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mathematics | A man swims downstream 72 km and upstream 45 km taking 9 hours each time; what is the speed of the current? | [
"1.9",
"1.5",
"1.1",
"1.3",
"1.2"
] | 72 --- 9 DS = 8
? ---- 1
45 ---- 9 US = 5
? ---- 1 S = ?
S = (8 - 5)/2 = 1.5
Answer: B
The answer is: B | B |
mathematics | which number need to add to 859622 to get a number exactly divisible by 456? | [
"389999",
"543248",
"798790",
"795320",
"859622"
] | Dividend = Quotient * Divisor + Reminder
859622 / 456 gives quotient = 1885 and reminder = 62.
So, the next number divisible by 456 is 456 places infront of 456 * 1885
Which means 456 – 62 = 394 should be added to 859622.
E
The answer is: E | E |
mathematics | John bought a total of 12 Mangoes and Oranges. Each Mango costs 80 cents and each orange costs 50 cents. If the average price of the 12 mangoes and oranges that John originally purchased was 65 cents, then how many oranges needs to return to raise the average price of his purchase to 72 cents? | [
"4",
"5",
"6",
"7",
"8"
] | Let number of mangoes be x, number of oranges be 12-x
0.80x +(12-x)0.50/12 = 0.65
solving for x, we get x = 6 --> Mangoes 6, Oranges 6
Now, number of oranges to be returned be y
[0.80*6 + (6-y)*0.50]/12-y = 0.72
solving for y, y = 4
Ans: A
The answer is: A | A |
mathematics | A committee has 5 men and 6 women. What are the number of ways of selecting 2 men and 3 women from the given committee? | [
"202",
"200",
"209",
"207",
"201"
] | The number of ways to select two men and three women = ⁵C₂ * ⁶C₃
= (5 *4 )/(2 * 1) * (6 * 5 * 4)/(3 * 2)
= 200
Answer:B
The answer is: B | B |
mathematics | If the selling price is doubled,the profit is tripled,what is the percentage of profit?? | [
"50%",
"100%",
"150%",
"200%",
"250%"
] | Let the profit be 10, then
SP-CP=10 and 2SP-CP=30
Solving the above equations we get SP=20 and CP=10, so CP=Profit
Hence the answer is B (100%)
The answer is: B | B |
mathematics | A Private Limited company have 20 staffs and they celebrated one festival. Director gives Rs.10000/- to his accountant and told him to 4500/- to each staff Rs. 2000/- each to cleaning staff and cooking staff and balance for you. Then how much amount accountant received? | [
"10500",
"20000",
"4500",
"6500",
"5000"
] | Total amount paid for 20 Staffs : 4500 * 19= 85500/-
Paid to Cleaning & Cooking Staff : 2000/- * 2 = 4000/-
Total amount paid for both : 85500/- + 4000/- =89500/-
Balance with Accountant : 100000 - 89500 = 10500/-
Answer is (A)
The answer is: A | A |
mathematics | If both 112 and 33 are factors of the number a * 43 * 62 * 1311, then what is the smallest possible value of a? | [
"121",
"3267",
"363",
"33",
"None of the above"
] | Explanatory Answer
Step 1: Prime factorize the given expression
a * 43 * 62 * 1311 can be expressed in terms of its prime factors as a * 28 * 32 * 1311
Step 2: Find factors missing after excluding 'a' to make the number divisible by both 112 and 33
112 is a factor of the given number.
If we do not include 'a', 11 is not a prime factor of the given number.
If 112 is a factor of the number, 112 should have been in 'a'
33 is a factor of the given number.
If we do not include 'a', the number has only 32 in it.
Therefore, if 33 has to be a factor of the given number 'a' has to contain 31 in it.
Therefore, 'a' should be at least 112 * 3 = 363 if the given number has 112 and 33 as its factors.
The smallest value that "a" can take is 363.
Choice C is the correct answer.
The answer is: C | C |
mathematics | The simple interest on 200 for 7 months at 5 paise per rupee per month is | [
"70",
"7",
"35",
"30.5",
"None of these"
] | ∵ Rate = 5 paise per rupee = 5%
∴ S.I. = 200×5×7/100=70
Answer A
The answer is: A | A |
mathematics | Working simultaneously at their respective constant rates, Machines A and B produce 800 nails in x hours. Working alone at its constant rate, Machine A produces 800 nails in q hours. In terms of x and q, how many hours does it take Machine B, working alone at its constant rate, to produce 800 nails? | [
"x/(x+y)",
"y/(x+y)",
"xy/(x+y)",
"xy/(x-y)",
"xq/(q-x)"
] | Pick some smart numbers for x and q.
Say x=1 hour and q=2 hours (notice that q must be greater than x, since the time for machine A to do the job, which is q hours, must be more than the time for machines A and B working together to do the same job, which is x hours).
In this case, the time needed for machine B to do the job must also be 2 hours: 1/2+1/2=1.
Now, plug x=1 and q=2 in the options to see which one yields 2. Only option E fits.
Answer: E.
The answer is: E | E |
mathematics | For a particular American football game, the probability of a team's quarterback throwing a completed pass on each throw is 3/10. What is the least number of times that the quarterback should throw the ball that will increase the probability of getting a completed pass at least once to more than 50%. | [
"10",
"5",
"2",
"3",
"1"
] | Rule of Subtraction: P(A) = 1 - P(A')
Rule of Multiplication: P(A ∩ B) = P(A) P(B)
The probability that the quarterback throws a completed pass at least once in 2 throws is 1- (7/10)^2 = 1 - 49/100 = 51/100 > 50%
Answer: C
The answer is: C | C |
mathematics | In 1998 the profits of company N were 10 percent of revenues. In 1999, the revenues of company N fell by 30 percent, but profits were 16 percent of revenues. The profits in 1999 were what percent of the profits in 1998? | [
"80%",
"105%",
"120%",
"112%",
"138%"
] | 0,112R = x/100*0.1R
Answer D
The answer is: D | D |
mathematics | A rectangular field has area equal to 150 sq m and perimeter 50 m. Its length and breadth must be? | [
"11",
"99",
"89",
"10",
"12"
] | lb = 150
2(l + b) = 50 => l + b = 25
l – b = 5
l = 15 b = 10
Answer:D
The answer is: D | D |
mathematics | It takes Avery 2 hours to build a brick wall while Tom can do it in 4 hour. If the two start working together and after an hour Avery leaves, how much time will it take Tom to complete the wall on his own? | [
"70",
"20",
"50",
"60",
"30"
] | Avery takes 2 hours
Tom takes 4 hours
Efficiency of Avery is 1/2 units/hr
Efficiency of Tom is 1/4 units/hr
Combined efficiency of Tom and Avery is 1/2 +1/4 = 3/4 units/hr
Since they worked for 1 hour they completed 3/4 units of work and 1/4 units of work is left which is to be completed by Tom ( Since Avery left )
So Time taken by Tom to complete the remaining work will be 1/4/1/4 hours => 1*60 = 60 minutes...
Answer will be (D)
The answer is: D | D |
mathematics | If 20 men can build a water fountain 56 metres long in 7 days, what length of a similar water fountain can be built by 35 men in 3 days? | [
"40 m",
"42 m",
"47 m",
"49 m",
"50 m"
] | Explanation :
Let the required length be x metres
More men, More length built (Direct Proportion)
Less days, Less length built (Direct Proportion)
Men 20: 35
Days 7: 3 : : 56 : x
Therefore (20 x 7 x x)=(35 x 3 x 56)
x=(35 x 3 x 56)/140=42
Hence, the required length is 42 m.
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 0.3, what is the probability that Malachi will return home at the end of the day on the following Monday? | [
"0.008",
"0.125",
"0.147",
"0.512",
"0.64"
] | Re-phrasing the question:
What is the probability of: Saturday: No rain, Sunday: No rain, Monday: Rain
Probability of rain = 0.3
Therefore, probability of no rain = 0.7
0.7*0.7*0.3 = 0.147
Hence C
The answer is: C | C |
mathematics | M and N invested in a shop. The profits were divided in the ratio of 4 : 5 respectively. If M invested Rs. 40,000, the amount invested by N is: | [
"35000",
"40000",
"50000",
"60000",
"None"
] | Suppose N invested Rs. x. Then, 40000/x = 4/5 or y = [40000 x 5/ 4] = 50000.
Answer C
The answer is: C | C |
mathematics | The ratio between a and y is 7/9; a and y are increased by 4, what is the ratio between the new values of a and y? | [
"7/9",
"14/9",
"7/18",
"11/13",
"It Cannot Be Determined"
] | Ratio = 7k/9k = 7/9, 14/18, etc.
a and y are increased by 4 --> (7k + 4)/(9k + 4)
New ratio can be 11/13, 18/22, etc.
Answer: E
The answer is: E | E |
mathematics | The cross-section of a cannel is a trapezium in shape. If the cannel is 15 m wide at the top and 4 m wide at the bottom and the area of cross-section is 1900 sq m, the depth of cannel is? | [
"150",
"200",
"140",
"240",
"145"
] | 1/2 * d (15 + 4) = 1900
d = 200
Answer: B
The answer is: B | B |
mathematics | Find a sum for first 4 prime no's from number series? | [
"24",
"28",
"30",
"17",
"36"
] | Required sum = (2 + 3 + 5 + 7 ) = 17
Note: 1 is not a prime number
Option D
The answer is: D | D |
mathematics | A rectangular photograph is surrounded by a border that is 1 inch wide on each side. The total area of the photograph and the border is M square inches. If the border had been 3 inches wide on each side, the total area would have been (M + 64) square inches. What is the perimeter of the photograph, in inches? | [
"16",
"24",
"32",
"40",
"48"
] | Let x and y be the width and length of the photograph.
(x+2)(y+2)=M and so (1) xy + 2x + 2y + 4 = M
(x+6)(y+6)=M and so (2) xy + 6x + 6y + 36 = M+64
Let's subtract equation (1) from equation (2).
4x + 4y + 32 = 64
2x + 2y = 16, which is the perimeter of the photograph.
The answer is A.
The answer is: A | A |
mathematics | If the average (arithmetic mean) of a and b is 40 and the average of b and c is 60, what is the value of c − a? | [
"25",
"40",
"90",
"140",
"It cannot be determined from the information given."
] | -(a + b = 80)
b + c=120
c-a=40
B. 40
The answer is: B | B |
mathematics | A person can walk at a constant rate of 8mph and can bike at a rate of 32mph. If he wants to travel 80 miles in 4 hours using bike and walking at their constant rates, how much distance would he require to walk? | [
"20",
"30",
"48",
"60",
"72"
] | Total distance = 80
Distance = Speed * Time
Walking speed = s1 = 8
Walking time = t1
Bike speed = s2 = 32
Time traveled in bike = t2
d1 + d2 = 80
s1t1 + s2t2 = 80
8*t1 + 32*t2 = 80
t1 + 4*t2 = 10 ----- (1)
Given: t1 + t2 =4 ----- (2)
(1) - (2) -->3 t2 = 6 , t2=2 and t1 = 8 - 2 = 6
Walking distance = s1*t1 = 8*6 = 48
Answer: C
The answer is: C | C |
mathematics | If the sales tax reduced from 3 1/2 % to 3 1/3%, then what difference does it make to a person who purchases an article with market price of Rs. 8400 ? | [
"Rs.10",
"Rs.12",
"Rs.14",
"Rs.16",
"Rs.18"
] | Required difference = [3 ½ % of Rs.8400] – [3 1/3 % of Rs.8400]
= [(7/20-(10/3)]% of Rs.8400 =1/6 % of Rs.8400
= Rs. [(1/6)8(1/100)*8400] = Rs. 14.
Option C
The answer is: C | C |
mathematics | Two trains are traveling from point A to point B such that the speed of first train is 65 kmph and the speed of 2 train is 29 kmph. Where is the distance b/w A and B such that the slower train reached 5 hrs late compared to the faster? | [
"3",
"65",
"9",
"5",
"31"
] | Answer:B
The answer is: B | B |
mathematics | Which of the following can be a perimeter r of a triangle inscribed in a circle of radius 1?
I. 0.001
II. 0.010
III. 0.100 | [
"I only",
"III only",
"II and III only",
"I, II, and III",
"Not I, II, or III"
] | Yes,the length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.
But how do you use the above property to solve the question?
The lower limit of the perimeter of an inscribed triangle in a circle of ANY radius is 0: r>0.
Answer is D.
The answer is: D | D |
mathematics | 1,3,6,10,15,? | [
"17",
"18",
"19",
"20",
"21"
] | 1 =1
1+2 = 3
3+3 = 6
6+4 = 10
10+5 = 15
15+6 = 21
ANSWER:E
The answer is: E | E |
mathematics | Solve the following quadratic equation by factoring.
x2-5x-14=0 | [
"-2,7",
"2,-7",
"1,8",
"1,-8",
"2,6"
] | We already have zero on one side of the equation, which we need to proceed with this problem. Therefore, all we need to do is actually factor the quadratic.
(x+2)(x-7)=0
x=-2 and x=7
ANSWER A
The answer is: A | A |
mathematics | In what time will a train 80 m long cross an electric pole, it its speed be 144 km/hr? | [
"2.0 sec",
"2.8 sec",
"7.5 sec",
"2.3 sec",
"1.5 sec"
] | Speed = 144 * 5/18
= 40 m/sec
Time taken = 80/40
= 2.0 sec.
Answer:A
The answer is: A | A |
mathematics | The sum of the ages of 4 children born at the intervals of 1 years each is 12 years. what is the age of the youngest child ? | [
"2.5",
"1.5",
"1",
"3.5",
"4.5"
] | Let x = the youngest child. Each of the other four children will then be x+1, x+2, x+3
We know that the sum of their ages is 12
so, x+(x+1)+(x+2)+(x+3) = 12
therefore The youngest child is 1.5 years old
Answer: B
The answer is: B | B |
mathematics | A, B and C enter into partnership. A invests some money at the beginning, B invests double the amount after 6 months, and C invests thrice the amount after 8 months. If the annual gain be Rs.21000. A's share is? | [
"2999",
"2778",
"7000",
"2889",
"6612"
] | x* 12 : 2x* 6: 3x* 4
1:1:1
1/3 * 21000 = 7000
Answer:C
The answer is: C | C |
mathematics | A merchant has selected two items to be placed on sale, one of which currently sells for 45 percent less than the other. If he wishes to raise the price of the cheaper item so that the two items are equally priced, by what percentage must he raise the price of the less expensive item? | [
"100 %",
"90%",
"80%",
"70%",
"60%"
] | Expensive item = $100;
Cheap item = $55;
We must increase $55 to $100, so by $45, which is approximately 80% increase: (100-55)/55 = 3/7 = ~0.81.
Answer: C.
The answer is: C | C |
mathematics | The age of man is three times the sum of the ages of his two sons.Five years hence,his age will be double of the sum of the ages of his sons.The father’s present age is : | [
"40 years",
"45 years",
"50 years",
"55 years",
"75 years"
] | Solution
Let the sum of present ages of the two sons be x years.
Then,father's present age = 3x years.
∴ (3x + 5)=2 (x +10) ⇔ 3x + 5 = 2x + 20 ⇔ x =15.
Hence,father's present age = 45 years. Answer B
The answer is: B | B |
mathematics | Current ages of Rahim and Thomas are in the ratio of 5 : 4 correspondingly. 0.5 decades hence, the ratio of their ages will become 11 : 9 correspondingly, What is Thomas’s current age in years? | [
"24 years",
"44 years",
"34 years",
"40 years",
"84 years"
] | 40 years
If current ages of Rahim and Thomas be 5A years and 4A years correspondingly
Then, 5A + 5 = 11
4A + 5 = 9
9(5A + 5)=11(4A + 5)
A = 10
Thomas’s current age = 4A
= 40 years.
D
The answer is: D | D |
mathematics | Three students appear at an examination of Mathematics. The probability of their success are 1/3, 3/4, 1/5 respectively. Find the probability of success of at least two. | [
"11/30",
"12/50",
"13/30",
"3/50",
"4/50"
] | The probability of success of at least two students will involve the following possibilities.
The first two students are successful, the last two students are successful, the first and third students are successful and all the three students are successful.
Therefore, the required probability = 1/3 x 3/4 x 4/5 + 3/4 x 1/5 x 2/3 + 1/3 x 1/5 x 1/4 + 1/3 x 3/4 x 1/5 = 11/30
ANSWER:A
The answer is: A | A |
mathematics | A group consists of 4 men, 6 women and 4 children. In how many ways can 2 men , 3 women and 1 child selected from the given group? | [
"400",
"480",
"287",
"278",
"281"
] | Explanation:
Two men, three women and one child can be selected in â´Câ‚‚ * â¶C₃ * âµCâ‚ ways
= (4 * 3)/(2 * 1) * (6 * 5 * 4)/(3 * 2) * 4
= 480 ways.
Answer:B
The answer is: B | B |
mathematics | If 893 × 78 = p, which of the following is equal to 893 × 79? | [
"p + 1",
"p + 78",
"p + 79",
"p + 893",
"p + 894"
] | Since 893 × 78 = p and 79=78+1, we have 893 × 79 = 893 ×(78+1)=893×78 + 893 ×1 = p + 893.
The answer is (D).
The answer is: D | D |
mathematics | The compounded ratio of (2 : 3), (6: 11) and (11 :2) is : | [
"1:2",
"5:9",
"2:1",
"11:24",
"None"
] | Answer: Option C
2/3 : 6/11 : 11/2 = 2:1
The answer is: C | C |
mathematics | A person borrows 20000 for 6 years at 8% p.a. simple interest. He immediately lends it to another person at 9 % p.a. for 6 years. Find his gain in the transaction per year. | [
"200",
"250",
"210",
"190",
"180"
] | Gain in 6 years
= [(20000×9×6/100)−(20000×6×8/100)]
= (10800 – 9600) = 1200
∴ Gain in 6 year = (1200/6) = 200
Answer A
The answer is: A | A |
mathematics | After spending Rs. 5000 on rent, Rs. 1500 on milk, Rs. 4500 on groceries, Rs.2500 On childrens education Rs. 2000 on petrol and Rs. 2500 on miscellaneous expenses, Mr. Kishore saved 10% of his monthly salary. How much did he save in Rs. ? | [
"2160",
"2350",
"2000",
"2300",
"None of these"
] | Explanation :
Total Exp = 5000+1500+4500+2500+2000+2500 = 18000
Exp in % = 100-10 = 90%, 18000 = 90%
Saving = 10 % = 18000 X 10/90 = Rs. 2000
Answer : C
The answer is: C | C |
mathematics | If the simple interest on a sum of money at thirteen percent per annum for two years is Rs.22400, compound interest on the same sum for the same period at the same rate of interest is | [
"28,356.00",
"25,638.00",
"23,856.00",
"23,685.00",
"25,865.00"
] | S I for 2 years = 22400 ie for one year =11200
The compound interest for Rs.11200 for the second year = 11200*13/100 = 1456
The CI for two years 22400+1456 = 23,856.00
ANSWER:C
The answer is: C | C |
mathematics | 24 oz of juice P and 25 oz of juice E are mixed to make smothies X and Y . The ratio of p to E in smothie X is 4 is to 1 and that in Y is 1is to 5.How many ounces of juice P are contained in the smothie X? | [
"5",
"10",
"15",
"20",
"25"
] | Easy way to solve this question is start from the answer and then conform the information provided in the question.
we can start from option D i.e 20 ... as a quantity of juice P in X because it is the only one option that gets divided by 4 is 20 ... since in the X the juice P to E ratio is 4:1
this gives us that quantity of juice P in X = 20 therefore quantity of Juice E will be 5 ... hence ratio = 4:1
This will lead to quantity of juice P in X = 4 and quantity of Juice E = 20 ... hence ratio 1:5
if we calculate total Juice P = 24 and total of juice V = 25
it fits because totals are same as what mentioned in the question ...
thus ans is D
The answer is: D | D |
mathematics | 240 is increased by 20%. Find the final number. | [
"200",
"210",
"180",
"288",
"220"
] | Explanation
Final number = Initial number + 20%(original number) = 240 + 20%(240) = 240 + 48 = 288.
Answer D
The answer is: D | D |
mathematics | In some quantity of ghee, 60% of pure ghee and 40% of is vanaspati. If 10kg of pure ghee is added, then the strength of vanaspati ghee becomes 20%. The original quantity was? | [
"5kg",
"10kg",
"15kg",
"20kg",
"25kg"
] | Let the original quantity be x kg
vanaspati ghee in x kg = 40/100 *x = 2x/5 kg
(2x/5)/(x+10) = 20/100
2x/(5x+50) = 1/5
5x = 50
x = 10kg
Answer is B
The answer is: B | B |
mathematics | From a container having pure milk, 10% is replaced by water and the process is repeated twice. At the end of the second operation, the milk is? | [
"50%",
"60%",
"55%",
"75%",
"81%"
] | Let the total quantity of original milk = 1000gm
Milk after 1st operation = 90% of 1000 = 900gm
Milk after second operation = 90% of 900 = 810gm
Strength of final mixture = 81%
Answer is E
The answer is: E | E |
mathematics | Calculate the fourth proportional to 5.2, 6.6 and 9.1? | [
"19.55",
"10.55",
"11.55",
"10.2",
"12.5"
] | Explanation:
Formula = Fourth propotional = (b × c)/a
A = 5.2 , B = 6.6 and C = 9.1
(6.6 × 9.1)/5.2 = 11.55
Answer: Option C
The answer is: C | C |
mathematics | A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 4 liters per minute. When the tank is full in inlet is opened and due to the leak the tank is empties in 8 hours. The capacity of the tank is? | [
"5768",
"5760",
"5762",
"5766",
"5712"
] | 1/x - 1/6 = -1/8
x = 24 hrs
24 * 60 * 4 = 5760
Answer: B
The answer is: B | B |
mathematics | A man counted his animals, 80 heads and 270 legs (ducks and goats). how many goats are there? | [
"30",
"40",
"50",
"60",
"55"
] | let no of ducks=d and no of goat=g
d+g=80(heads)----------> eq 1
each duck has 2 legs and goat has 4 legs
2d+4g=270 and divide 2d+4g=270 by 2 we get d+2g=135 -----------> eq2
subtract eq1 from eq2
we get no of goats=55
ANSWER:E
The answer is: E | E |
mathematics | Difference between the length &breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is? | [
"2400 m^2",
"2500 m^2",
"2520 m^2",
"2560 m^2",
"2580 m^2"
] | Solving the two equations, we get: l = 63 and b = 40.
Area = (l x b) = (63 x 40) m2 = 2520 m^2
C
The answer is: C | C |
mathematics | A chair is bought for Rs.600/- and sold at a loss of 10% find its selling price | [
"Rs.500/-",
"Rs.540/-",
"Rs.600/-",
"Rs.640/-",
"Rs.660/-"
] | 100 % ------> 600 (100 * 6 = 600)
90 % ------> 540 (90 * 6 = 540)
Selling price = Rs.540/-
B
The answer is: B | B |
mathematics | Two trains start simultaneously from opposite ends of a 160-km route and travel toward each other on parallel tracks. Train X, traveling at a constant rate, completes the 160-km trip in 5 hours. Train Y, travelling at a constant rate, completes the 160-km trip in 3 hours. How many kilometers had Train X traveled when it met Train Y? | [
"56",
"58",
"60",
"62",
"64"
] | If the two trains cover a total distance D, then Train X travels (3/8)*D while Train Y travels (5/8)*D. If the trains travel 160 km to the meeting point, then Train X travels (3/8)*160 = 60 km. The answer is C.
The answer is: C | C |
mathematics | The diagonal of the floor of a rectangular closet is 7 feet. The shorter side of the closet is 4 feet. What is the area of the closet in square feet? | [
"26",
"27",
"28",
"29",
"32"
] | Other side =
15 2 - 9 2
2 2
ft
=
225 - 81
4 4
ft
=
144
4
ft
= 6 ft.
Area of closet = (6 x 4.5) sq. ft = 27 sq. ft.
B)
The answer is: B | B |
mathematics | Doug, who runs track for his high school,
was challenged to a race by his younger
brother, Matt. Matt started running first,
and Doug didn’t start running until Matt
had finished a quarter-mile lap on the
school track. Doug passed Matt as they
both finished their sixth lap. If both boys
ran at a constant speed, with Doug running
2 miles an hour faster than Matt, what was
Matt’s speed? | [
"10.5 miles per hour",
"10 miles per hour",
"9 miles per hour",
"8 miles per hour",
"7.5 miles per hour"
] | Doug runs 2 miles an hour faster than Matt, so let Matt’s speed equal x miles per hour.
Then Doug’s speed equals x + 2 miles per hour. Each lap is one-quarter of a mile, so Doug
runs 1.5 miles in the time it takes Matt to run 1.25 miles. Place this information in a chart:
DOUGH RATE:x-2 TIME:1.5/1 DISTANCE:1.5
MATT RATE:X TIME:1.25/X DISTANCE:1.25
The two boys took the same amount of time from the time Doug started, so make an
equation by setting the two times in the chart equal to each other, and then solve for x:
1.5/X+2=1.25/X
1.5X=1.25(X+2)
1.5X=1.25X+2.5
0.25X=2.5
X=10
So Matt ran at 10 miles per hour.
correct answer B)10 miles per hour
The answer is: B | B |
mathematics | Currently apples cost 60 cents/pound. Due to a disease affecting the apple trees it is expected that next month apples will cost 200% more than they do currently. How much are apples expected to cost next month? | [
"200 cents /pound",
"150 cents /pound",
"160 cents /pound",
"180 cents /pound",
"170 cents /pound"
] | If a new cost is p percent greater than the old cost, then (new cost) = (old cost) + (p/100)(old cost).
In this case, (new cost) = 60 cents/pound + (200/100)(60 cents/pound)
= 60 cents/pound + 120 cents/pound
= 180 cents /pound
Answer : D
The answer is: D | D |
mathematics | A candidate appearing for an examination has to secure 42% marks to pass paper I. But he secured only 60 marks and failed by 20 marks. What is the maximum mark for paper I? | [
"110",
"120",
"130",
"140",
"190"
] | he secured 60 marks nd fail by 20 marks so
total marks for pass the examinatn=80
let toal marks x
x*42/100=80
x=190
ANSWER:E
The answer is: E | E |
mathematics | If each side of a square is increased by 25%, find the percentage change in its area. | [
"26.25%",
"36.25%",
"46.25%",
"56.25%",
"66.25%"
] | Let each side of the square be a. Then, area = a2.
New side =(125a/100) =(5a/4). New area = (5a/4) 2=(25a2)/16.
Increase in area = ((25 a2)/16)-a2=(9a2)/16.
Increase% = [((9a2)/16)*(1/a2)*100] % = 56.25%.
Option D
The answer is: D | D |
mathematics | A garrison of 2000 men has provisions for 54 days. At the end of 18 days, a reinforcement arrives, and it is now found that the provisions will last only for 20 days more. What is the reinforcement? | [
"1977",
"1600",
"1979",
"1900",
"1278"
] | 2000 ---- 54
2000 ---- 36
x ----- 20
x*20 = 2000*36
x = 3600
2000
-------
1600
Answer: B
The answer is: B | B |
mathematics | Sum of the squares of three numbers is 138 and the sum of their products taken two at a time is 131. Find the sum? | [
"20",
"21",
"23",
"25",
"27"
] | (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 138 + 2* 131
a + b + c = √400 = 20
A
The answer is: A | A |
mathematics | How many numbers from 10 to 1000 are exactly divisible by 9? | [
"100",
"10",
"11",
"12",
"14"
] | 10/9 = 1 and 1000/9 = 111 ==> 111 - 1 = 100. Therefore 100
Answer : A
The answer is: A | A |
mathematics | If it takes 6 identical printing presses exactly 4 hours E to print 5,000 newspapers, how long would it take 3 of these presses to print 3,000 newspapers? | [
"3 hours, 20 minutes",
"4 hours, 20 minutes",
"4 hours, 48 minutes",
"5 hours, 48 minutes",
"6 hours, 50 minutes"
] | 6 presses - 5,000 newspapers - 4 hours ;
3 presses - 2,500 newspapers - 4 hours ;
3 presses - 3,000 newspapers - 4 hours + 1/5*4 hours = 4 hours, 48 minutes (since 2,500+1/5*2,500=3,000) = E.
Answer: C.
The answer is: C | C |
mathematics | If a(a + 5) = 6 and b(b + 5) = 6, where a ≠ b, then a + b = | [
"−5",
"−2",
"2",
"46",
"48"
] | a(a + 5) = 6 and b(b + 5) = 6
=> a, b must be integers and if a is -6 or 1, b will be 1 and -6 respectively
=> a+b = -5
Ans: A
The answer is: A | A |
mathematics | A teacher will pick a group of 5 students from a group of 9 students that includes Bart Lisa and john. If one of all the possible 5-student groups is picked at random, what is the probability of picking a group that includes john Bart and Lisa? | [
"5/97",
"3/41",
"7/41",
"5/42",
"2/21"
] | Probability = Favorable Outcomes / Total Outcomes
Total Outcomes= Total No. of ways of Picking Group of 5 out of 9 = 9C5 = 9! / (5! * 4!) = 126
Favorable Outcomes= Total No. of ways of Picking Group of 5 out of 9 such that J, B and L are always in the group (i.e. we only have to pick remaining 2 out of remaining 6 as J, B and L must be there is group) = 6C2 = 15
Hence,Probability=15/126=5/42
Answer: Option D
The answer is: D | D |
mathematics | In Township K each property is taxed at 10 percent of its assessed value. If the assessed value of a property in Township K is increased from $20,000 to $28,000, by how much will the property tax increase? | [
"$800",
"$1000",
"$600",
"$400",
"$500"
] | Increase in house value = $28,000 - $20,000 =$8000
So, tax increase = 10% of$8000=$800
Answer: A
The answer is: A | A |
mathematics | If a, b and c are even integers, which of the following could be the value of a^2 + b^2 + c^2? | [
"a)82",
"b)84",
"c)85",
"d)87",
"e)90"
] | a, b and c are even integers which means that, supposing that x, y and z are integers, then a=2x, b=2y and c=2z
Therefore we have: a^2+b^2+c^2=2^2*x^2+2^2*y+2^2*z=4x^2+4y^2+4z^2=4(x^2+y^2+z^2).
Which means that the total a^2+b^2+c^2 must be divisible by 4.
The only choice which is divisible by 4 is: B)
84=8^2+4^2+2^2
Answer: B.
The answer is: B | B |
mathematics | In an election between two candidates, the winner has a margin of 20% of the votes polled. If 1000 people change their mind and vote for the loser, the loser would have won by a margin of 20% of the votes polled. Find the total number of votes polled in the election? | [
"10000",
"5000",
"15000",
"20000",
"6000"
] | Winner - Looser
60% - 40%
If 1000 people change their mind and vote for the loser:
Winner - Looser
40% - 60%
Thus 1,000 people compose 20% of all voters, which means that the total number of votes is 5,000.
Answer: B
The answer is: B | B |
mathematics | The size of a flat-screen television is given as the length of the screen’s diagonal. How many square inches greater is the screen of a square 24-inch flat-screen television than a square 17-inch flat-screen television? | [
"143.5",
"154",
"160",
"148.75",
"142.25"
] | If we take a square with side length x and draw a diagonal, we get two isosceles right triangles.
If we focus on one such right triangle, we see that the legs have length x.
square 24-inch flat-screen television
The diagonal (hypotenuse) = 24
So, we can apply the Pythagorean Theorem to get x² + x² = 24²
Simplify: 2x² = 24²
Divide both sides by 2 to get: x² = 24²/2
Since the area of the square = x², we can see that the area of this square is 24²/2
square 17-inch flat-screen television
The diagonal (hypotenuse) = 17
So, we can apply the Pythagorean Theorem to get x² + x² = 17²
Simplify: 2x² = 17²
Divide both sides by 2 to get: x² = 17²/2
Since the area of the square = x², we can see that the area of this square is 17²/2
DIFFERENCE IN AREAS =24²/2-17²/2
= 288 -144.5 i.e = 143.5
A
The answer is: A | A |
mathematics | Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 36 kmph. In how much time will the trains cross each other? | [
"12 sec",
"13 sec",
"15 sec",
"16 sec",
"17 sec"
] | D
Relative speed = (54 + 36)* 5/18 = 5 * 5 = 25 mps.
The time required = d/s = (100 + 100 + 200)/25
= 400/25 = 16 sec.
The answer is: D | D |
mathematics | A man invested Rs. 14,400 in Rs. 100 shares of a company at 20% premium.If the company declares 6% dividend at the end of the year,then how much does he get ? | [
"Rs. 500",
"Rs. 600",
"Rs. 650",
"Rs. 720",
"None"
] | Solution
Number of shares = (14400/120) = 120.
Face value = Rs. (100x120 ) = Rs. 12000.
Annual income = Rs.(6/100x12000) = Rs. 720.
Answer D
The answer is: D | D |
mathematics | The probability of Sam passing the exam is 1/4. The probability of Sam passing the exam and Michael passing the driving test is 1/3. What is the probability of Michael passing his driving test? | [
"1/24.",
"1/2.",
"1/3.",
"2/3.",
"2/5"
] | 1/3 *1/m= 1/6 , 1/m = 1/2
Answer B
The answer is: B | B |
mathematics | From 6 positive numbers and 6 negative numbers, how many groups S of 4 numbers, yielding a positive product, can be formed? | [
"720",
"625",
"30",
"960",
"255"
] | Potential combinations of 4 numbers that will yield positive product
++++ 4C6
---- 4C6
++-- 2C6*2C6
4C6 + 4C6 + 2C6*2C6
S=15 +15 + 15*15 = 255=E
The answer is: E | E |
mathematics | A 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform? | [
"350",
"289",
"208",
"270",
"287"
] | Speed = [300 / 18] m/sec = 50/3 m/sec.
Let the length of the platform be x meters.
Then, x + 300 / 39 = 50/3
3(x + 300) = 1950 è x
= 350m.
Answer: A
The answer is: A | A |
mathematics | The average temperature of Monday, Tuesday, Wednesday and Thursday was 38∘ and that of Tuesday, Wednesday, Thursday and Friday was 40∘. If the temperature on Monday was 36∘, the temperature of Friday was : | [
"44∘",
"40∘",
"38∘",
"30∘",
"None of these"
] | Explanation:
M+T+W+Th=(4×38)=152
Monday temperature is 36. So T+W+Th=(152-36)=116
T+W+Th+F=(4×40)=160
F = (160-116)=44∘
Correct Option: A
The answer is: A | A |
mathematics | Find the value of * in the following
(1 5/3) ÷ 3/11 × */11 = (2 2/3 × 7/5 × 6/7) | [
"2.7",
"3",
"3.6",
"4.5",
"4.7"
] | Option 'C'
The answer is: C | C |
mathematics | From the integer n, if n*n is odd, then what is true from below options? | [
"n is odd",
"n*n*n is even",
"n is even and n*n*n is even",
"n is even",
"All of the above"
] | n is odd
Option A
The answer is: A | A |
mathematics | A, B and C completed a piece of work, A worked for 6 days, B for 9 days and C for 4 days. Their daily wages were in the ratio of 3:4:5. Find the daily wages of C, if their total earning was Rs.1628? | [
"s.109",
"s.108",
"s.110",
"s.103",
"s.102"
] | 3x 4x 5x
6 9 4
18x + 36x + 20x = 1628
74x = 1628 => x = 22
5x = 110 Rs.
Answer:C
The answer is: C | C |
mathematics | A drawer has six loose blue socks and six loose white socks. If four socks are removed from the drawer at random and without replacement. What is the probability that one pair of each color was selected? | [
"2/33",
"5/66",
"5/33",
"5/11",
"1/2"
] | No of Loose blue socks = 6 (3 pairs)
No. of Loose white Socks = 6 (3 pairs)
total no. of blue and white socks = 12
Total no. of socks to be selected = 4
So we have C (12,4) = no of ways the socks can be selected = 495
No of ways One pair of blue socks is selected ( 2 blue socks) , C (6,2) , No of ways one pair of white socks can be selected C (6,2) ..Because we have to find a scenario where EXACTLY one pair of Blue socks and ONE pair of WHITE socks is selected we will multiply the two .. ie 15 x 15 ..
Filling the information in the Probability formula we get P (A) = (15 x 15) / 495 = 5 /11
ANSWER : (D)
The answer is: D | D |
mathematics | A train 330 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going? | [
"5",
"6",
"7",
"18",
"9"
] | Speed of train relative to man = 60 + 6 = 66 km/hr.
= 66 * 5/18 = 55/3 m/sec.
Time taken to pass the men = 330 * 3/55 = 18 sec.
Answer: Option D
The answer is: D | D |
mathematics | The length and breadth of a rectangular courtyard is 75 m and 32 m. Find the cost of leveling it at the rate of $3 per m2. Also, find the distance covered by a boy to take 4 rounds of the courtyard. | [
"3573",
"3455",
"8600",
"7000",
"7200"
] | Length of the courtyard = 75 m
Breadth of the courtyard = 32 m
Perimeter of the courtyard = 2 (75 + 32) m
= 2 × 107 m
= 214 m
Distance covered by the boy in taking 4 rounds = 4 × perimeter of courtyard = 4 × 214 = 856 m
We know that area of the courtyard = length × breadth
= 75 × 32 m2
= 2400 m2
For 1 m2, the cost of levelling = $3
For 2400 m2, the cost of levelling = $3 × 2400 = $7200 ANSWER : E
The answer is: E | E |
mathematics | Suppose you have access to a large vat of distilled water, several gallons large. You have two precise measuring pipettes, one to measure exactly 1/5 of an ounce and one to measure exactly 1/6 of an ounce. You can pour precisely measured amounts into a beaker, which initially is empty. You can use either pipette to remove distilled water from the vat or from the beaker and use either pipette to dispense water into either of those receptacles, but you cannot use either pipette to take any quantity of distilled water other than the amount for which it is designed. Which of the following represents, in ounces, a precise amount of distilled water you can transfer from the vat to the beaker?
I. 1/6
II. 1/7
III. 1/12 | [
"I only",
"III only",
"1/30 and 11/30",
"II and III only",
"I, II, and III"
] | 1/5-1/6=1/30
1/5+1/6=11/30
Answer: C
The answer is: C | C |
mathematics | Which of the following are roots of an equation (x^-2)-(2x^-1)-35=0 | [
"1/5 and -1/7",
"-1/5 and 1/7",
"1/5 and 1/7",
"-1/5 and -1/7",
"-5/2 and -1/7"
] | Given: (x^-2) - (2x^-1) - 35 = 0
Rewrite as: 1/(x²) - 2/x - 35 = 0
Remove fractions by multiplying both sides by x² to get: 1 - 2x - 35x² = 0
Rearrange to get: 35x² + 2x - 1 = 0
Factor to get: (5x + 1)(7x - 1) = 0
So, EITHER 5x + 1 OR 7x - 1 = 0
If 5x + 1 = 0, then x = -1/5
If 7x - 1 = 0, then x = 1/7
So, the roots (solutions) are -1/5 and 1/7
The answer is B.
The answer is: B | B |
mathematics | Christine selects an item at a 25% off ticket price sale. The item is ticket priced at $25. How much should Christine expect to pay at the register? | [
"22.5",
"20.0",
"18.75",
"12.5",
"10.0"
] | R.P.=$25.00
Sale%=25
S.P.=R.P.*(1-(Sale%/100))=25*(1-(25/100))=18.75
ANSWER:C
The answer is: C | C |
mathematics | Find the compound interest on $ 10,000 in 2 years at 4% per annum, the interest being compounded half-yearly | [
"824",
"824.36",
"824.32",
"824.24",
"824.26"
] | Principal = $ 10000; Rate = 2% per half-year; Time = 2 years = 4 half-years.
Amount = $ [10000 * (1+(2/100))4] = $(10000 * (51/50) * (51/50) * (51/50) * (51/50))
= $ 10824.32.
:. C.I. = $ (10824.32 - 10000) = $ 824.32.
Answer C.
The answer is: C | C |
mathematics | An alloy is to contain copper and zinc in the ratio 9:4. The zinc required to be melted with 24kg of copper is? | [
"12kg",
"8.3kg",
"10.7kg",
"15.5kg",
"7kg"
] | Let the required quantity of copper be x kg
9:4::24:x
9x = 4*24
x = 10 2/3 kg = 32/3 = 10.7kg
Answer is C
The answer is: C | C |
mathematics | What is the probability of flipping a fair coin three times and the coin landing on heads on exactly one flip? | [
"3/8",
"5/8",
"7/8",
"1/8",
"1/4"
] | Probability = (Favorable combination)/(Total combination)
Favorable combination = (HTT, TTH, THT) ==> 3
Total combination = 8 (2^3)
Probability = (3)/(8)
(A)
The answer is: A | A |
mathematics | When a certain number X is divided by 66, the remainder is 14. What is the remainder when X is divided by 11? | [
"2",
"3",
"7",
"9",
"10"
] | Let possible value of x is 80
least possible value of x/11 is 80/11 =>7 quotient with remainder 3
Thus answer is (B) 3
The answer is: B | B |
mathematics | The area of a square is equal to 2 times the area of a rectangle of dimensions 8 cm * 64 cm. What is the perimeter of the square? | [
"482",
"268",
"800",
"128",
"632"
] | Area of the square = s * s = 2(8 * 64)
=> s = 4 * 8 = 32 cm
Perimeter of the square = 4 * 32 = 128 cm.
Answer: D
The answer is: D | D |
mathematics | A boat crossed a lake from North to East at the speed of 7 km/h, entered a river and covered twice as much distance going upstream at 6 km/h. It then turned around and stopped at the south shore of the lake. If it averaged 3.8 km/h that day, what was its approximate downstream speed? | [
"4",
"5",
"6",
"7",
"8"
] | One way of solving this is:
Speed of boat on still water (lake)=7kmph
Speed upstream = 6kmph = speed in still water - speed of river => speed of river = 1kmph
=>Speed downstream = speed in still water + speed of river = 7+1 =8kmph
Ans is E
The answer is: E | E |
mathematics | A certain country had a total annual expenditure of $1.2x10^12. If the population of the country was 240 million last year, what was the per capita expenditure? | [
"$500",
"$1000",
"$2000",
"$3000",
"$5000"
] | Explanation:
In scientific notation 240 million is 2.4x10^8. So the per capita expenditure was:
($1.2x10^12)/(2.4x10^8)=($1.2)/(2.4)x10^12-8=$0.5x10^4=$5000
Answer: Option E
The answer is: E | E |
mathematics | Evaluate 20% of 450 + 45% of 200 | [
"232",
"242",
"252",
"262",
"180"
] | Explanation:
= (20/100) * 450 + (45/100) * 200
= 180
Option E
The answer is: E | E |
mathematics | A farmer has an apple orchard consisting of Fuji and Gala apple trees. Due to high winds this year 10% of his trees cross pollinated. The number of his trees that are pure Fuji plus the cross-pollinated ones totals 170, while 3/4 of all his trees are pure Fuji. How many of his trees are pure Gala? | [
"30",
"33",
"55",
"77",
"88"
] | Let f = pure fuji , g = pure gala and c - cross pollinated.
c = 10% of x where x is total trees.
c = .1x
also 3x/4 = f and c+f = 170 => .1x + 3/4x = 170 => x = 200
200 - 170 = pure gala = 30.
Answer A
The answer is: A | A |
mathematics | An industrial loom weaves 1.14 meters of cloth every second. Approximately, how much time will it take to weave 52 meters of cloth ? | [
"29.32 sec",
"42.51 sec",
"39.25 sec",
"45.61 sec",
"None of these"
] | Explanation:
Given loom weaves 1.14 mts of cloth in one second then 52 mts of cloth can be weaved by loom in,
1.14 ----- 1
52.0 ------?
=> 52/1.14 = 45.61 sec
Answer IS D
The answer is: D | D |
mathematics | A motorcyclist goes from Bombay to Pune, a distance of 160 kms at an average of 32 kmph speed. Another man starts from Bombay by car 2 ½ hours after the first, and reaches Pune ½ hour earlier. What is the ratio of the speed of the motorcycle and the car? | [
"1:2",
"2:5",
"1:4",
"1:1",
"1:6"
] | T = 160/32 = 5 h
T = 5 - 3 = 2
Time Ratio = 5:2 = 5:2
Speed Ratio = 2:5
Answer: B
The answer is: B | B |
mathematics | A = {0, 1, 3, 6, -8}
B = {-1, 2, -4, 7,-5}
If a is a number that is randomly selected from Set A, and b is a number that is randomly selected from Set B, what is the probability that ab > 0? | [
"1/4",
"1/3",
"2/5",
"9/25",
"1/2"
] | For the product of 2 numbers to be positive either both of them must be positive or both of them must be negative:
P(positive, positive) = 3/5*2/5 = 6/25;
P(negative, negative) = 1/5*3/5 = 3/25.
P = 6/25 + 3/25
= 9/25
Answer: D
The answer is: D | D |
mathematics | Ayesha's father was 38 years of age when she was born while her mother was 36 years old when her brother three years younger to her was born. What is the difference between the ages of her parents? | [
"2 years",
"4 years",
"5 years",
"7 years",
"8 years"
] | Mother's age when Ayesha's brother was born = 36 years.
Father's age when Ayesha's brother was born = (38 + 3) years = 41 years.
Required difference = (41 - 36) years = 5 years.
Answer: Option C
The answer is: C | C |
mathematics | A class of 40 students has an average height of 120 cm. four students whose average height is 160 cm, left the class and four others whose average height is 124 cm, joined. Calculate the new average height of the students of the class (in cm) is? | [
"292.4 cm",
"296.4 cm",
"206.4 cm",
"294.4 cm",
"236.4 cm"
] | Total height = 120 * 40 = 4800 cm.
Total height of those who left = 160 * 4 = 640
Total height of those who joined = 124 * 4 = 496
New average
= [12000 - 640 + 496 ] / 40 = 11856/40 cm.
= 296.4 cm
Answer:B
The answer is: B | B |
mathematics | A and B are two multiples of 14, and Q is the set of consecutive integers between A and B, inclusive. If Q contains 10 multiples of 14, how many multiples of 7 are there in Q? | [
"20",
"19",
"18",
"17",
"16"
] | Halfway between the multiples of 14, there will be another multiple of 7.
The total number of multiples of 7 is 10+9 = 19.
The answer is B.
The answer is: B | B |
mathematics | In a coconut grove, (x + 2) trees yield 40 nuts per year, x trees yield 120 nuts per year and (x – 2) trees yield 180 nuts per year. If the average yield per year per tree be 100, find x. | [
"3",
"4",
"5",
"6",
"7"
] | (x+2)×40+x×120+(x−2)×180/(x+2)+x+(x−2)=100
⇒ 340x−280/3x = 100
⇒ 40x = 280 ⇒ x = 7
Answer E
The answer is: E | E |
mathematics | What percent of 30 is 80? | [
"133 1⁄3",
"75",
"266.66",
"33 1⁄3",
"25"
] | To find out the % of 80 in 30
Do 80/30 = 266.66%
Answer C)
The answer is: C | C |
mathematics | In how many different number of ways 5 men and 2 women can sit on a shopa which can accommodate persons? | [
"210",
"220",
"230",
"240",
"250"
] | 7p3 = 7 × 6 × 5 = 210
A)
The answer is: A | A |
mathematics | A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is: | [
"40",
"50",
"60",
"70",
"80"
] | Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45 ==> x = 50 km/hr.
Answer: Option B
The answer is: B | B |
mathematics | The average of 25 result is 18.The average of 1st 12 of them is 14 & that of last 12 is 17.Find the 13th result. | [
"68",
"80",
"78",
"60",
"87"
] | Clearly 13th result=(sum of 25 results)-(sum of 24 results)
=(18*25)-(14*12)+(17*12)
=450-(168+204)
=450-372
=78.
Answer is C.
The answer is: C | C |
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