager, a shipping clerk, and a receptionist. The company has narrowed its candidate search and plans to interview all remaining candidates including 7 persons for the position of sales manager, 4 persons for the position of shipping clerk, and 10 persons for the position of receptionist. How many different hirings of these three people are possible? | [
"7 + 4 + 10",
"7 × 4 × 10",
"21 × 20 × 19",
"7! + 4! + 10!",
"7! × 4! × 10!"
]
| Number of ways one person can be hired for the position of Sales Manager= C71C17=7
Number of ways one person can be hired for the position of Shipping Clerk= C41=4
Number of ways one person can be hired for the position of Receptionist= C101=10
Therefore total number of different hiring possible for the three positions = 7 * 4 * 10
Answer: B
The answer is: B | B |
mathematics | How many 2's are there between the terms 112 to 375? | [
"A)156",
"B)157",
"C)158",
"D)159",
"E)160"
]
| Let us calculate total 2's in the units place. (122, 132, 142 ... 192), (201, 212, 222, ... 292), (302, 312, ... 372) = 8 + 10 + 8 = 26
Total 2's in tenth's place, (120, 121, 122, ..., 129) + (220, 221, ..., 229) + (320, 321, ..., 329) = 30
Total 2's in hundred's place = (200, 201, ... 299) = 100.
Total 2's between 112 and 375 = 26 + 30 + 100 = 156
Answer:A
The answer is: A | A |
mathematics | A solution contains 8 parts of water for every 7 parts of Lemonade syrup. How many parts of the solution should be removed and replaced with water so that the solution will now contain 10% lemonade syrup? | [
"1.5",
"1.75",
"2.14",
"2.34",
"2.64"
]
| Let the total solution is 150 L with 80 L water70 L syrup.
To make 10% syrup solution, the result solution must have 135 L syrup and 15 L syrup.
Therefore we are taking 55 L of syrup from initial solution and replacing with water.
using urinary method:
70 L syrup in 150 L solution
55 L syrup in 117.9 L solution
We started by multiplying 10
Now to get to the result we need to divide by 55 => amount of solution to be replaced with water = (117.9/55) = 2.14.
Correct option : C
The answer is: C | C |
mathematics | 10% people of a village in Sri Lanka died by bombardment, 20% of the remainder left the village on account of fear. If now the population is reduced to 4554, how much was it in the beginning? | [
"7349",
"6300",
"6325",
"6939",
"2989"
]
| X * (90/100) * (80/100) = 4554
X = 6325
Answer: C
The answer is: C | C |
mathematics | How many different ways can you select a pilot and a co pilot if you have 70 people to choose from? | [
"199",
"200",
"398",
"4950",
"4830"
]
| 1) PERMUTATION:-
since it is selection, we have to find permutation..
70P2= 70!/(70-2)!=4830
ANS:E
The answer is: E | E |
mathematics | A sum of money at simple interest amounts to Rs. 1072 in 2 years and to Rs. 1144 in 4 years. The sum is: | [
"Rs. 1000",
"Rs. 850",
"Rs. 500",
"Rs. 1200",
"Rs. 900"
]
| S.I. for 2 years = Rs. (1144 - 1072) = Rs. 72.
S.I. for 1 year = Rs. 72/2 = Rs. 36.
Principal = Rs. (1072 - 72) = Rs. 1000.
Answer: Option A
The answer is: A | A |
mathematics | Meera purchased two three items from a shop. Shop keeper says for one wallet : Rs.250/- and Shoe : 1250/- Meera give Rs. 2000/- to shop keeper. He paid balance Rs. 750/- to meera. How much she got? | [
"250",
"500",
"600",
"350",
"400"
]
| Cost of Wallet =250/-
Cost of Shoe = 1250/-
Total cost = 1500/-
amount paid to shop keeper = 2000/-
Balance is : 2000 - 1500 = 500 (250 Balance + 250 additional)
Answer is A
The answer is: A | A |
mathematics | The salary of all officers is increased twice successively by 20%. What is the net percentage increase in their salaries? | [
"20%",
"40%",
"21%",
"44%",
"48%"
]
| M . F = 120/100*120/100 = 36/25
Net % increase = ( M . F -1 ) *100 =( 36/25-1) * 100
11/25 *100 = 44 %
ANSWER:D
The answer is: D | D |
mathematics | If 'Pink' is called 'Orange', 'Orange' is called 'Blue', 'Blue' is called 'Red', 'Red' is called 'Green', 'Green' is called 'Black' and 'Black' is called 'white', what would be the color of charcoal ? | [
"White",
"BLUE",
"PINK",
"ORANCE",
"BLACK"
]
| Explanation:
Pink → Orange
Orange → Blue
Blue → Red
Red → Green
Green → Black
Black → White
The color of charcoal is 'Black' but in coding language, 'Black' is called 'White'.
ANSWER: A
The answer is: A | A |
mathematics | A and B together can do a piece of work in 6 days and A alone can do it in 10 days. In how many days can B alone can do it? | [
"12 days",
"18 days",
"15 days",
"21 days",
"22 days"
]
| Explanation:
A and B can do work 1/6 in 1 day
A alone can do 1/10 work in 1 day
B alone can do (1/6 -1/10) =1/15 work in 1 day
=> complete work can be done in 15 days by B
Answer: Option C
The answer is: C | C |
mathematics | A certain collage has total of 600 seniors each majoring in exactly one of six subjects. A minimum of 20 seniors major in each six subjects. If three quarter of the seniors major in one of four subjects, what is the greatest possible number of seniors majoring in one of the other two subjects? | [
"100",
"130",
"75",
"60",
"50"
]
| Answer B
600 = 450 + 20 + x => x = 130
= 3/4 * 600 in 4 subjects + 20 min for 5th subject + x = 600
The answer is: B | B |
mathematics | f1(x)f1(x) = 2x - 1 and fn(x)=f1(fn−1(x))fn(x)=f1(fn−1(x)) for n ≥≥ 2. Find f5(2) | [
"7",
"6",
"78",
"9",
"1"
]
| Answer:A
The answer is: A | A |
mathematics | Which fraction will come next, 1/2,3/4,5/8,7/16,? | [
"9/30",
"11/32",
"9/28",
"9/32",
"9/28"
]
| Numerators are getting increased by 2. i.e., numerators goes like 1,3,5,7,...
Hence, next numerator = 7+2 = 9
Denominators are getting multiplied by 2. i.e., denominators goes like 2,4,8,16,...
Hence, next denominator = 16×2 = 32
So, the next fraction is 9/32
The answer is: D | D |
mathematics | A candy company sells premium chocolate at $5 per pound and regular chocolate at $2 per pound in increment of whole pound only.If Barrett buys a pack of candies which costs him $31, how many pounds of premium chocolates are in the box? | [
"[A] 1",
"[B] 2",
"[C] 3",
"[D] 4",
"[E] 5"
]
| This question is a bit of Special equations with a single set of unique values.
the Equation stands : 5X + 2Y = 31
Subtract multiple of 5 from 31 and check whether the remaining total is divisible by 4
31 - 5 = 26 -> Not divisible by 4
31 - 10 = 21 -> Not divisible by 4
31 - 15 =16 -> Divisible by 4
31 - 20 =11 -> Not divisible by 4
31 - 25 =6 -> Not divisible by 4
31 - 30 =1 -> Not divisible by 4
Any multiple of 5 hereon will give a negative value for regular chocolates bought and hence, inadmissible
Thus Amount spent on regular chocolate= $16
Amount spent on Premium chocolate= $15
Price per premium chocolate = $5
No. Of boxes of premium chocolate bought = 10 / 5 = 2
Correct Option : B
The answer is: B | B |
mathematics | The salary of a person was reduced by 10%. By what percent should his reduced salary be raised so as to bring it at par with his original salary? | [
"10%",
"11 1/9%",
"13 2/7%",
"15 3/11%",
"12 1/3%"
]
| Let the original salary be $100
New salary = $90
Increase on 90 =10
Increase on 100 = 10/90 * 100 = 11 1/9%
Answer is B
The answer is: B | B |
mathematics | In a sample of 800 high school students in which all students are either freshmen, sophomores, juniors, or seniors, 23 percent are juniors and 75 percent are not sophomores. If there are 160 seniors, how many more freshmen than sophomores are there among the sample of students? | [
"42",
"48",
"56",
"64",
"72"
]
| 200 are sophomores.
The number of freshmen is 600 - 160 - 0.23(800) = 256
The answer is C.
The answer is: C | C |
mathematics | Month Average Price
per Dozen
April $1.26
May $1.20
June $1.08
The table above shows the average (arithmetic mean) price per dozen of the large grade A eggs sold in a General store during three successive months. If 2/3 as many dozen were sold in April as in May, and twice as many were sold in June as in April, what was the average price per dozen of the eggs sold over the three-month period? | [
"1.4",
"1.3",
"1.2",
"1.1",
"1.16"
]
| Say x dozen eggs were sold in May.
Then 2x/3 dozen eggs were sold in April and 2*2x/3=4x/3 dozen eggs were sold in May.
Total x+2x/3+4x/3=3x dozen eggs were sold in three months.
Total sales: 2x/3*1.26+x*1.2+4x/3*1.08=$3.48x. The average price per dozen 3.48x/3x=$1.16.
E
The answer is: E | E |
mathematics | During a certain two-week period, 72 percent of the movies rented from a video store were comedies, and of the remaining movies rented, there were 6 times as many dramas as action movies. If no other movies were rented during that two-week period and there were A action movies rented, then how many comedies, in terms of A, were rented during that two-week period? | [
"1/20 A",
"10 A",
"15 A",
"18 A",
"23 A"
]
| Movies: 72 % comedies. 28 % remaining genre.
Now in this 28 %, there are only 2 categories. Action movies and Drama Movies.
If Action = x; Drama movies = 6x. Total 7x.
7x = 28; x = 4
Action movies: 4 %
Drama movies: 24 %
we can say that out of 100z,:
comedies: 72z
action: 4z
drama: 24 z
Now action movies were A
This means:
A = 4z.
z = (A/4)
Comedies: 72z = 72 * (A/4)
18 A
D is the answer.
The answer is: D | D |
mathematics | Working alone at its constant rate, machine A produces x boxes in 5 minutes and working alone at its constant rate, machine B produces 2x boxes in 10 minutes. How many minutes does it take machines A and B, working simultaneously at their respective constant rates, to produce 3x boxes? | [
"3 minutes",
"7.5 minutes",
"5 minutes",
"6 minutes",
"12 minutes"
]
| Rate = Work / Time
Given Rate of Machine A = 2X / 10 min
Machine B Produces 2x boxes in 10 min hence , Machine B produces 2x boxes in 10 min .
Rate of Machine B = 2x / 10
we need tofind the combined time that machines A and B, working simultaneouslytakeat their respective constant rates
let's first find the combined Rate of Machine A and B
Rate of Machine A = 2X / 10 min + Rate of Machine B = 2x / 10 = 4X/10
Now combine Time = combine work needs to be done / Combine Rate = 3x/4x * 10 = 7.5 Min
Ans: B
The answer is: B | B |
mathematics | In a fuel station the service costs $1.75 per car, every liter of fuel costs 0.65$. Assuming that a company owns 12 cars and that every fuel tank contains 60 liters and they are all empty, how much money total will it cost to fuel all cars? | [
"320$",
"389$",
"420$",
"450$",
"489$"
]
| Total Cost = ( 1.75*12 ) + ( 0.65 * 12 * 60 ) =489
Hence answer will be (E)
The answer is: E | E |
mathematics | A coin is tossed live times. What is the probability that there is at the least one tail? | [
"31/32",
"31/17",
"31/19",
"31/12",
"31/13"
]
| Let P(T) be the probability of getting least one tail when the coin is tossed five times.
= There is not even a single tail.
i.e. all the outcomes are heads.
= 1/32 ; P(T) = 1 - 1/32
=31/32
Answer:A
The answer is: A | A |
mathematics | Sharron bakes 6 cookies for 6 friends. 2 of the friend arrive early and eat 3 cookies each. How many cookies are left over if the other friends all have the same number of cookies? | [
"1",
"2",
"3",
"4",
"5"
]
| Sharron made 6*6 cookies = 36 cookies. 2 friends eat 3 cookies, leaving 30 remaining for 4 friends.
30=2*3*5. 30 is not divisible by 4. The 4 friends ate a cumulative number of cookies less than 30 that must be divisible by 4, because the number is the same.
A 30 -1=29. 29=1*29, cannot be divided by four
B 30-2=28. 28=2*2*7, can be divided by four
C 30-3 = 27. 27=3*3*3, cannot be divided by four
D. Because there are 4 people, 4 cannot be a remainder (remainder = 0)
E. Because there are 4, people, 5 cannot be a remainder (remainder = 1)
B is the correct answer
The answer is: B | B |
mathematics | By selling 9 pencils for a rupee a man loses 20%. How many for a rupee should he sell in order to gain 20%? | [
"8",
"9",
"7",
"4",
"6"
]
| 80% --- 9
120% --- ?
80/120 * 9 = 6
Answer: E
The answer is: E | E |
mathematics | In given series 582, 605, 588, 611, 634, 617, 600 only one number is incorrect. Find out that wrong number | [
"615",
"634",
"600",
"620",
"617"
]
| 582+23=605
605-17=588
588+23=611
611-17=594....so 634 is wrong.
594+23=617
617-17=600
ANSWER:B
The answer is: B | B |
mathematics | Fresh grapes contain 90% by weight while dried grapes contain 20% water by weight. What is the weight of dry grapes available from 40 kg of fresh grapes? | [
"5 kg",
"2.4 kg",
"2.5 kg",
"10 kg",
"none of these"
]
| The weight of non-water in 20 kg of fresh grapes (which is 100-90=10% of whole weight) will be the same as the weight of non-water in x kg of dried grapes (which is 100-20=80% of whole weight), so 40∗0.1=x∗0.8--> x=5
Answer: A
The answer is: A | A |
mathematics | Find the compound ratio of (1:2), (1:3) and (3:5) is | [
"1:10",
"2:3",
"3:4",
"4:5",
"3:2"
]
| Required ratio = 1/2 * 1/3 * 3/5 = 1/10 = 1:10
Answer is A
The answer is: A | A |
mathematics | John spent a total of $135 on baseball tickets. The price of a ticket is either $12 for the field seats or $5 for the balcony. What is the minimum amount Q of dollars he could have spent for the $12 tickets? | [
"$48",
"$60",
"$84",
"$96",
"$120"
]
| 60 ..... 12 *5 Q= 60. (min). Thus answer .B
The answer is: B | B |
mathematics | A composer’s guild is planning its spring concert, and eleven pieces have been submitted for consideration. The director of the guild knows that they will only have time to present three of them. If the pieces can be played in any order, how many combinations of pieces are possible? | [
"402",
"165",
"154",
"512",
"126"
]
| Combination question..
11C3 = 165..
IMO option B is correct..
The answer is: B | B |
mathematics | Two trains running in opposite directions cross a man standing on the platform in 47 seconds and 38 seconds respectively and they cross each other in 40 seconds. The ratio of their speeds is: | [
"3 : 1",
"3 : 2",
"2 : 7",
"3 : 25",
"3 : 4"
]
| Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 47 x meters, and length of the second train = 38 y meters. (47 x + 37 y) / (x + y) = 40 ==>
47 x + 38 y = 40x + 40 y ==> 7x = 2 y ==> x/y = 2/7
Answer: Option C
The answer is: C | C |
mathematics | If the average (arithmetic mean) of x, x + 2, and x + 4 is 33, what is the value of x? | [
"30",
"31",
"32",
"32",
"37"
]
| AM of x, x + 2, and x + 4 = x + (x + 2) + (x + 4) / 3 = 3x + 6 /3 = x + 2
Given that x + 2 = 33
x = 31
Correct Option: B
The answer is: B | B |
mathematics | If a is a positive integer, which of the following could NOT be the square of a? | [
"2432",
"7426",
"5966",
"3415",
"2155"
]
| A number ending in 2 cannot be a perfect square.
2432 ends in a number 2, making that the correct answer
(A) 2432
The answer is: A | A |
mathematics | If (2^32 + 1) is completely divisible by a whole number, which of the following numbers is completely divisible by this number? | [
"(2^96+1)",
"(7 × 223 )",
"(2^16 - 1)",
"(2^15 + 1)",
"(2^17 + 1)"
]
| Explanation:
Let
2
32
=
x
232=x.
Then
(
2
32
+
1
)
=
(
x
+
1
)
(232+1)=(x+1)
Assume that
(
x
+
1
)
(x+1) is completely divisible by a whole number, N
(
2
96
+
1
)
=
(
2
32
)
3
+
1
=
(
x
3
+
1
)
=
(
x
+
1
)
(
x
2
−
x
+
1
)
(296+1)=(232)3+1=(x3+1)=(x+1)(x2−x+1)
if
(
x
+
1
)
(x+1) is completely divisible by N,
(
x
+
1
)
(
x
2
−
x
+
1
)
(x+1)(x2−x+1) will also be divisible by N
Hence
(
2
96
+
1
)
(2^96+1) is completely divisible N
A)
The answer is: A | A |
mathematics | If the sum of two numbers is 12 and the sum of their squares is 124, then the product of the numbers is | [
"10",
"44",
"80",
"88",
"90"
]
| Sol.
Let the numbers be x and y.
Then, (x+y) = 12 and x2 + y2 = 124.
Now, 2xy = (x+y)2 - (x2 + y2)
= (12)2 - 124 = 144 - 124 = 20
xy = 10.
Answer A
The answer is: A | A |
mathematics | How many days will there be from 28th January,1996 to 15th May,1996(both days included)? | [
"102",
"103",
"111",
"109",
"121"
]
| Explanation:
Number of days from 28-Jan-1996 to 15-May-1996 (both days included)
= 4(Jan) + 29(Feb) + 31 (Mar) + 30(Apr)+ 15(May) = 109
Answer: Option D
The answer is: D | D |
mathematics | The average of marks obtained by 120 boys was 38. If the average of marks of passed boys was 39 and that of failed boys was 15, the number of boys who passed the examination is? | [
"100",
"110",
"115",
"125",
"140"
]
| Let the number of boys who passed = X.
Then, 39 x X + 15 x (120 - X) = 120 x 38
24X = 4560 - 1800
=> X = 2760/24
X = 115.
Hence, the number of boys passed = 115.
ANSWER:C
The answer is: C | C |
mathematics | Find the least number of complete years in which a sum of money put out at 25% compound interest will be more than double of itself? | [
"6 years",
"7 years",
"9 years",
"4 years",
"1 years"
]
| 4 years
Answer: D
The answer is: D | D |
mathematics | A part of certain sum of money is invested at 8% per annum and the rest at 12% per annum, if the interest earned in each case for the same period is equal, then ratio of the sums invested is? | [
"3:2",
"4:8",
"4:3",
"4:0",
"4:9"
]
| 12:8
= 3:2
Answer: A
The answer is: A | A |
mathematics | John and Jacob set out together on bicycle traveling at 15 and 9 miles per hour, respectively. After 40 minutes, John stops to fix a flat tire. If it takes John one hour to fix the flat tire and Jacob continues to ride during this time, how many hours will it take John to catch up to Jacob assuming he resumes his ride at 15 miles per hour? (consider John's deceleration/acceleration before/after the flat to be negligible) | [
"3",
"3 1/3",
"3 1/2",
"4",
"1 1/4"
]
| John's speed - 15 miles/hr
Jacob's speed - 9 miles/hr
After 40min (i.e 2/3hr), distance covered by John = 15x2/3 = 10 miles.
Jacob continues to ride for a total of 1hour and 40min (until John's bike is repaired). Distance covered in 1 hour 40min (i.e 5/3hr) = 9x5/3 = 15 miles.
Now, when John starts riding back, the distance between them is 7.5 miles. Jacob and John are moving in the same direction.For John to catch Jacob, the effective relative speed will be 15-9 = 6 miles/hr.
Thus, to cover 7.5 miles at 6 miles/hr, John will take 7.5/6 = 1.25 hours
Answer E
The answer is: E | E |
mathematics | Two pipes P and Q can fill a cistern in 12 and 19 minutes respectively. Both are opened together, but at the end of 3 minutes the first is turned off. How much longer will the cistern take to fill? | [
"11 1/2 min",
"14 1/4 min",
"11 2/4 min",
"11 1/5 min",
"11 7/4 min"
]
| 3/12 + x/19 = 1
x= 14 1/4
Answer: B
The answer is: B | B |
mathematics | A student's mark was wrongly entered as 83 instead of 63. Due to that the average marks for the class got increased by 1/2. What is the number of students in the class? | [
"20",
"30",
"10",
"40",
"50"
]
| Let the total number of students = x
The average marks increased by 1/2 due to an increase of 83 - 63 = 20 marks.
But total increase in the marks = (1/2)x=x/2
Hence we can write as
x/2=20
⇒x=20×2=40
Answer is D.
The answer is: D | D |
mathematics | Three friends James, David and Charlie divide $1230 amongs them in such a way that if $5, $10 and $15 are removed from the sums that James, David and Charlie received respectively, then the share of the sums that they got will be in the ratio of 9: 10 : 11. How much did Charlie receive? | [
"$600",
"$575",
"$550",
"$580",
"$615"
]
| A+B+C = 1230
Given ratio 9:10:11
Let us say the shares of A,B,C deducting 5,10,15 be a,b,c
a+b+c = 1230-30= 1200 = 30K
c share = (1200X30)/60 = 600
C = charlie share = 600+15= 615
Option E
The answer is: E | E |
mathematics | If A's height is 40% less than that of B, how much percent B's height is more than that of A? | [
"66.66%",
"66.68%",
"66.766%",
"86.66%",
"66.65%"
]
| Excess of B's height over A's = [(40/(100 - 40)] x 100%
= 66.66%
Answer: A) 66.66%
The answer is: A | A |
mathematics | The ratio of men to women in a class is 6 to 5. If 6 men and 6 woman drop out of the class and the ratio of men to women after the drop out is 4 to 3, then how many men are currently in the class? | [
"10",
"11",
"14",
"15",
"12"
]
| Equation on the basis of question
6x-6/5x-6=4/3
x=3
Original number of men = 6*3=18
Original Number of Women = 5*3=15
Current number of men = 18-6=12 (Answer)
Current number of women = 15-6=9
Ratio = 12/9= 4/3 ( Just to verify)
Ans E
The answer is: E | E |
mathematics | In a certain game, a large bag is filled with blue, green, purple and red chips worth 1, 5, x and 11 points each, respectively. The purple chips are worth more than the green chips, but less than the red chips. A certain number of chips are then selected from the bag. If the product of the point values of the selected chips is 28160, how many purple chips were selected? | [
"1",
"2",
"3",
"4",
"5"
]
| 28160 = 1*5*8^3*11
The factors of 8 must come from the purple point value, so there are 3 purple chips.
The answer is C.
The answer is: C | C |
mathematics | Two persons start running simultaneously around a circular track of length 700 m from the same point at speeds of 15 km/hr and 25 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions? | [
"63",
"10",
"28",
"27",
"12"
]
| Time taken to meet for the first time anywhere on the track
= length of the track / relative speed
= 700 / (15 + 25)5/18 = 700* 18 / 40 * 5 = 63 seconds.
Answer: A
The answer is: A | A |
mathematics | A can do a piece of work in 21 days and B in 28 days. Together they started the work and B left after 4 days. In how many days can A alone do the remaining work? | [
"33",
"276",
"27",
"14",
"66"
]
| Let A worked for x days.
x/21 + 4/28 = 1 => x/21 = 6/7 => x = 18
A worked for 18 days. So, A can complete the remaining work in 18 - 4 = 14 days.
Answer: D
The answer is: D | D |
mathematics | A clock shows the time as 3:30 P.m. If the minute hand gains 2 minutes every hour, how many minutes will the clock gain by 5 a.m.? | [
"23 Minutes",
"24 Minutes",
"25 Minutes",
"27 Minutes",
"None of these"
]
| if the minute hand gains 2 minutes in 1 hour the from 3:30 p.m-4:00 p.m it gains 1 min
then from 4:00p.m-4:00 a.m =13*2=26 total=27
ANSWER:D
The answer is: D | D |
mathematics | If a copier makes 5 copies every 5 seconds, then continues at this rate, how many minutes will it take to make 6,000 copies? | [
"100",
"200",
"150",
"125",
"130"
]
| 5 copies 5 seconds
6000 copies = (6000*5)/5seconds
= 6000/60 minutes
= 100 minutes
Answer : B
The answer is: B | B |
mathematics | John deposited $10,000 to open a new savings account that earned 4 percent annual interest, compounded quarterly. If there were no other transactions in the account, what was the amount of money in John’s account 6 months after the account was opened? | [
"$10,100",
"$10,101",
"$10,200",
"$10,201",
"$10,400"
]
| Approach #1:
4 percent annual interest compounded quarterly --> 1% in 3 moths.
For the first 3 moths interest was 1% of $10,000, so $100;
For the next 3 moths interest was 1% of $10,000, plus 1% earned on previous interest of $100, so $100+$1=$101;
Total interest for 6 months was $100+$101=$201, hence balance after 6 months was $10,000+ $201=$10,201.
Answer: D.
Approach #2:
If the interest were compounded every 6 moths instead of every 3 months (quarterly) then in 6 months the interest would be 4%/2=2% of $10,000, so $200. Now, since the interest is compounded quarterly then there would be interest earned on interest (very small amount) thus the actual interest should be a little bit more than $200, only answer choice D fits.
Answer: D.
The answer is: D | D |
mathematics | Eight friends met for lunch at an expensive restaurant, and everyone decided to contribute equally to the total bill of $680. If one of the friends had a coupon for 12% off the total bill, and if each friend still contributed equally after the coupon was applied to the bill, how much did each friend pay? | [
"$90",
"$74",
"$45",
"$37",
"$35"
]
| 680 * 0,12 = 81
680 - 81 = 599
599 / 8 = 74
Answer B
The answer is: B | B |
mathematics | A man can row 30 km downstream and 20 km upstream in 4 hours. He can row 45 km downstream and 40 km upstream in 7 hours. Find the speed of man in still water? | [
"12.6",
"82.5",
"12.4",
"12.5",
"12.0"
]
| Let the speed of the man in still water be a kmph and let the speed of the stream be b kmph.
Now 30/(a + b) + 20/(a - b) = 4 and 45/(a + b) + 40/(a - b) = 7
Solving the equation, the speed of man in still water is 12.5 kmph.
Answer: D
The answer is: D | D |
mathematics | S = { 1,2,3,5,6,9}
T = { 4,5,6,7,1,3}
what is the probability that x chosen from S and y chosen from T will result x*y = even | [
"5/9",
"3/2",
"1/2",
"5/6",
"6/5"
]
| p: the probability that x*y is even, then p=1-p(x*y is odd)
p(x*y odd)=p(x odd)*p(y odd)=4/6*4/6=16/36=4/9
And p=1-4/9=5/9
Option: A
The answer is: A | A |
mathematics | A sum of money is divided among A, B, C & D in the ratio 3:5:8:9 respectively. If the share of D Rs.1872 more than the share of A, then what is the total amount of money of B & C together? | [
"Rs. 4000",
"Rs. 4056",
"Rs. 5000",
"Rs. 5050",
"Rs. 6500"
]
| Sol. Share of B + C = -3 x (5 + 8) = Rs. 4056
B
The answer is: B | B |
mathematics | A bag is filled with pennies and nickels in the ratio of 2 to 1. There are 10 nickles in the bag, how many coins are there in that bag? | [
"30",
"50",
"65",
"70",
"80"
]
| A ratio of pennies to nickels of 2 to 1 means that we can write the number of pennies and nickels in the form
number of pennies = 2x and number of nickels = x
But we know the number of nickels, 10. Hence
x = 10
The total number of coins is given by
2x + x = 3x = 3 × 10 = 30
Answer : A
The answer is: A | A |
mathematics | Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is? | [
"7",
"8.2",
"2",
"10.8",
"11.2"
]
| Answer: Option D
Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other = 140 + 160 = 300 m.
Required time = 300 * 9/250 = 54/5 = 10.8 sec
The answer is: D | D |
mathematics | If X = the product of eight distinct prime numbers, how many factors does X have besides 1 and itself? | [
"166",
"188",
"210",
"232",
"254"
]
| Since X has 8 distinct prime factors, X has a total of 2^8 = 256 factors.
Besides 1 and itself, X has 254 factors.
The answer is E.
The answer is: E | E |
mathematics | A watch which gains 5 seconds in 3 minutes was set right at 7 a.m. In the afternoon of the same day, when the watch indicated quarter past 4 o'clock, the true time is: | [
"4 am",
"4 pm",
"5 am",
"6 am",
"6 pm"
]
| time 7 am to 4.15 pm = 37/4
37/720 hrs 1/20==>37/4
clock(1/20*720/37*37/4)= 9 hrs after 7 am
==> 4 pm
ANSWER B
The answer is: B | B |
mathematics | A student has to obtain 35% of the total marks to pass. He got 100 marks and failed by 40 marks. The maximum marks are? | [
"280",
"400",
"420",
"480",
"520"
]
| Let the maximum marks be x
Then, 35% of x = 100+40
35x/100 = 140
35x= 140*100= 14000
x = 400
Answer is B
The answer is: B | B |
mathematics | Mr. Kramer, the losing candidate in a two-candidate election, received 942,568 votes, which was exactly 42 percent of all votes cast. Approximately what percent of the remaining votes would he need to have received in order to have won at least 50 percent of all the votes cast? | [
"10%",
"12%",
"14%",
"17%",
"20%"
]
| Let me try a simpler one.
Lets assume that candidate got 42% votes and total votes is 100.
Candidate won = 42
Remaining = 58
To get 50%, candidate requires 8 votes from 100 which is 8% and 8 votes from 58.
8/58 = .137 = 13.7%
Which is approx 14%. Hence the answer is C.
The answer is: C | C |
mathematics | Ayush was born two years after his father's marriage. His mother is five years younger than his father but 20 years older than Ayush who is 10 years old. At what age did the father get married ? | [
"23 years",
"25 years",
"33 years",
"35 years",
"37 years"
]
| Explanation:
Ayush's present age = 10 years.
His mother's present age = (10 + 20) years = 30 years.
Ayush's father's present age = (30 + 5) years = 35 years.
Ayush's father's age at the time of Ayush's birth = (35 - 10) years = 25 years.
Therefore Ayush's father's age at the time of marriage = (25 - 2) years = 23 years.
Answer: A) 23 year
The answer is: A | A |
mathematics | Anand and Deepak started a business investing Rs. 500 and Rs. 600 respectively. Out of a total profit of Rs. 420. Deepak's share is? | [
"s. 220.01",
"s. 450.20",
"s. 845.01",
"s. 320.01",
"s. 229.09"
]
| Ratio of their shares = 500 : 600 = 5 : 6
Deepak's share = Rs. (420* 6/11) = Rs. 229.09 ANSWER "E
The answer is: E | E |
mathematics | In how many ways can 6 apples (identical) be distributed among 3 children? (Some children may get no apples.) | [
"32",
"34",
"36",
"28",
"30"
]
| Generalised form for n = number of identical objects, and r = number of children is n+r-1Cr-1.
n=6 r= 3
8C2 =28
Answer : D
The answer is: D | D |
mathematics | 350 is increased by 50%. Find the final number. | [
"725",
"625",
"225",
"525",
"425"
]
| Explanation
Final number = Initial number + 50%(original number) = 350 + 50%(350) = 350 + 175 = 525.
Answer D
The answer is: D | D |
mathematics | A 110 cm long wire is to be cut into two pieces so that one piece will be 2/5th of the other, how many centimeters will the shorter piece be? | [
"35",
"20",
"47",
"36",
"31"
]
| 1: 2/5 = 5: 2
2/7 * 110 =31
Answer:E
The answer is: E | E |
mathematics | Line m lies in the xy-plane. The y-intercept of line m is -2, and line m passes through the midpoint of the line segment whose endpoints are (2, 4) and (6, -10). What is the slope of line m ? | [
"-3",
"1",
"-1/3",
"0",
"Undefined"
]
| Ans: B
Solution: line m goes through midpoint of (2, 4) and (6, -10). midpoint is (4,-3)
as we can see that the y axis of intercept point is (0,-2) means line m is parallel to x axis
slope M= 1
Ans: B
The answer is: B | B |
mathematics | There are a lot of houses such that the numbers of their doorplates are odd numbers and the first number of the doorplates is 445, the last number of the doorplates is 705. How many houses are there? | [
"141",
"111",
"121",
"131",
"101"
]
| So it starts from 445 and goes like 447, 449,...... 705. and both first and last number are inclusive. Since every other number is odd, it's just 1/2 of the numbers and since it starts with an odd and ends with an odd inclusive add one to the result.
i.e., ([705-445][/2]+1 = 131
Ans D
The answer is: D | D |
mathematics | There are 50 girls in a dance group in a private school. 30% of them dance hip hop and 80% dance ballet. How many of them dance both hip hop or ballet? | [
"5",
"10",
"15",
"20",
"25"
]
| The total number of girls in the class is n = 50.
The number of girls dancing hop hop is 30% of it, thus
n (A)=30/100×50=30/2=15.
The number of girls dancing ballet is 80%, thus
n (B)=80/100×50=80/2=40.
In order to calculate the number of girls dancing both hip hop and ballet we can use the following equation:
n (AnB)=n (A)+n (B) -n =15+40-50=5.
So, 5 girls in this dance class dance both hip hop and ballet.
ANSWER: A
The answer is: A | A |
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