divelab/Sys2Bench huggingface dataset:
Question: A raffle is being held at a party with 25 guests. Each guest has a numbered ticket (1 through 25). Three numbers will be randomly chosen and prizes given out. Paul and Jane have numbers 22 and 23. What is the probability both will win a prize?
Options:
A)1/2
B)1/3
C)1/100
D)1/10
E)3/25
Rationale: Combination Formula: nCr = n!/(r!(n - r)!), where n is the population/set, and r is the sample/subset.
Total number possible = 25C3 - 5!/(3!(5 - 3)!) = 2,300
Number 22 possible = 1C1 = 1
Number 23 possible = 1C1 = 1
Number other possible = 23C1 = 23
Probability Formula: P(A) = (Number Favorable Outcomes)/(Total Number Possible Outcomes)
P(22, 23) = (1C1)(1C1)(23C1)/25C3 = 23/2,300 = 1/100
Answer: C
Answer: C
Question: A train 200 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 10 km/hr in the direction opposite to that in which the train is going?
Options:
A)5
B)6
C)10
D)9
E)5
Rationale: Speed of train relative to man = 60 + 10 = 70 km/hr.
= 70 * 5/18 = 175/9 m/sec.
Time taken to pass the men = 200 * 9/175 = 10 sec.Answer: C
Answer: C
Question: If w is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3^k is a factor of w ?
Options:
A) 10
B) 12
C) 14
D) 16
E) 18
Rationale: Answer is C.
numbers in format of 3^k in the series from 1 to 30 inclusive w are: 3*1, 3*2, 3*3, 3*4, 3*5, 3*3*2, 3*7, 3*8, 3*3*3, 3*10. Total number of 3 = 13. So k=14.
Answer: C
Question: Excluding stoppages, the speed of a train is 45 kmph and including stoppages it is 36 kmph. Of how many minutes does the train stop per hour?
Options:
A)19
B)17
C)12
D)15
E)18
Rationale: T = 9/45 * 60 = 12.Answer:C
Answer: C
Question: The overall age of X and Y is 10 year greater than the overall age of Y and Z. Z is how many decades younger that X?
Options:
A)11
B)10
C)12
D)17
E)19
Rationale: B
10
(X + Y) â€“ (Y + Z) = 10
X â€“ Z = 10
Answer: B
Question: A survey was conducted to find out how many people in a housing colony of 144 residents could swim, dance and drive a car. It was found that the number of people who could not swim was 89, the number of people who could not dance was 105 and that the number of people who could not drive a car was 91. If the number of people who could do at least two of these things, was found to be 37 and the number of people who could do all these things was found to be 6, how many people could not do any of these things?
Options:
A)52
B)46
C)40
D)35
E)38
Rationale: T=n(A)+n(B)+n(C)-n(Exactly two of the events)-2*n(All 3 Events)+n(None of the events)
T=144
n(A)=T-n(A')=144-89=55
n(B)=T-n(B')=144-105=39
n(C)=T-n(C')=144-91=53
n(Exactly two of the events)=n(At least 2 Events)-n(All 3 Events)=37-6=31
n(All 3 Events)=6
144=55+39+53-31-2*6+n(None of the events)
n(None of the events)=144-55-44-53+31+12=40
Ans:C
Answer: C
Question: A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 5 employees to 3 different offices?
Options:
A)234
B)243
C)273
D)284
E)325
Rationale: Each of three employee can be assigned to either of offices, meaning that each has 2 choices --> 3*3*3*3*3=3^5=243.
Answer: B.
Answer: B
Question: A 120 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?
Options:
A)220 meter
B)225 meter
C)380 meter
D)435 meter
E)None of these
Rationale: Explanation:
As trains are running in opposite directions so their relative speed will get added
So, Relative speed = 120 +80 = 200 kmph
= 200*(5/18) = 500/9 m/sec
Let the length of other train is x meter then
x+120 /9=500 /9
=>x+120=500
=>x=380
So the length of the train is 380 meters
Option C
Answer: C
Question: If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 2 years the amount to be paid is?
Options:
A)Rs.8082
B)Rs.7800
C)Rs.8100
D)Rs.8112
E)none of these
Rationale: A = 7500(26/25)2 = 8112
ANSWER:D
Answer: D
Question: The CITY club has exactly 5 new members at the end of its first week. Every subsequent week, each of the previous week's new members (and only these members) brings exactly P new members into the club. If y is the number of new members brought into the club during the twelfth week, which of the following could be y?
Options:
A) 5^1/12
B) 3^11 * 5^11
C) 3^12 * 5^12
D) 3^11 * 5^12
E) 60^12
Rationale: At the end of the first week, there are 5 new members;
At the end of the second week, there are 5P new members (since each 5 new members from the previous week brings P new members);
At the end of the third week, there are 5P^2 new members (since each 5P new members from the previous week brings P new members);
...
At the end of the twelfth week, there are 5P^11 new members (since each 5P^10 new members from the previous week brings P new members).
We are given that 5P^11=y. Out of the answers only D yields integer value for P: 5P^11=3^11 * 5^12 --> P=3*5=15.
Answer: D.
Answer: D
Question: If the average marks of three batches of 55, 60 and 65 students respectively is 50, 46, 60, then the average marks of all the students is
Options:
A)54.48
B)54.68
C)52.27
D)54.58
E)None of these
Rationale: Explanation:
(55Ã—50)+(60Ã—46)+(65Ã—60) / 55+60+65
9410 / 180=52.27
Option C
Answer: C
Question: Jeff received a 10% raise each month for three consecutive months. What was his starting salary if after the three raises his salary is $1331?
Options:
A)$1,000
B)$1,100
C)$1,200
D)$1,300
E)$1,400
Rationale: S * 1.1 * 1.1 * 1.1 = 1331 thus,
S = 1000
Answer: A
Answer: A
Question: Ajay and Balu together can do a piece of work in 12 days. Balu and Charan together can do the same work in 16 days. After Ajay has been working at it for 5 days and Balu for 7 days, Charan finishes it in 13 days. In how many days will Charan alone be able to do the work?
Options:
A)16 days
B)24 days
C)36 days
D)48 days
E)58 days
Rationale: Let the total work be 48 units.
Ajay and Balu’s One day work = 48/12 = 4 units.
Balu and Charan’s one day work = 48/16 = 3 units.
Ajay’s one day work = 4 - Balu’s one day work.
Balu’s one day work = 3 - Charan’s one day work.
Therefore, Ajay’s one day work = 1 + Charan’s one day work.
Also given,
5 x Ajay’s one day work + 7 x Balu’s one day work + 13 x Charan’s one day work = 48
Equating all the equations formed, we get Charan’s one day work is 2 units .
Hence, Charan can finish the whole work in 48/2 = 24 days.
ANSWER:B
Answer: B
Question: If 10 spiders make 5 webs in 5 days, then how many days are needed for 1 spider to make 1 web?
Options:
A)10
B)9
C)5
D)15
E)20
Rationale: Explanation:
Let, 1 spider make 1 web in x days.
More spiders, Less days (Indirect proportion)
More webs, more days (Direct proportion)
Hence we can write as
(spiders)10:1
(webs) 1:5}::x:5
â‡’10Ã—1Ã—5=1Ã—5 Ã— x
â‡’x=10
Answer: Option A
Answer: A
Question: The cost of cultivating a square field at the rate of Rs.135 per hectare is Rs.1215. The cost of putting a fence around it at the rate of 75 paise per meter would be :
Options:
A)s.360
B)s.810
C)Rs.900
D)s.1800
E)s.1900
Rationale: Area= Total cost/ Rate= (1215/135) hectares= (9*10000) sq.m.
Therefore, side of the square= Ö90000=300m.
Perimeter of the field= (300*4)m= 1200m
Cost of fencing= Rs.(1200*3/4)= Rs.900
ANSWER:C
Answer: C
Question: A department of ten people - four men and six women - needs to send a team of five to a conference. If they want to make sure that there are no more than three members of the team from any one gender, how many distinct groups are possible to send?
Options:
A)100
B)120
C)150
D)180
E)200
Rationale: They can make a team of 3 men and 2 women.
The number of ways to do this is 4C3*6C2=4*15 = 60
They can make a team of 2 men and 3 women.
The number of ways to do this is 4C2*6C3=6*20 = 120
The total number of distinct groups is 180.
The answer is D.
Answer: D
Question: After decreasing 24% in the price of an article costs Rs.912. Find the actual cost of an article?
Options:
A)1400
B)1300
C)1200
D)1100
E)1000
Rationale: Explanation:
CP* (76/100) = 912
CP= 12 * 100 => CP = 1200
ANSWER IS C
Answer: C
Question: On dividing a number by 999, the quotient is 366 and the remainder is 103. The number is:
Options:
A)364724
B)365387
C)365737
D)366757
E)366767
Rationale: Required number= 999*366+103
= (1000-1)*366+103
= 366000-366+103
= 365737.
ANSWER:C
Answer: C
Question: Two trains are moving at 75 kmph and 70 kmph in opposite directions. Their lengths are 150 m and 100 m respectively. The time they will take to pass each other completely is?
Options:
A)6 6/29 sec
B)7 1/7 sec
C)7 2/2 sec
D)8 1/2 sec
E)7 1/19 sec
Rationale: 70 + 75 = 145 * 5/18 = 725/18 mps
D = 150 + 100 = 250 m
T = 250 * 18/725 = 180/29 = 6 6/29 sec
Answer: A
Answer: A
Question: The distance traveled by earth in one year approximately 6590000000000 miles.The distance traveled by the earth by in 100 years?
Options:
A)10<16>
B)10<10>
C)10<13>
D)10<15>
E)10<18>
Rationale: The distance traveled by earth in one year = 65,900,000,000,000 miles
The distance traveled by earth in 100 years =65,900,000,000,000 *100 years = 6,590,000,000,000,000 miles
=659*10<13> (exponent) Answer: C
Answer: C
Question: If a woman lost 4% by selling oranges at the rate of 12 a rupee at how many a rupee must he sell them to gain 44%?
Options:
A)2
B)9
C)23
D)12
E)8
Rationale: Option E
Explanation:
96% ---- 12
144% ---- ?
96/144 * 12 = 8
Answer: E
Question: A train running at the speed of 60 km/hr crosses a pole in 7 sec. What is the length of the train?
Options:
A)112.21
B)27.21
C)117.66
D)277
E)116.66
Rationale: Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 7
= 116.66
Answer: E
Answer: E
Question: The probability that a visitor at the mall buys a pack of candy is 30%. If three visitors come to the mall today, what is the probability W that exactly two visitors will buy a pack of candy?
Options:
A)0.343
B)0.147
C)0.189
D)0.063
E)0.027
Rationale: 3C2 * (3/10)^2 * 7/10
= 3 * 9/100 * 7/10
= 189/1000
= 0.189=W
Answer - C
Answer: C
Question: The ratio of three numbers is 3:4:7 and their product is 18144. The numbers are
Options:
A)9,12,21
B)15,00,25
C)18,24,42
D)24,16,17
E)30,15,17
Rationale: Let the numbers be 3x, 4x and 7x
3x x 4x x 7x=18144
X3=216
X=6
The numbers are 18,24,42
ANSWER C
Answer: C
Question: 8 hens weigh equal to as many duck as are equal to 7 cats. All of them weigh 264kg only. Hen's weighs are?
Options:
A)6
B)5
C)2
D)7
E)11
Rationale: 8h = xd = 7c
8h + xd + 7c ----- 264kg.
8h+8h+8h ----- 264kg.
24h ------ 264kgs. => 1h = 11kg
Answer: E
Answer: E
Question: In a mixture of milk and water, the proportion of milk by weight was 80%. If, in a 210-gram mixture, 40 grams of pure milk is added, what would be the percentage of milk in the resulting mixture?
Options:
A)82.2%
B)83.2%
C)84.2%
D)85.2%
E)86.2%
Rationale: The amount of milk is 0.8(210) + 40 = 208 grams.
The proportion is 208/250 = 0.832 which is 83.2%
The answer is B.
Answer: B
Question: The ratio of the length and the breadth of a rectangle is 4 : 3 and the area of the rectangle is 6912 sq cm. Find the ratio of the breadth and the area of the rectangle?
Options:
A)1:96
B)1:98
C)1:96
D)1:95
E)1:91
Rationale: Let the length and the breadth of the rectangle be 4x cm and 3x respectively.
(4x)(3x) = 6912
12x2 = 6912
x2 = 576 = 4 * 144 = 22 * 122 (x > 0)
=> x = 2 * 12 = 24
Ratio of the breadth and the areas = 3x : 12x2 = 1 : 4x =1:96.
Answer: A
Answer: A
Question: The length of the bridge, which a train 150 metres long and travelling at 54 km/hr can cross in 30 seconds, is?
Options:
A)340 m.
B)350 m.
C)320 m.
D)330 m.
E)360 m.
Rationale: Speed = [54X 5/18] m/sec = [15] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30
= 15 => (130 + x)/30
= 320 => x
= 320 m.
Answer:C
Answer: C
Question: During a certain week, a seal ate 65% of the first 80 smelt it came across, and 30% of the remaining smelt it came across. If the seal ate 40% of the smelt it came across during the entire week, how many smelt did it eat?
Options:
A)32
B)40
C)55
D)64
E)112
Rationale: Total smelt = x.
Then, 0.65*80+0.3(x-80)=0.4*x --> x=280 --> 0.4*x=112.
Answer: E.
Answer: E
Question: If the average (arithmetic mean) of 5 positive temperatures is x degrees Fahrenheit, then the sum S of the 3 greatest of these temperatures, in degrees Fahrenheit, could be
Options:
A)6x
B)S=4x
C)S=5x/3
D)S=3x/2
E)3x/5
Rationale: OA please. Yeah so 5x is the sum of the 5, then I guess 4x could be the answer (B)
But what about C,D,E? Any ideas why these could be wrong?
Note that we have 5positivetemperatures.
Next, as the average is x then the sum of the temperatures is 5x and as all the temperatures are positive then the sum of the 3 greatest must be more than (or equal to) 3x (as the average of the 3 greatest must be at least x) and less than 5x: 3x<SUM<5x --> only option B fits.
Answer: B.
Answer: B
Question: What is the sum of all the prime numbers greater than 30 but less than 50?
Options:
A)126
B)199
C)198
D)188
E)122
Rationale: Required sum = (31 + 37 + 41 + 43 + 47) = 199
Note: 1 is not a prime number
Answer B
Answer: B
Question: Find the invalid no.from the following series 18, 24, 29, 35, 40, 42
Options:
A)13
B)18
C)40
D)37
E)42
Rationale: The differences between two successive terms from the beginning are 6, 5,6, 5, 6, 5. So, 42 is wrong.
Answer : E
Answer: E
Question: A truck covers a distance of 296 km at a certain speed in 8 hours. How much time would a car take at an average speed which is 18 kmph more than that of the speed of the truck to cover a distance which is 6.5 km more than that travelled by the truck ?
Options:
A)6 hours
B)5 hours
C)5.5 hours
D)8 hours
E)None
Rationale: Explanation :
Speed of the truck = Distance/time = 296/8 = 37 kmph
Now, speed of car = (speed of truck + 18) kmph = (37 + 18) = 55 kmph
Distance travelled by car = 296 + 6.5 = 302.5 km
Time taken by car = Distance/Speed = 302.5/55 = 5.5 hours.
Answer – C
Answer: C
Question: How many zeroes are there at the end of the number N, if N = 90! + 180! ?
Options:
A)15
B)18
C)21
D)24
E)27
Rationale: The number of zeroes at the end of 90! will be less than the number of zeroes at the end of 180!
Hence it is sufficient to calculate the number of zeroes at the end of 90!
The number of zeroes = [90/5] + [90/25] + [90/125] = 18 + 3 + 0 = 21
The answer is C.
Answer: C
Question: Two trains of equal lengths take 5 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction?
Options:
A)22
B)12
C)7.5
D)99
E)21
Rationale: Speed of the first train = 120/5 = 24 m/sec.
Speed of the second train = 120/15 = 8 m/sec.
Relative speed = 24 + 8 = 32 m/sec.
Required time = (120 + 120)/32 = 7.5 sec.
Answer: C
Answer: C
Question: In the floor of a particular kitchen owned by an abstract artist, each row of tiles to the right of the first row contains two fewer tiles than the row directly to its left. If there are nine rows in all and a total of 540 tiles in the floor, how many tiles does the leftmost row contain?
Options:
A)52
B)56
C)60
D)64
E)68
Rationale: This question can be solved in a variety of ways: with algebra, by TESTing THE ANSWERS and by using a great Number Property shortcut involving consecutive integers.
We're given a few facts to work with:
1) There are 9 rows of tiles.
2) When going from 'left to right', each row contains TWO FEWER tiles than the one next to it.
3) There are a total of 540 tiles
We're asked how many tiles the left-most most row holds (meaning the one with the MOST tiles).
To start, 540 is divisible by 9, so we can figure out the AVERAGE number of tiles per row. That is 540/9 = 60. Since we're dealing with a set of 9 consecutive integers that differ by 2 each, we know that the '5th row' will have 60 tiles (the average). Then we just have to 'add 2s' until we get to the first row...
60 +2 +2 +2 +2 = 68.
Final Answer:
E
Answer: E
Question: The area of sector of a circle whose radius is 12 metro and whose angle at the center is 36Â° is?
Options:
A)52.6
B)45.3
C)52.8
D)52.1
E)52.2
Rationale: 36/360 * 22/7 * 12 * 12 = 45.3 m2
Answer: B
Answer: B
Question: KIM CAN DO A WORK IN 3 DAYS WHILE DAVID CAN DO THE SAME WORK IN 2 DAYS. BOTH OF THEM FINISH THE WORK TOGETHER AND GET RS. 150. WHAT IS THE SHARE OF KIM?
Options:
A)RS. 30
B)RS. 60
C)RS. 70
D)RS. 75
E)NONE OF THESE
Rationale: KIM'S WAGES: DAVID'S WAGES= KIM'S 1 DAY'S WORK: DAVID'S 1 DAY'S WORK=1/3:1/2=2:3
KIM'S SHARE = RS. (2/5*150)=RS. 60
CORRECT OPTION: B
Answer: B
Question: . In digging a pond 34 m * 16 m *9 m the volumes of the soil extracted will be?
Options:
A)3323
B)4896
C)4788
D)4790
E)6000
Rationale: 34 * 16 * 9 = 4896
Answer: B
Answer: B
Question: Find the average of all even numbers upto 75.
Options:
A)35
B)36
C)38
D)34
E)32
Rationale: Exp. Average of all even numbers upto 75 = [ 35/2* ( first even number +
greatest even number before 75) ]/35 = ½ *(2 +74 ) = 76/2 = 38.
Answer: C
Answer: C
Question: The list price of an article is Rs.65. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is?
Options:
A)7%
B)4percent
C)5%
D)2%
E)1%
Rationale: 65* (90/100)*((100-x)/100)
= 56.16
x = 4%
Answer: B
Answer: B
Question: It is given that 2^32 + 1 is exactly divisible by a certain number. Which one of the following is also divisible by the same number X?
Options:
A)a. 2^96 + 1
B)b. 2^16 - 1
C)c. 2^16 + 1
D)d. 7 * 2^33
E)e. 2^64 + 1
Rationale: a³ + b³ =(a+b)(a² -ab +b²)
Now, let (2^32 + 1) be (a+b)
a³ + b³ = (2^96 + 1)
Now, as mentioned in formula above,
a³ + b³ is always divisible by (a+b)
So any factor of X=(a+b) is a factor of (a³ + b³)
Henca A
Answer: A
Question: An uneducated retailer marks all its goods at 50% above the cost price and thinking that he will still make 25% profit,offers a discount of 25% on the marked price.what is the actual profit on the sales?
Options:
A)12.5
B)10.5
C)9.5
D)14.5
E)None of them
Rationale: Let C.P =Rs 100.then, marked price =Rs100
S.P=75% of Rs 150=Rs112.50
Hence,gain%=12.50%
Answer is A.
Answer: A
Question: Positive integer n leaves a remainder of 4 after division by 6 and a remainder of 3 after division by 5. If n is greater than 30, what is the remainder that n leaves after division by 40?
Options:
A)3
B)12
C)18
D)22
E)30
Rationale: The theory says:
if a # x is devided by y and leave the positive # r as the remainder then it can also leave negative # (r-y) as the remainder.
e.g:
9 when devided by 5 leves the remainder 4 : 9=5*1+4
it can also leave the remainder 4-5 = -1 : 9=5*2 -1
back to the original qtn:
n leaves a remainder of 4 after division by 6 and a remainder of 3 after division by 5
==> n leaves a remainder of -2 (i.e. 4-6) after division by 6 and a remainder of -2 (i.e. 3-5) after division by 5
==> n when devided by 5 and 6 leaves the same remainder -2.
what is n?
LCM (5,6)-2 = 30-2 = 28
CHECK: 28 when devided by 6 leaves the remainder 4 and when devided by 5 leaves the remainder 3
However, the qtn says n > 40
so what is the nex #, > 28, that can give the said remainders when devided by 6 and 5
nothing but 28 + (some multiple of 6 and 5) as thissome multiple of 6 and 5will not give any remainder when devided by 5 or 6 but 28 will give the required remainders.
hence n could be anything that is in the form 28 + (some multiple of 6 and 5)
observe thatsome multiple of 6 and 5is always a multiple of 30 as LCM (5,6) = 30.
hence when n (i.e. 28 + some multiple of 6 and 5) is devided by 30 gives the remainder 28.
E
Answer: E
Question: A, B and C start swimming in a pool simultaneously from the same end. To complete 10 laps, A takes 10 minutes, B takes 6 minutes and C takes 6 minutes. What is the ratio of speeds A:B:C?
Options:
A)3:5:5
B)12:15:20
C)5:4:3
D)4:6:5
E)12:15:25
Rationale: The slowest one is A, then comes B and the fastest one is C. So, the the ratio of speeds A:B:C must be in ascending order. Eliminate options C, D, and E.
A's speed (distance)/(time) = 10/10 = 1 lap per minute = 3 laps in 3 minute;
B's speed (distance)/(time) = 10/6= 5/3 lap per minute = 5 laps in 3 minutes;
C's speed (distance)/(time) = 10/6 = 5/3 lap per minute = 5 laps in 3 minutes/
Therefore, the the ratio of speeds A:B:C is 3:5:5.
Answer: A.
Answer: A
Question: Niharika covers a distance in 30 min , if she drives at a speed of 60 km/h on an average. Find the speed at which she must drive at to reduce the time of the journey by 30%.
Options:
A)84.71 kmph.
B)85.74 kmph.
C)83.71 kmph.
D)85.71 kmph.
E)84.71 kmph.
Rationale: Given Speed = 60 Kmph.
It means Niharika covered 60 km in 60 min (1 hour). So, in 30 min he will cover 30 km.
30% time reduced = 30 - 30% of 30= 21 min.
Thus, Niharika needs to cover 30 km in 21 min (0.35 hour).
Speed * Time = Distance.
Speed * 0.35 = 30
Speed = 85.71 kmph.
ANSWER : OPTION D
Answer: D
Question: In an election contested by two parties, Party D secured 12% of the total votes more than Party R. If party R got 132,000 votes, by how many votes did it lose the election?
Options:
A)24,000
B)36,000
C)168,000
D)240,000
E)300,000
Rationale: D + R = 100 ---- (1)
D - R = 12 ---- (2)
Solving (1) and (2) D = 56% and R = 44%
44% of Total = 132000
Total = 300000
D = 168000
Difference = 168000 - 132000 = 36000
Answer: B
Answer: B
Question: At a reception, one-third of the guests departed at a certain time. Later two-fifths of the guests departed. Even later two-thirds of the remaining guests departed. If six people were left, how many were originally present at the party?
Options:
A)28
B)37
C)20
D)45
E)27
Rationale: Explanation:
Let Original members be x
First One third guest departed i.e x/3
Remaining guests = x – (x/3) = 2x/3
Now from the remaining (2x/3) two-fifths departed = 2/5(2x/3) = 4x/15
i.e. Now remaining guests will be (2x/3 – 4x/15) = 2x/5
Now from remaining (2x/5) two-thirds departed = 2/3(2x/5) = 4x/15
Now remaining guests = (2x/5 – 4x/15) = 2x/15
Given 2x/15 = 6 ⇒ x = 45
Answer: D
Answer: D
Question: A dishonest dealer professes to sell goods at the cost price but uses a false weight and gains 25%. Find his false weight age?
Options:
A)337
B)2399
C)800
D)287
E)221
Rationale: Explanation:
25 = E/(1000 - E) * 100
1000 - E = 4E
1000 = 5E => E = 200
1000 - 200 = 800
Answer:C
Answer: C
Question: Because he’s taxed by his home planet, Mork pays a tax rate of 10% on his income, while Mindy pays a rate of 20% on hers. If Mindy earned 3 times as much as Mork did, what was their combined tax rate?
Options:
A) 32.5%
B) 17.5%
C) 20%
D) 36%
E) 37.5%
Rationale: Say Morks income is - 100
So tax paid will be 10
Say Mindys income is 3*100 = 300
So tax paid is 20% * 300 = 60
Total tax paid = 10+60 = 70.
Combined tax % will be 70/100+300 = 15.5%
Answer: B
Question: Pipe A can fill a tank in 8 minutes and pipe B cam empty it in 24 minutes. If both the pipes are opened together after how many minutes should pipe B be closed, so that the tank is filled in 30 minutes?
Options:
A)18
B)27
C)98
D)27
E)66
Rationale: Let the pipe B be closed after x minutes.
30/8 - x/24 = 1 => x/24 = 30/8 - 1 = 11/4
=> x = 11/4 * 24
= 66.
Answer:E
Answer: E
Question: How many words can be formed by using all letters of the word 'AROUND' ?
Options:
A)712
B)720
C)757
D)736
E)742
Rationale: The word AROUND contains 6 different letters
Required number of words = 6P6 = 6! = 6*5*4*3*2*1 = 120
Answer is B
Answer: B
Question: The original price of a shirt was $20. It was decreased to $15 . What is the percent decrease of the price of this shirt.
Options:
A)25%
B)35%
C)45%
D)55%
E)65%
Rationale: The absolute decrease is
20 - 15 = $5
The percent decrease is the absolute decrease divided by the the original price (part/whole).
percent decease = 5 / 20 = 0.25
Multiply and divide 0.25 to obtain percent.
percent decease = 0.25 = 0.25 * 100 / 100 = 25 / 100 = 25%
Answer A
Answer: A