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mathematics | In a rectangular coordinate system, points O (2,2), P (2,12), and Q (10,2) represent the sites of three proposed housing developments. If a fire station can be built at any point in the coordinate system, at which point would it be equidistant from all three developments? | [
"(5,6)",
"(8,7)",
"(5,8)",
"(6,6)",
"(6,7)"
]
| All points equidistant from O and Q lie on the line x = 6, so the fire station should lie on this line.
All points equidistant from O and P lie on the line y = 7, so the fire station should lie on this line.
These two intersect at (6,7) and that will be the point equidistant from all 3 points.
The answer is E.
The answer is: E | E |
mathematics | What was the day of the week on, 19th July, 1776? | [
"Friday",
"Wednesday",
"Monday",
"Saturday",
"SUNDAY"
]
| 16th July, 1776 = (1775 years + Period from 1st Jan, 1776 to 16th July, 1776)
Counting of odd days :
1600 years have 0 odd day.
100 years have 5 odd days.
75 years = (18 leap years + 57 ordinary years) = [(18 x 2) + (57 x 1)] = 93 (13 weeks + 2 days) = 2 odd days.
1775 years have (0 + 5 + 2) odd days = 7 odd days = 0 odd day.
Jan Feb Mar Apr May Jun Jul
31 + 29 + 31 + 30 + 31 + 30 + 16 = 198 days= (28 weeks + 5 days)
Total number of odd days = (0 + 5) = 5.
Required day was 'Friday'.
Answer:A
The answer is: A | A |
mathematics | The price of a coat in a certain store is $500. If the price of the coat is to be reduced by $150, by what percent is the price to be reduced? | [
"10%",
"15%",
"20%",
"25%",
"30%"
]
| price of a coat in a certain store = $500
the price of the coat is to be reduced by $150
% change = (Final Value - Initial Value)*100 / Initial Value
% Reduction= (Reduction in Price)*100 / Initial Value
i.e. % Reduction= (150)*100 / 500 = 30%
Answer: Option E
The answer is: E | E |
mathematics | A fort had provision of food for 150 men for 45 days. After 10 days, 30 men left the fort. The number of days for which the remaining food will last, is: | [
"29 1/5",
"37 1/4",
"43 3/4",
"54",
"48"
]
| After 10 days : 150 men had food for 35 days.
Suppose 120 men had food for x days.
Now, Less men, More days (Indirect Proportion)
Therefore 120 : 150 :: 35 : x <=> 120 x x = 150 x 35
=> x =150 x 35/120
=> x = 43 3/4.
Correct answer is C
The answer is: C | C |
mathematics | Sahil purchased a machine at Rs 10000, then got it repaired at Rs 5000, then gave its transportaƟon
charges Rs 1000. Then he sold it with 50% of profit. At what price he actually sold it | [
"Rs. 22000",
"Rs. 24000",
"Rs. 26000",
"Rs. 28000",
"None of these"
]
| Explanation:
Question seems a bit tricky, but it is very simple.
Just calculate all Cost price, then get 150% of CP.
C.P. = 10000 + 5000 + 1000 = 16000
150% of 16000 = 150/100 * 16000 = 24000
Answer: B
The answer is: B | B |
mathematics | A sum was put at simple interest at certain rate for 3 years. Had it been put at 1% higher rate it would have fetched Rs. 72 more. The sum is: A. Rs. 2,400 B. Rs. 2,100 C. Rs. 2,200 D.Rs. 2,480 | [
"2000",
"2100",
"2200",
"2300",
"2400"
]
| 1 percent for 3 years= 72
1 percent for 1 year = 24
=> 100 percent = 2400
ANSWER:E
The answer is: E | E |
mathematics | A does half as much work as Band C does half as much work as A and B together. If C alone can finish the work in 80 days, then together ,all will finish the work in : | [
"13 1/3 days",
"16 days",
"15 days",
"20 days",
"30 days"
]
| C alone can finish the work in 80 days.
(A + B)can do it in 20 days
(A + B)s 1 days wok = 1/20.
As 1 days work : Bs 1 days Work = 1/2 : 1 = 1:2.
A’s 1 day’s work = (1/20) * (1/3) = (1/60). [Divide 1/20 in the raio 1:2] Bs 1 days work = (1/20) * (2/3) = 1/30
(A+B+c)S 1 day’s work = (1/60) + (1/30) + (1/80) = 1/16
All the three together will finish it in 16 days.
ANSWER:B
The answer is: B | B |
mathematics | Reena took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 432 as interest at the end of the loan period, what was the rate of interest? | [
"7",
"6",
"5",
"4",
"3"
]
| Let rate = R% and time = R years.
Then, (1200 * R * R) / 100 = 432
12R2 = 432
R2 = 36 => R = 6.
Answer: B
The answer is: B | B |
mathematics | Set C consists of the following unique integers: -2, 17, 3, n, 2, 15, -3, and -27; which of the following could be the median of set C? | [
"5",
"6",
"7",
"1",
"766"
]
| Whenever a question asks you to deal with the MEDIAN of a group of numbers, you MUST put the numbers in order from least to greatest (or at the very least,group offthe numbers so that you can restrict the potential value of the median).
Here, we have 8 values (one of the values is the variable N). We're told that the values are UNIQUE, so N CANNOT be any of the other 7 values listed. We're asked which of the following answers COULD be the median, so if we determine that one of the answer choices is a POSSIBLE median, then we can stop working....
Since the group includes 8 values, the median will be the AVERAGE of the 4th and 5th values...
Putting the 7 numbers in order, we have:
-27, -3, -2, 2, 3, 15, 17
This means that the2will either be the 4th term or the 5th term (depending on the value of N).
IF....
N is REALLY BIG, then the 4th and 5th terms will be 2 and 3, so the median will = 2.5
N is REALLY SMALL, then the 4th and 5th terms will be -2 and 2, so the median will = 0
Neither of those answers is among the choices though, so N must be something relativelycloseto 2.....
IF....
N = 0, then the 4th and 5th terms will be 0 and 2, so the median will = 1. That answer IS among the choices, so we're done.
D
The answer is: D | D |
mathematics | If a:b=3:1 and b:c=1:4 find a:b:c? | [
"1:6:2",
"3:1:4",
"2:3:4",
"2:3:3",
"1:4:2"
]
| a:b = 3:1, b:c = 1:4
3:1
1:4
(a = a × b, b = b × b and c = b × c)
a:b:c = 3:1:4
B
The answer is: B | B |
mathematics | Two trains each 150m in length each, are running on two parallel lines in opposite directions. If one goes at the speed of 95km/h while the other travels at 85km/h. how long will it take for them to pass each other completely. | [
"25 sec",
"23 sec",
"34 sec",
"22 sec",
"6 sec"
]
| Explanation:
D = 150 m + 150 m = 300 m
RS = 95 + 85 = 180 * 5/18 = 50
T = 300 * 1/50 = 6 sec
Answer: Option E
The answer is: E | E |
mathematics | In Cliff’s impressive rock collection, there are half as many igneous rocks as sedimentary rocks. Of the igneous rocks, 1/3 are shiny and the rest are matte, while 1/5 of the sedimentary rocks are shiny. If there are 30 shiny igneous rocks, how many total rocks does Cliff have? | [
"30",
"45",
"270",
"90",
"135"
]
| We can start with the known quantity and then go on to find the others.
Shiny igneous ricks are 30. These are (1/3) of total igneous rocks.
(1/3)*Total igneous rocks = 30
Total igneous rocks = 30 * (3) = 90
Total sedimentary rocks = 2*Total igneous rocks = 2*90 = 180
Total number of rocks = 90 + 180 = 270
Answer (C)
The answer is: C | C |
mathematics | The average earning of a mechanic for the first-four days of a week is Rs. 18 and for the last four days is Rs. 22. If he earns Rs . 41 on the fourth day, his average earning for the whole week is ? | [
"Rs . 18.95",
"Rs 16",
"Rs. 17",
"Rs. 25.71",
"None of these"
]
| Answer
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 -41
= Rs. 119
∴ Average earning = 119 / 7
= Rs. 17
Correct Option: C
The answer is: C | C |
mathematics | Total number of 4 digit number do not having the digit 3 or 6. | [
"22",
"28",
"27",
"19",
"11"
]
| Answer:D
The answer is: D | D |
mathematics | A man can row upstream at 25 kmph and downstream at 35 kmph, and then find the speed of the man in still water? | [
"11",
"77",
"30",
"88",
"34"
]
| US = 25
DS = 35
M = (35 + 25)/2 = 30
Answer:C
The answer is: C | C |
mathematics | The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 6 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each? | [
"s.4538",
"s.4518",
"s.4518",
"s.4530",
"s.5436"
]
| Area of the four walls = 2h(l + b)
Since there are doors and windows, area of the walls = 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft.
Total cost = 906 * 6 = Rs.5436
Answer: E
The answer is: E | E |
mathematics | If 6 parallel lines in a plane is intersected by a family of another 8 parallel lines, how many parallelograms are there in the network thus formed? | [
"80",
"63",
"420",
"160",
"1260"
]
| parallelogram can formed by 2 horizontal and 2 vertical lines
for horizontal 6c2
for vertical 8c2
total parallelogram is 6 c2*8c2=15*28
=420
ANSWER:C
The answer is: C | C |
mathematics | Dimitri weighs 4x-3x pounds more than Allen weighs. Together, Allen and Dimitri weigh a total of y pounds. Which of the following represents Allen’s weight? | [
"y - x/2",
"2x - y/2",
"(y - x)/2",
"y - 2x",
"2x - y"
]
| These type of multi-variable story problems are usually perfect for TESTing VALUES.
Here, we're told that Dimitri weighs 4X-3X or X pounds more than Allen weighs and that they weight a combined TOTAL of Y pounds.
IF....
Dimitri = 30
Allen = 20
X = 10
Y = 50
We're asked for Allen's weight, so we're looking for an answer that equals 20 when X = 10 and Y = 50.
Answer A: 50 - (10/2) = 45 NOT a match
Answer B: 20 - (50/2) = -5 NOT a match
Answer C: (50-10)/2 = 20 This IS a match
Answer D: 50 - 20 = 30 NOT a match
Answer E: 20 - 50 = -30 NOT a match
Final Answer:
C
The answer is: C | C |
mathematics | A customer pays 40 dollars for a coffee maker after a discount of 20 dollars
What is the original price of the coffe maker? | [
"50",
"40",
"70",
"60",
"20"
]
| Let x be the original price.
x - 20 = 40
x - 20 + 20 = 40 + 20
x + 0 = 60
x = 60
Answer is D
The answer is: D | D |
mathematics | A CAN FINISH A WORK IN 9 DAYS AND B CAN DO THE SAME WORK IN15 DAYS. B WORKED FOR 10 DAYS AND LEFT THE JOB. IN HOW MANY DAYS, A ALONE CAN FINISH THE REMAINING WORK? | [
"3",
"5 1/2",
"6",
"8",
"NONE OF THESE"
]
| B'S 10 DAY'S WORK=(1/15*10)=2/3 REMAINING WORK = (1-2/3)=1/3
NOW, 1/18 WORK IS DONE BY A IN 1 DAY
1/3 WORK IS DONE BY A IN (9*1/3)=3 DAYS.
CORRECT OPTION:A
The answer is: A | A |
mathematics | A local bank that has 15 branches uses a two-digit code to represent each of its branches. The same integer can be used for both digits of a code, and a pair of two-digit numbers that are the reverse of each other (such as 17 and 71) are considered as two separate codes. What is the fewest number of different integers required for the 15 codes? | [
"3",
"4",
"5",
"6",
"7"
]
| Consider the code XY. If there are nn digits available then X can take nn values and Y can also take nn values, thus from nn digits we can form n2n2 different 2-digit codes: this is the same as from 10 digits (0, 1, 2, 3, ..., 9) we can form 10^2=100 different 2-digit numbers (00, 01, 02, ..., 99).
We want # of codes possible from nn digit to be at least 15 --> n2≥15n2≥15 --> n≥4n≥4, hence min 4 digits are required.
Answer: B.
The answer is: B | B |
mathematics | if 12401 is divided by any no. then quotient is 76 and remainder is 13.what is divisor? | [
"154",
"124",
"153",
"163",
"183"
]
| divisor=(dividend-remainder)/quotient=(12401-13)/76=12388/76=163
divisor = 163
answer D
The answer is: D | D |
mathematics | Roger can read a book in k minutes. What part of the book can he read in 6 minutes? (k>8) | [
"8+k",
"8/k",
"k/8",
"(k+ 8)/k",
"(k-8) / k"
]
| Let's sayk = 24
That is, it takes 24 minutes to read the entire book.
So, in 8 minutes, Roger can read1/3of the book
So, we're looking for the answer choice that yields an OUTPUT of1/3whenk = 24
A) 8+24=32ELIMINATE
B) 8/24=1/3KEEP
C)24/8 =3ELIMINATE
D) (24+ 8)/24=32/24 = 4/3ELIMINATE
E) (24-8) /24=16/24 = 2/3ELIMINATE
Answer:D
The answer is: D | D |
mathematics | The average of 5 quantities is 10. The average of 3 of them is 4. What is the average of remaining 2 numbers? | [
"19",
"14",
"8",
"9.5",
"None of these"
]
| ANSWER: A
(5x10-3x4)/2=19
The answer is: A | A |
mathematics | Each of the following numbers has a remainder of 3 when divided by 8 except: | [
"11",
"19",
"3",
"83",
"26"
]
| It's E
26 = 8*3+2
The answer is: E | E |
mathematics | The population of a town has increased from 133575 to 138918. The percent increase in population is : | [
"2.5",
"3",
"4.5",
"4",
"3.5"
]
| (133575-138918)/138918*100=4
ANSWER:D
The answer is: D | D |
mathematics | The ratio of boys to girls in Class A is 3 to 5. The ratio of boys to girls in Class B is 4 to 5. If the two classes were combined, the ratio of boys to girls in the combined class would be 17 to 22. If Class A has one more boy and two more girls than class B, how many girls are in Class A? | [
"8",
"9",
"10",
"11",
"12"
]
| Since it is given that the ratio of boys to girls in Class A is 3 to 4 - so we can quickly eliminate the answer choices which are not multiples of 4.
so ans can either be 8 0r 12.
With 8 as answer - no of girls = 8
With 12 as answer - no of girls = 12
Now Class A has one more boy and two more girls than class B and also the ratio of boys to girls in Class B is 4 to 5.
So we are looking for number of girls in B to be divisible by 5.
With 8 as answer -> Girls = 8-2 = 6. (Not possible)
With 12 as answer -> Girls = 12-2 = 5.
So, answer = 10. ( C)
The answer is: C | C |
mathematics | If two positive numbers are in the ratio 1/8 : 1/7, then by what percent is the second number more than the first? | [
"14.3%.",
"70%.",
"60%.",
"68%.",
"80%."
]
| Given ratio = 1/8 : 1/7 = 7 : 8
Let first number be 7x and the second number be 8x.
The second number is more than first number by 1x.
Required percentage = 1x/7x * 100 = 14.3%.
Answer: A
The answer is: A | A |
mathematics | The length of a rectangular plot is thrice its width. If the area of the rectangular plot is 675 sq meters, then what is the width (in meters) of the rectangular plot? | [
"12",
"15",
"18",
"21",
"24"
]
| Area = L*W = 3W^2 = 675
W^2 = 225
W = 15
The answer is B.
The answer is: B | B |
mathematics | A thief goes away with a SANTRO car at a speed of 40 kmph. The theft has been discovered after half an hour and the owner sets off in a bike at 55 kmph when will the owner over take the thief from the start? | [
"A)1.33",
"B)5",
"C)7",
"D)5",
"E)8"
]
| Explanation:
|-----------20--------------------|
55 40
D = 20
RS = 55 – 40 = 15
T = 20/15 = 1.33 hours
Answer: Option A
The answer is: A | A |
mathematics | The average (arithmetic mean) of five numbers is 5. If 2 is subtracted from each of four of the numbers, what is the new average? | [
"3.4",
"4.5",
"6.2",
"5.7",
"6.9"
]
| Let the numbers be a , b, c , d , e ,f
So, Total of these 5 numbers must be 25
Or, a + b + c + d + e = 25
So, 12 must be subtracted from the total sum
i.e a + b + c + d + e - 8
Or, 25 - 8 = 17
Hence average of the 5 numbers now is 17/5 =>3.4
So, Answer will be A
The answer is: A | A |
mathematics | Zinc and copper are melted together in the ratio 9 : 11. What is the weight of melted mixture, if 26.1 kg of zinc has been consumed in it? | [
"58 kg",
"60 kg",
"64 kg",
"70 kg",
"None"
]
| Sol.
For 9 kg Zinc, mixture melted = (9+11) kg.
For 26.1 kg Zinc, mixture, melted = [20/9 x 26.1] kg
= 58 kg.
Answer A
The answer is: A | A |
mathematics | Jar X is 1/5 full of water. Jar Y, which has half the capacity of Jar X, is 1/2 full of water. If the water in Jar Y is poured into Jar X, then Jar X will be filled to what fraction of its capacity? | [
"2/5",
"3/5",
"7/10",
"7/20",
"9/20"
]
| Let P be the capacity of Jar X.
The amount of water in Jar Y is 1/2*P/2=P/4
Then the total amount in Jar X is P/5+P/4=9/20
The answer is E.
The answer is: E | E |
mathematics | Two trains are running at 40 kmph and 20 kmph respectively in the same direction.Fast train completely passes a man sitting in the slower train in 4 seconds.What is the length of the fast train? | [
"23 m",
"22 2/9 m",
"27m",
"27 7/9m",
"29 7/9m"
]
| relative speed=20kmph=50/9m/sec
length of the train=50/9*4= 22 2/9m
ANSWER:B
The answer is: B | B |
mathematics | Running at the same rate, 8 identical machines can produce 560 paperclips a minute. At this rate, how many paperclips could 30 machines produce in 6 minutes? | [
"1344",
"3360",
"8400",
"12600",
"67200"
]
| 8 machines produce 560 in 1 min
8 machines produce 560* 6 in 6 min
30 machine produce 560*6*(30/8) in 6 minutes
560*6*30/8=12600 answer is D.
The answer is: D | D |
mathematics | If (2 to the x) - (2 to the (x-2)) = 3 (2 to the 5), what is the value of x? | [
"7",
"11",
"13",
"15",
"17"
]
| (2 to the power x) - (2 to the power (x-2)) = 3 (2 to the power 5)
2^x - 2^(x-2) = 3. 2^5
Hence x = 7.
Answer is A
The answer is: A | A |
mathematics | While flying over the Pacific, an airplane makes a 25° turn to the right to avoid a storm. If, as a result, the airplane is traveling in a direction 8° east of north, in what direction was it originally flying? | [
"(a) 30° west of north",
"(b) 30° east of north",
"(c) 17° west of north",
"(d) 17° east of north",
"(e) 5° west of north"
]
| If after a turn of 25° you are 8°NEast, with a 17° turn you would be perfectly pointing at north. So you were, before the turn, 17° to the other side (West).
Answer C)
The answer is: C | C |
mathematics | A discount of 10 percent on an order of goods followed by a discount of 40 percent amounts to | [
"the same as one 46 percent discount",
"the same as one 40 percent discount",
"the same as one 36 percent discount",
"the same as one 30 percent discount",
"the same as one 25 percent discount"
]
| 0.9*0.6*x=0.54x from initial value, meaning 0.46 or 46% discount
A
The answer is: A | A |
mathematics | the present average age of a couple and their daughter is 35 years. Fifteen years from now, the age of the mother will be equal to the sum of present ages of the father and the daughter. Find the present age of mother? | [
"38",
"49",
"55",
"45",
"50"
]
| D
45
(f + m + d)/3 = 35
=> f + m + d = 105 --- (1)
m + 15 = f + d
Substituting f + d as m + 15 in (1), we get
2m + 15 = 105
2m = 90 => m = 45 years.
The answer is: D | D |
mathematics | When positive integer n is divided by 5, the remainder is 1. When n is divided by 7, the remainder is 3. What is the smallest positive integer k such that k+n is a multiple of 38? | [
"3",
"4",
"7",
"32",
"35"
]
| n = 5p + 1 = 6,11,16,21,26,31
n = 7q + 3 = 3,10,17,24,31
=>n = 38m + 31
To get this, we need to take LCM of co-efficients of p and q and first common number in series.
So we need to add 7 more to make it
38m + 38
Answer - C
The answer is: C | C |
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.18300. A's share is? | [
"8876",
"2765",
"6000",
"1298",
"6100"
]
| x* 12 : 2x* 6: 3x* 4
1:1:1
1/3 * 18300 = 6100
Answer:E
The answer is: E | E |
mathematics | What should come in place of the question mark(?) in the following equation?
4 1⁄2 × 4 1⁄3 - 8 1⁄3 ÷ 5 2⁄3 = ? | [
"8",
"18 1⁄34",
"1 33⁄34",
"7⁄17",
"None of these"
]
| ? = 9⁄2 × 13⁄3 - 25⁄3 × 3⁄17
= 39⁄2 - 25⁄17 = 663−50/34=61334=18 1/34
Answer B
The answer is: B | B |
mathematics | V is the volume of a cylinder; the radius of the cylinder is 3.5. The height of the cylinder is 650% more than the radius. Which of the following is true? | [
"100 < V < 300",
"300 < V < 500",
"500 < V < 700",
"700 < V < 900",
"900 < V < 1100"
]
| As we see the answers are in form of range we can use approximation
Volume of cylinder is πr^2h
Given π= 22/7 and r = 3.5 so r^2 ~ 12 and h = 6.5 * 3.5 ~ 23
So 22/7 * 12 * 23 ~ 868
so answer should be
D. 700 < V < 900
Answer : D
The answer is: D | D |
mathematics | A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train? | [
"199",
"87",
"120",
"150",
"388"
]
| Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train = (Speed x Time) = (50/3 * 9) m = 150 m.Answer:D
The answer is: D | D |
mathematics | Tough and Tricky questions: Percents.
Over the course of a year, a certain microbrewery increased its beer output by 90 percent. At the same time, it decreased its total working hours by 5 percent. By what percent did this factory increase its output per hour? | [
"200",
"100",
"300",
"400",
"500"
]
| Lets assume the initial production was 100 litres of beer for 100 hr.
With the 90% increase the total amount of beer production will be 190 litres and with 5 % decrease in total hours will be reduced to 95 hr.
100hr ----> 100 lts
1hr -----> 1 lts
95hr -----> 190 lts
1hr -----> 2 lts
Total Increase in production for 1 hr = 200%
Answer A
The answer is: A | A |
mathematics | If a coin is tossed three times, what is the probability that on the first toss the coin lands on heads and then lands on tails the next two tosses? | [
"1/8",
"1/3",
"1/4",
"1/2",
"1"
]
| P(HTT) = 1/2*1/2*1/2=1/8
The answer is A.
The answer is: A | A |
mathematics | Which of the following numbers is divisible by 11? | [
"4424",
"2232",
"1522",
"8524",
"9515"
]
| 9515. This is the only option with last two digits divisible by 11
Answer:E
The answer is: E | E |
mathematics | Alice deposited Rs 2 million in bank at 4 % simple interest per year. After 10 year how many Rs she will get from bank? | [
"75000",
"90000",
"10000",
"80000",
"60000"
]
| i = (200000*10*4)/100
i = 80000
Answer: D
The answer is: D | D |
mathematics | In a 8*8 chess board, what is the total number of squares refer model? | [
"201",
"202",
"203",
"204",
"205"
]
| 1x1 8 8 64
2x2 7 7 49
3x3 6 6 36
4x4 5 5 25
5x5 4 4 16
6x6 3 3 9
7x7 2 2 4
8x8 1 1 1
total 204
ANSWER:D
The answer is: D | D |
mathematics | If one-seventh of a number exceeds its eleventh part by 100 then the number is… | [
"770",
"870",
"1825",
"1925",
"925"
]
| let no be :x
1/7x-1/11x=100
4x/77=100
x=7700/4=1925
ANSWER:D
The answer is: D | D |
mathematics | Country C imposes a two-tiered tax on imported cars: the first tier imposes a tax of 10% of the car's price up to a certain price level. If the car's price is higher than the first tier's level, the tax on the portion of the price that exceeds this value is 8%. If Ron imported a $14,000 imported car and ended up paying $1440 in taxes, what is the first tier's price level? | [
"$1600",
"$6000",
"$6050",
"$7050",
"$8000"
]
| Let T be the tier price, P be total price = 14000
Per the given conditions:
0.10T + 0.08(P-T) = 1440 ----> T= 1600. A is the correct answer.
The answer is: A | A |
mathematics | One out of every 500 light bulbs are defected. If 2 out of every 10 defected light bulbs have a broken glass and there are 16 broken glass light bulbs in the shipment, how many light bulbs total are there in the shipment? | [
"2,000",
"5,000",
"10,000",
"40,000",
"52,000"
]
| out of 500 only 1 bulb is defective.So for 10 defective bulbs, we must have 5000 bulbs
Now out of these 10 bulbs, 2 bulbs, have broken glass
i.e 2 broken glass out of 5000 bulbs
16 broken glass will be from 40000 bulbs
Answer is D
The answer is: D | D |
mathematics | The bankers discount and the true discount of a sum at 20% per annum simple interest for the same time are Rs.200 and Rs.150 respectively. What is the sum and the time? | [
"Sum = Rs.600 and Time = 1.6 years",
"Sum = Rs.500 and Time = 1.6 years",
"Sum = Rs.400 and Time = 1.6 years",
"Sum = Rs.600 and Time = 3 years",
"None of these"
]
| Explanation :
BD = Rs.200
TD = Rs.150
R = 20%
F = BD ×TD/(BD – TD)=200×150/(200–150)=200×150/50=Rs. 600
BD = Simple Interest on the face value of the bill for unexpired time =FTR/100
⇒200 = (600×T×20)/100
⇒200 = 6 × T × 20 ⇒20 = 12 × T
⇒ T = 20/12 = 1.6 years Answer : Option A
The answer is: A | A |
mathematics | Look at this series: 53, 53, 48, 48, 43, 43, ... What number should come next? | [
"A)12",
"B)14",
"C)38",
"D)53",
"E)86"
]
| In this series, each number is repeated, then 5 is subtracted to arrive at the next number.
Answer: C
The answer is: C | C |
mathematics | If 16% of 40% of a number is 8, then the number is | [
"200",
"225",
"125",
"320",
"None of these"
]
| Explanation:
Let 16/100×40/100×a=8
a = 8×100×100/16×40=125
Correct Option: C
The answer is: C | C |
mathematics | A shopkeeper sells two articles at Rs.1000 each, making a profit of 20% on the first article and a loss of 20% on the second article. Find the net profit or loss that he makes? | [
"neither profit nor loss",
"3%",
"5%",
"4%",
"6%"
]
| SP of first article = 1000
Profit = 20%
CP = (SP)*[100/(100+P)] = 5000/6 = 2500/3
SP of second article = 1000
Loss = 20%
CP = (SP)*[100/(100-L)] = 5000/4 = 1250
Total SP = 2000
Total CP = 2500/3 + 1250 = 6250/3
CP is more than SP, he makes a loss.
Loss = CP-SP = (6250/3)- 2000 = 250/3
Loss Percent = [(250/3)/(6250/3)]*100 =
0.04 * 100 = 4%
ANSWER:D
The answer is: D | D |
mathematics | Kiran travels from A to B by car and returns from B to A by cycle in 7 hours. If he travels both ways by car he saves 3 hours. What is the time taken to cover both ways by cycle? | [
"10",
"76",
"88",
"55",
"12"
]
| Let the time taken to cover from A to B in car and cycle be x hours and y hours respectively.
x + y = 7 --- (1) ; 2x = 4 --- (2)
solving both the equations, we get y = 5
So, time taken to cover both ways by cycle = 2y hours = 10 hours.
Answer: A
The answer is: A | A |
mathematics | The average of ten numbers is 7. If each number is multiplied by 12 ,then the average of new set of numbers is : | [
"22",
"29",
"27",
"84",
"19"
]
| The avg will be = 12×7= 84
Answer: D
The answer is: D | D |
mathematics | In an office in Singapore there are 60% female employees. 50 % of all the male employees are computer literate. If there are total 62% employees computer literate out of total 1600 employees, then the no. of female employees who are computer literate ? | [
"690",
"674",
"672",
"960",
"None"
]
| Solution: Total employees,
= 1600
Female employees, 60% of 1600.
= (60 *1600) /100 = 960.
Then male employees,
= 640
50 % of male are computer literate,
= 320 male computer literate.
62 % of total employees are computer literate,
= (62 *1600) /100 = 992 computer literate.
Thus, Female computer literate = 992 - 320
= 672.
Answer: Option C
The answer is: C | C |
mathematics | A person purchased a TV set for Rs. 12000 and a DVD player for Rs. 6250. He sold both the items together for Rs. 31150. What percentage of profit did he make? | [
"16.68%",
"87.68%",
"70.68%",
"17.68%",
"18.68%"
]
| The total CP = Rs. 12000 + Rs. 6250 = Rs. 18250 and SP
= Rs. 31150
Profit(%) = (31150 - 18250)/18250 * 100
= 70.68%
Answer:C
The answer is: C | C |
mathematics | It takes 1.5 hours for Tim to mow the lawn. Linda can mow the same lawn in 2 hours. How long will it take John and Linda, work together, to mow the lawn? | [
"51.1 minutes",
"51.3 minutes",
"51.5 minutes",
"51.7 minutes",
"51.9 minutes"
]
| We first calculate the rate of work of John and Linda
John: 1 / 1.5 and Linda 1 / 2
Let t be the time for John and Linda to mow the Lawn. The work done by John alone is given by
t * (1 / 1.5)
The work done by Linda alone is given by
t * (1 / 2)
When the two work together, their work will be added. Hence
t * (1 / 1.5) + t * (1 / 2) = 1
Multiply all terms by 6
6 (t * (1 / 1.5) + t * (1 / 2) ) = 6
and simplify
4 t + 3 t = 6
Solve for t
t = 6 / 7 hours = 51.5 minutes.
Answer C
The answer is: C | C |
mathematics | 5⁄7 of 4⁄15 of a number is 8 more than 2⁄5 of 4⁄9 of the same number. What is half of that number? | [
"630",
"315",
"210",
"105",
"None of these"
]
| Let the number be x.
∴ 5⁄7 × 4⁄15 × x - 2⁄5 × 4⁄9 × x = 8
or, x = 8×31512=2108×31512=210
∴ Half of the number = 105
Answer D
The answer is: D | D |
mathematics | What percentage of numbers from 1 to 100 have cube that end in the digit 5? | [
"1",
"10.5",
"25",
"20",
"22"
]
| Clearly, the numbers which have 1 or 9 in the unit's digit, have squares that end in the digit 1. Such numbers from 1 to 95 are 5,15,25,35,45,55,65,75,85,95.
Number of such numbers = 95.
Required percentage = (10/95 * 100) = 10.5%
ANSWER:B
The answer is: B | B |
mathematics | Of all the players in a professional baseball league, 1/2 are foreign-born, including 1/3 of the pitchers. If 3/4 of the players are pitchers, what percentage of the players who are not pitchers are foreign-born? | [
"100%",
"75%",
"66 2/3%",
"50%",
"25%"
]
| Assume that the total number of players is 100.
1/2 are foreign born, so 50 are foreign born. 75 players are pitchers out of which 1/3 are foreign born. 25 players are foreign born and pitchers. The other 25 who are foreign born are thus not pitchers.
Thus out of 25 non pitchers, 25 are foreign born. Answer: A - 100%
ANSWER:A
The answer is: A | A |
mathematics | If f(2, 3) = 17 and f(2, 4) = 24, what is the value of f(2, 5)? | [
"107",
"127",
"147",
"33",
"Cannot be determined"
]
| Solution:
The function f(a, b) = a3 + b2
f(2, 3) therefore is = 17 and
f(2, 4) = 24
Therefore, f(2, 5) = 33
Answer D
The answer is: D | D |
mathematics | If (m-8) is a factor of m^2-sm-24, then s= | [
"3",
"5",
"6",
"11",
"16"
]
| (m-8)(m-a)=m^2-sm-24
A=-3
s=8+a=5=D=B
The answer is: B | B |
mathematics | If a train, travelling at a speed of 160 kmph, crosses a pole in 9 sec, then the length of train is? | [
"281",
"125",
"288",
"266",
"400"
]
| D = 160 * 5/18 * 9
= 400 m
Answer: E
The answer is: E | E |
mathematics | A FIVE DIGIT NUMBER IS FORMED BY USING THE DIGITS 1,2,3,4,5 WITH OUT REPETITIONS . WHAT IS THE PROBABILITY THE NUMBER IS DIVISIBLE BY5? | [
"12/15",
"5/6",
"4/5",
"7/3",
"2/7"
]
| If a number is divisible by 5 the last 1 digits of the number has 5.
If the number ends with 15: Number of possibilities = 4*3 * 2 * 1 = 24
number ends with 25: Possibilities = 4*3 * 2 * 1 = 24
number ends with 35: Possibilities =24
number ends with 45: Possibilities =24
Total number of possibilities with restriction = 24*4= 96
Total number of possibilities without restriction = 5! = 120
Probability = 96/120 = 12/15
Answer: A
The answer is: A | A |
mathematics | Rashmi can do a piece of work in 16 days. Ravina can do the same work in 12 days while Gitika can do it in 32 days. All of them started to work together but Rashmi leaves after 4 days. Ravina leaves the job 3 days before the completion of the work. How long the work last? | [
"14",
"15",
"16",
"17",
"18"
]
| x/3=x/6+3
x=18.
ANSWER:E
The answer is: E | E |
mathematics | In how many different number of ways 4 men and 2 women can sit on a shopa which can accommodate persons? | [
"17",
"18",
"20",
"21",
"30"
]
| 6p2 = 6 x 5 = 30
Answer : E
The answer is: E | E |
mathematics | In a class there are 10 boys and 15 girls. In how many ways can a boy and a girl be selected? | [
"150",
"500",
"600",
"530",
"630"
]
| Explanation:
We can select one boy from 10 boys in 10 ways.
We select one girl from 15 girls in 15 ways
We select a boy and girl in 10 * 15 ways i.e., = 150 ways.
Answer: Option A
The answer is: A | A |
mathematics | A man could buy a certain number of notebooks for Rs.300. If each notebook cost is Rs.5 more, he could have bought 10 notebooks less for the same amount. Find the price of each notebook? | [
"10",
"8",
"6",
"4",
"2"
]
| Let the price of each note book be Rs.x.
Let the number of note books which can be brought for Rs.300 each at a price of Rs.x be y.
Hence xy = 300
=> y = 300/x
(x + 5)(y - 10) = 300 => xy + 5y - 10x - 50 = xy
=>5(300/x) - 10x - 50 = 0 => -150 + x2 + 5x = 0
multiplying both sides by -1/10x
=> x2 + 15x - 10x - 150 = 0
=> x(x + 15) - 10(x + 15) = 0
=> x = 10 or -15
As x>0, x = 10.
ANSWER:A
The answer is: A | A |
mathematics | of polynomial for degree of x>+1 where f(x2)=f(x)2=f(f(x)) | [
"0",
"1",
"2",
"3",
"4"
]
| Let f(x) = x2
f(x2)=[x2]2=x4
(f(x))2=[x2]2=x4
f(f(x))=f(x2)=[x2]2=x4
Only 1
ANSWER:B
The answer is: B | B |
mathematics | Bruno and Sacha are running in the same direction around a stadium. Sacha runs at a constant speed of 8 meters per second, and Bruno runs at a constant speed of 5 meters per second. At a certain point Sacha overtakes Bruno. If one minute afterward, Sacha stops and waits for Bruno to reach him, then how many seconds does he have to wait? | [
"12",
"24",
"36",
"60",
"72"
]
| the difference of the speed is 3m per second so in one minute Sacha will be 180 m ahead of Bruno..
Bruno will cover this in 180/5=36 secs..
C
The answer is: C | C |
mathematics | 39! is divided by 41. Then what is the remainder? | [
"1",
"2",
"3",
"5",
"7"
]
| Substituting p = 41 in the wilson's theorem, we get
40!+141=0
40×39!+141=0
−1×39!41=−1
Cancelling -1 on both sides,
39!41=1
A
The answer is: A | A |
mathematics | A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 68 percent of the distribution lies within one standard deviation d of the mean, what percent Q of the distribution is less than m +d ? | [
"16%",
"32%",
"48%",
"84%",
"92%"
]
| D
The prompt says that 68% of the population lies between m-d and m+d.
Thus, 32% of the population is less than m-d or greater than m+d.
Since the population is symmetric, half of this 32% is less than m-d and half is greater than m+d.
Thus, Q=(68+16)% or (100-16)% of the population is less than m+d.
The answer is: D | D |
mathematics | A person travels equal distances with speeds of 4 km/hr, 5 km/hr and 6 km/hr and takes a total time of 47 minutes. The total distance is? | [
"2 km",
"4 km",
"7 km",
"9 km",
"5 km"
]
| Let the total distance be 3x km.
Then, x/4 + x/5 + x/6 = 47/60
37x/60 = 47/60 => x = 1.27
Total distance = 3 * 1.27 = 3.81 km.
Answer:B
The answer is: B | B |
mathematics | Cost of an item is Rs 12.60 & profit is 10% over selling price what is the selling price | [
"12.86",
"13.86",
"14.86",
"15.86",
"16.86"
]
| Profit=( SP-CP/CP )*100
CP=12.60
(SP-12.60)/12.60*100 =10
SP=13.86
ANSWER:B
The answer is: B | B |
mathematics | Excluding stoppages, the speed of a bus is 58 kmph and including stoppages, it is 40 kmph. For how many minutes does the bus stop per hour? | [
"19",
"19.13",
"10.5",
"11.35",
"None of these"
]
| Due to stoppages, it covers 18 km less.
Time taken to cover 18 km = ((18/58)×60) = 19 min.
Option(A) is correct
The answer is: A | A |
mathematics | If the product of the integers w, x, y and z is 840, and if 1 < w < x < y < z, what is the value of w + z? | [
"10",
"11",
"16",
"18",
"21"
]
| 840= 4* 5 * 6* 7
So w = 4, x = 5, y = 6, z = 7
w + z = 4+ 7= 11
Answer - B
The answer is: B | B |
mathematics | Three coins are tossed. What is the probability of getting at most two tails | [
"4/8",
"7/8",
"6/8",
"9/8",
"2/4"
]
| Since three coins are tossed, sample space = 8
Getting at most two tails=7
p(E) =7/8
ANSWER:B
The answer is: B | B |
mathematics | A vendor sells 60 percent of apples he had and throws away 15 percent of the remainder. Next day he sells 50 percent of the remainder and throws away the rest. What percent of his apples does the vendor throw? | [
"17",
"23",
"75",
"77",
"None of these"
]
| Let the number of apples= 100
sold 60% = 60 apples...remaining =40
Thrown away 15%= 6 apples
Remaining =40-6=34
sold 50 % of remaining = 34/2=17
Remaining thrown away = 17 apples
Total thrown away =6+17=23
Percentage thrown = 23/100=23%
Answer: B
The answer is: B | B |
mathematics | 2,300 has how many positive divisors? | [
"12",
"15",
"18",
"24",
"30"
]
| By factorization, we can write 2300 as 2300=2^2*5^2*23.
The number of factors is (2+1)(2+1)(1+1) = 18
The answer is C.
The answer is: C | C |
mathematics | Pipes A and B can fill a tank in 5 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in: | [
"3 9 /17 hours",
"1 13 /17 hours",
"2 8 /11 hours",
"4 1 /2 hours",
"None of these"
]
| Explanation:
Solution 1
Pipes A and B can fill the tank in 5 and 6 hours respectively. Therefore,
part filled by pipe A in 1 hour =1/5
part filled by pipe B in 1 hour =1/6
Pipe C can empty the tank in 12 hours. Therefore,
part emptied by pipe C in 1 hour =1/12
Net part filled by Pipes A,B,C together in 1 hour =1/5 +1/6+1/12 =17/60
i.e., the tank can be filled in 60/17=3 9/17 hours.
ANSWER IS A
The answer is: A | A |
mathematics | In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.40 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for ? | [
"160",
"175",
"180",
"195",
"200"
]
| Explanation:
Suppose the man works overtime for x hours.
Now, working hours in 4 weeks = (5 x 8 x 4) = 160.
160 x 2.40 + x x 3.20 = 432
3.20x = 432 - 384 = 48
x = 15.
Hence, total hours of work = (160 + 15) = 175.
ANSWER IS B
The answer is: B | B |
mathematics | In how many years will a sum of money doubles itself at 25% per annum on simple interest? | [
"4%",
"8%",
"10%",
"12%",
"15%"
]
| P = (P*25*R)/100
R = 4%
Answer:A
The answer is: A | A |
mathematics | Rs.8000 become Rs.8487.20 in a certain interval of time at the rate of 3% per annum of C.I. Find the time? | [
"6 years",
"8 years",
"9 years",
"3 years",
"2 years"
]
| 8487.20 = 8000(34/30)N
(34/30)^2 = (34/30)N => N = 2
At the end of three years what will be the comp.Answer: E
The answer is: E | E |
mathematics | Two boats are heading towards each other at constant speeds of 5 miles/hr and 23 miles/hr respectively. They begin at a distance 20 miles from each other. How far are they (in miles) one minute before they collide ? | [
"1/12",
"7/12",
"1/6",
"1/3",
"1/5"
]
| The question asks: how far apart will they be 1 minute=1/60 hours before they collide?
Since the combined rate of the boats is 5+23=25 mph then 1/60 hours before they collide they'll be rate*time=distance --> 28*1/60=7/15 miles apart.
Answer: B.
The answer is: B | B |
mathematics | There are 7 identical pens and 9 identical books. In how many different ways can a person select at least one object from this set? | [
"16",
"31",
"48",
"79",
"90"
]
| We can select from 0 to 7 pens and from 0 to 9 books.
Thus the total possible ways to select objects is 8*10 = 80
We must subtract 1 for the case with 0 pens and 0 books.
The answer is D.
The answer is: D | D |
mathematics | Jeni has 7 flavors of cake in his bakery. How many options are there for Sheera to pick a one-flavor, two-flavor,three-flavor, four-flavor, five-flavor, six-flavor or seven-flavor order? | [
"423",
"325",
"142",
"171",
"127"
]
| 7C1 + 7C2+ 7C3+7C4+7C5+7C6+7C7 =127 .
Answer: E
The answer is: E | E |
mathematics | What is the probability of getting exactly 4 heads in a single throw of five fair coins? | [
"1/4",
"3/8",
"3/16",
"5/32",
"7/32"
]
| One possible case is HHHHT.
P(HHHHT) = 1/2*1/2*1/2*1/2*1/2 = 1/32
There are 5C4 = 5 possible cases.
P(4 heads) = 5*1/32 = 5/32
The answer is D.
The answer is: D | D |
mathematics | If |x| = 7x - 5, then x = ? | [
"1",
"1/2",
"1 and 1/2",
"2",
"-1"
]
| Answer: A
Approach:
Substituted option A i.e x=1. Inequality satisfied.
D
The answer is: D | D |
mathematics | X can do a piece of work in 15 days. If he is joined by Y who is 50% more efficient, in what time will X and Y together finish the work? | [
"10 days",
"6 days",
"18 days",
"Data insufficient",
"None of these"
]
| X’s one day’s work = 1⁄15 th work.
Y’s one day’s work = 1⁄15 + 50% of 1⁄15 = 1⁄10 th work.
∴ (X + Y)’s one day’s work = 1⁄15 + 1⁄10 = 1⁄6 th work.
Hence, they together finish the work in 6 days.
Answer B
The answer is: B | B |
mathematics | On dividing a number by 357, we get 38 as remainder.On dividing the same number by 17, what will be the remainder ? | [
"4",
"5",
"8",
"7",
"2"
]
| Let x be the number and y be the quotient.Then,
x=357*y+38
=(17*21*y)+(17*2)+4
=17*(21y+2)+4.
Required number =4.
Answer is A
The answer is: A | A |
mathematics | A train traveling with constant speed crosses a 90m long platform in 12 seconds and a 120m long platform in 15 seconds.Find the length of the train and its speed. | [
"30",
"40",
"60",
"50",
"NOne"
]
| Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 12 => y = x/12
(x + 90)/12 = x+120/15 => x = 30 m.
Answer:A
The answer is: A | A |
mathematics | The area of a parallelogram is 72 sq m and its altitude is twice the corresponding base. Then the length of the base is? | [
"6",
"16",
"8",
"36",
"none"
]
| 2x * x = 72 => x
= 6
Answer:A
The answer is: A | A |
mathematics | The sector of a circle has radius of 21 cm and central angle 135o. Find its perimeter? | [
"91.5 cm",
"91.8 cm",
"61.8 cm",
"91.6 cm",
"92.5 cm"
]
| Perimeter of the sector = length of the arc + 2(radius)
= (135/360 * 2 * 22/7 * 21) + 2(21)
= 49.5 + 42 = 91.5 cm
Answer:A
The answer is: A | A |
mathematics | Two trains started at the same time, one from A to B and the other from B to A . If they arrived at B and A respectively 16 hours and 49 hours after they passed each other the ratio of the speeds of the two trains was | [
"2:1",
"3:2",
"4:3",
"7:4",
"1:2"
]
| Explanation:
Note : If two trains (or bodies) start at the same time from points A and B towards each other and after crossing they take a and b sec in reaching B and A respectively, then: (A's speed) : (B's speed) = (b : a)
Therefore, Ratio of the speeds of two trains = = 7 : 4. Answer: D
The answer is: D | D |
mathematics | A train covers a certain distance at a speed of 300kmph in 4 hours. To cover the same distance in 2 hours, it must travel at a speed of | [
"600km/hr",
"700km/hr",
"800km/hr",
"900km/hr",
"1000km/hr"
]
| Explanation:
Distance = 300×4 = 1200km
Required speed = (1200/2) = 600km/hr
Answer: Option A
The answer is: A | A |
mathematics | Robert is traveling on his cycle and has calculated to reach point A at 2 p.m. if he travels at 10 km/hr; he will reach there at 12 noon if he travels at 15 km/hr. At what speed must he travel to reach A at 1 p.m.? | [
"22",
"88",
"12",
"77",
"99"
]
| Let the distance traveled be x km.
Then, x/10 - x/15 = 2
3x - 2x = 60 => x = 60 km.
Time taken to travel 60 km at 10 km/hr = 60/10 = 6 hrs.
So, Robert started 6 hours before 2. p.m. i.e., at 8 a.m.
Required speed = 60/5 = 12 kmph.
Answer:C
The answer is: C | C |
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