divelab/Sys2Bench huggingface dataset:
Question: Ten percent of Ram's monthly salary is equal to eight percent of Shyam's monthly salary. Shyam's monthly salary is twice Abhinav's monthly salary. If Abhinav's annual salary is Rs. 1.92 lakhs, find Ram's monthly salary?
Options:
A)28888
B)28892
C)25600
D)27772
E)17713
Rationale: Let the monthly salaries of Ram and Shyam be Rs. r and Rs. s respectively.
10/100 r = 8/100 s
r = 4/5 s
Monthly salary of Abhinav = (1.92 lakhs)/12 = Rs. 0.16 lakhs
s = 2(0.16 lakhs) = 0.32 lakhs
r = 4/5(0.32 lakhs) = Rs. 25600
Answer: C
Answer: C
Question: The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, then the weight of B is:
Options:
A)17 kg
B)20 kg
C)22 kg
D)26 kg
E)31 kg
Rationale: Let A, B, C represent their respective weights. Then, we have:
A + B + C = (45 x 3) = 135 .... (i)
A + B = (40 x 2) = 80 .... (ii)
B + C = (43 x 2) = 86 ....(iii)
Adding (ii) and (iii), we get: A + 2B + C = 166 .... (iv)
Subtracting (i) from (iv), we get : B = 31.
B's weight = 31 kg.
Answer: Option E
Answer: E
Question: A man rows to a place 24 km distance and come back in 7 hours. He finds that he can row 2 km with the up stream in the same time as 3 km against the down stream. The rate of the stream is
Options:
A)10/3 km/hr
B)13/3 km/hr
C)20/7 km/hr
D)30/7 km/hr
E)40/7 km/hr
Rationale: Explanation:
Speed down stream = distance/time = 3/x
Speed up stream = distance/time = 2/x
Time taken to row 24 km up stream and down stream is
= 48/(2/x) + 48/(3/x)
= 48x/2 + 48x/3 = 48x(5/6) = 8x+5 = 40x
40x = 7
x = 7/40 hr
Speed of down stream 3/(7/40) = 120/7
speed of up stream = 2/(7/40) = 80/7
Rate of stream = 1/2(a - b) = 1/2[(120/7)-(80/7)]
= 1/2(40/7)
= 20/7 km/hr
Answer: Option C
Answer: C
Question: What is the remainder when 3^381 is divided by 5 ?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: I also agree that the remainder is '3' (using the last digit of the powers of 7). Could we have the official answer please?D
Answer: D
Question: P alone can complete a piece of work in 6 days. Work done by Q alone in one day is equal to one-third of the work done by P alone in one day. In how many days can the work be completed if P and Q work together?
Options:
A)6 (1/4) days
B)6 (3/4) days
C)7 (3/4) days
D)8 (3/4) days
E)9 (3/4) days
Rationale: Work done by P alone in one day = 1/9th of the total work done by Q alone in one day = 1/3(of that done by P in one day) = 1/3(1/9 of the total) = 1/27 of the total.
Work done by P and Q, working together in one day = 1/9 + 1/27 = 4/27 of the total
They would take 27/4 days = 6 (3/4) days to complete the work working together.
ANSWER:B
Answer: B
Question: A runs twice as fast as B and gives B a start of 60m.How long should the racecourse be so that A and B might reach in the same time?
Options:
A)120 m.
B)80 m.
C)150 m.
D)100 m.
E)None of the above
Rationale: ratio of speeds of a and b is 2:1
b is 60m away from a but we know that a covers 1 meter(2-1) more in every second than b
the time taken for a to cover 60m is 60/1=60m
so the total time taken by a and b to reach =2*60=120m
ANSWER:A
Answer: A
Question: If 5 is added to twice a number and this sum is multiplied by 10, the result is the same as if the number is multiplied by 5 and 20 is added to the product. What is the number?
Options:
A)-5
B)-8
C)-2
D)10
E)11
Rationale: let the number be x;
10(5+2x)=5x+20;
x=-2
ANSWER:C
Answer: C
Question: Laxman went 15 kms from my house, then turned left and walked 20 kms. He then turned east and walked 25 kms and finally turning left covered 20kms. How far was he from his house?
Options:
A)40*1.414
B)30*1.414
C)45*1.414
D)20*1.414
E)48*1.414
Rationale: If we plot a graph for the given motion then we find that total distance in a direction is 40 km. and there is 40 km. in perpendicular to that direction so direct distance of Laxman from the initial position will be sqrt(40^2 + 40^2) = 40 sqrt(2) = 40*1.414
ANSWER:A
Answer: A
Question: A sum of money invested for a certain number of years at 8% p.a. simple interest grows to Rs.180. The same sum of money invested for the same number of years at 4% p.a. simple interest grows to Rs.120. For how many years was the sum invested?
Options:
A)25 years
B)40 years
C)33 years and 4 months
D)Cannot be determined
E)None of these
Rationale: Solution:
From the information provided we know that,
Principal + 8% p.a. interest on principal for n years = 180 …….. (1)
Principal + 4% p.a. interest on principal for n years = 120 ……… (2)
Subtracting equation (2) from equation (1), we get
4% p.a. interest on principal for n years = Rs.60.
Now, we can substitute this value in equation (2),
i.e Principal + 60 = 120
= Principal = Rs.60.
We know that SI = pnr/100, where p is the principal, n the number of years and r the rate percent of interest.
In equation (2), p = Rs.60, r = 4% p.a. and the simple interest = Rs.60.
Therefore, 60 = (60 X n X 4)/100
=> n = 100/4 = 25 years.
Answer A
Answer: A
Question: Calculate the number of urns of water needed to fill a tank of dimensions of 10x10x5m to 90% full, if the volume of the urn is 0.8m3 and can only be filled to 80%.
Options:
A)520
B)650.2
C)685.5
D)703.1
E)712.2
Rationale: Volume of the tank that needed to be filled=10x10x5x0.9=450
Volume of the urn that can be filled=0.8x0.8=0.64
No. of urns of water needed to fill the tank=450/0.64= 703.1
Answer: D
Answer: D
Question: A clock is set right at 5 a.m. The clock loses 16 minutes in 24 hours.What will be the true time when the clock indicates 10 p.m. on 4th day?
Options:
A)11pm
B)12pm
C)10pm
D)09pm
E)08pm
Rationale: Time from 5 am. on a day to 10 pm. on 4th day = 89 hours.
Now 23 hrs 44 min. of this clock = 24 hours of correct clock.
356/15 hrs of this clock = 24 hours of correct clock
89 hrs of this clock = (24 x 31556 x 89) hrs of correct clock.
= 90 hrs of correct clock.
So, the correct time is 11 p.m.
Answer:A
Answer: A
Question: 7 speakers gathered to deliver speeches on two topics. Even though 7 speeches were initially planned to be delivered, due to lack of time only 2 speeches were finally decided to be delivered. Topics are to be spoken in a specific order and the speeches differ with respect to speaker or topic. How many such two speeches are possible?
Options:
A)2
B)49
C)50
D)47
E)1024
Rationale: 1)there are 7 speeches in ONE topic and 7 in OTHER..
2)there is a specific order for topics, so
a) both the topics are to be spoken on- so ONE from each
b) the order does not matter since there is ONLY one specific order..
so 7C1∗7C1=7∗7=49
ANSWER:B
Answer: B
Question: Bill is golfing with two friends and can either buy generic golf tees that are packaged by the dozen or the higher quality Aero flight tees that come by the pair. What is the minimum number of packages of Aero flight tees Bill must purchase to ensure that he has at least 10 golf tees for each member of his foursome, if he will buy no more than 2 packages of the generic golf tees?
Options:
A)3
B)10
C)8
D)4
E)2
Rationale: At least 10 golf tees for each member of his threesome = total of at least 3*10 = 30 tees.
2 packages of the generic golf tees, that are packaged by the dozen = 2*12 = 24 tees.
So, Bill must by at least 6 Aero tees. They come by the pair, hence he must by at least 6/2 = 3 packages of Aero flight tees.
Answer: A
Answer: A
Question: What is the selling price of a car? cost of car is Rs 60 & profit 10% profit over selling price
Options:
A)63
B)64
C)65
D)66
E)67
Rationale: sp=1.1*60=66
ANSWER:D
Answer: D
Question: Two unbiased coins are tossed. Find the probability of getting at most one head?
Options:
A)1/2
B)3/4
C)2/5
D)2/3
E)1/4
Rationale: S = {HH,HT,TH,TT}
E = Event of getting at most one head
E = {TT,HT,TH}
P(E) = 3/4
Answer is B
Answer: B
Question: Compound interest of Rs.5000 at 10% per annum for 1 1/2years will be (interest compounded half yearly).
Options:
A)Rs.473
B)Rs.374
C)Rs.495
D)Rs.788
E)None of the above
Rationale: 10% interest per annum will be 5% interest half yearly for 3 terms( 1 1/2 years)
So compound interest=5000[1+(5/100)]^3 - 5000=5000[(21/20)^3 -1]
=5000(9261-8000)/8000
=5*1261/8
=788
ANSWER:D
Answer: D
Question: An airplane flies against the wind from A to B in 8 hours. The same airplane returns from B to A, in the same direction as the wind, in 7 hours. Find the ratio of the speed of the airplane (in still air) to the speed of the wind.
Options:
A)5
B)10
C)15
D)20
E)25
Rationale: Let x = speed of airplane in still air, y = speed of wind and D the distance between A and B. Find the ratio x / y
Against the wind: D = 8(x - y), with the wind: D = 7(x + y)
8x - 8y = 7x + 7y, hence x / y = 15
correct answer C
Answer: C
Question: A contractor undertakes to complete the construction of a tunnel 720 meters long in 240 days and employs 60 men for the purpose. After 120 days, he finds that only 240 meters of the tunnel is complete. How many more men should be employ in order to complete the work in time?
Options:
A)76 men
B)60 men
C)78 men
D)87 men
E)75 men
Rationale: In 120days, only 240m of the tunnel is constructed by 60 men.
The remaining 120days, 480m of the tunnel can be constructed by 120 men.
Additional number of men required
= 120 - 60
= 60 men.
Answer: B
Answer: B
Question: The length of the bridge, which a train 130 metres long and travelling at 36 km/hr can cross in 45 seconds, is:
Options:
A)320 m
B)225 m
C)245 m
D)250 m
E)240 m
Rationale: Speed = [36X 5/18] m/sec = 10 m/sec
Time = 45 sec
Let the length of bridge be x metres.
Then, (130 + x)/45 = 10 => 130 + x = 450 => x = 320 m.
ANSWER:A
Answer: A
Question: Which of the following is equal to the value of 2^7 + 2^7 + 3^7 + 3^7 + 3^7 ?
Options:
A)2^8 + 3^8
B)2^6 + 3^8
C)2^8 + 3^6
D)2^9 + 3^9
E)2^5 + 3^5
Rationale: 2^7 + 2^7 + 3^7 + 3^7 + 3^7
= 2 (2^7) + 3 (3^7)
= 2^1 (2^7) + 3^1 (3^7)
= 2^(1+7) + 3^(1+7)
= 2^8 + 3^8
Ans: A
Answer: A
Question: Fred and Sam are standing 50 miles apart and they start walking in a straight line toward each other at the same time. If Fred walks at a constant speed of 5 miles per hour and Sam walks at a constant speed of 5 miles per hour, how many miles has Sam walked when they meet?
Options:
A)5
B)9
C)25
D)30
E)45
Rationale: relative distance =50 miles
relative speed =5+5 =10 miles per hour
time taken =50/10=5 hours
distance travelled by sam =5*5=25 miles= C
Answer: C
Question: If -1 < x < 0, which of the following must be true?
I. x^7 < x^3
II. x^3 < 1 – x
III. x^5 < x^3
Options:
A)II,III only
B)I,II,III only
C)I only
D)II only
E)III only
Rationale: Answer : B
Answer: B
Question: On a trip, a cyclist averaged 8 miles per hour for the first 12 miles and 12 miles per hour for the remaining 24 miles. If the cyclist returned immediately via the same route and took a total of 7.5 hours for the round trip, what was the average speed (in miles per hour) for the return trip?
Options:
A)9
B)10
C)11
D)12
E)13
Rationale: The time to go 36 miles was 12/8+24/12=1.5+2=3.5 hours.
The average speed for the return trip was 36 miles/4 hours= 9 mph.
The answer is A.
Answer: A
Question: A man can do a piece of work in 5 days, but with the help of his son he can do it in 3 days. In what time can the son do it alone ?
Options:
A)13/2
B)19/2
C)21/2
D)15/2
E)None
Rationale: Son's one day work = (1/3âˆ’1/5)=2/15
So son will do whole work in = 15/2 days
Answer: C
Answer: C
Question: At present, the ratio between the ages of Arun and Deepak is 4:3. After 6 years, Arun's age will be 30 years. What is the age of Deepak at present?
Options:
A)77 years
B)15 years
C)66 years
D)18 years
E)55 years
Rationale: Let the present ages of Arun and Deepak be 4x and 3x years respectively.
Then, 4x + 6 = 30 => x = 6
Deepak's age = 3x = 18 years.
Answer: D
Answer: D
Question: Calculate the amount that an investor needs to be invest to earn $441 in interest in 12 months if the investor plans to invest x dollars in a savings account that pays interest at an annual rate of 7% compounded semi-annually?
Options:
A)6209
B)6200
C)6799
D)6199
E)6685
Rationale: the approach is substitution,
our interest requirement is $441 after 12 months, 2 compounding period.
calculate the compound interest on each option and find out the one that yields $441 in 12 months
6200 yielded $441
using the formula
A = P(1 + r/n)nt
hence answer is B
Answer: B
Question: What least number should be added to 1052, so that the sum is completely divisible by 23
Options:
A)A)4
B)B)1
C)C)6
D)D)3
E)E)5
Rationale: Explanation:
(1052 / 23) gives remainder 17
17 + 6 = 23, So we need to add 6
Answer: Option C
Answer: C
Question: The population of a bacteria colony doubles every day. If it was started 9 days ago with 2 bacteria and each bacteria lives for 11 days, how large is the colony today?
Options:
A)512
B)768
C)4096
D)2048
E)1024
Rationale: 9 days ago- 2
8 days ago- 4
7 days ago- 8
6 days ago- 16
5 days ago- 32
4 days ago- 64
3 days ago- 128
2 days ago- 256
Yesterday- 512
Today- 1024
Ans:E
Answer: E
Question: Given 2x + y + z = 3 and 5x + 3y + z = 15, what is the value of x + y - z?
Options:
A)5
B)6
C)7
D)8
E)9
Rationale: (1) 5x + 3y + z = 15
If 2x + y + z = 3, then (2) 4x + 2y + 2z = 6
Let's subtract equation (2) for equation (1).
x + y - z = 9
The answer is E.
Answer: E
Question: A woman takes 5hr 45min in walking to certain place and riding back. She would have gained 2hrs by riding both ways. The time she would take to walk both ways is?
Options:
A)6 hr 45 min
B)3 hr 45 min
C)8 hr 55 min
D)7 hr 45 min
E)4 hr 60 min
Rationale: D
7 hr 45 min
Let x be the speed of walked
Let y be the speed of ride
Let D be the distance
Then D/x + D/y = 23/4 hr -------------------(1)
D/y + D/y = 23/4 – 2 hr
D/y = 15/8 ----------------------------------(2)
substitute 2 in 1
D/x + 15/8 = 23/4
D/x = 23/4 -15/8 =46-15/8 =31/8
Time taken for walk one way is 31/8 hr
time taken to walk to and fro is 2*31/8 = 31/4 hr
=7 hr 45 min
Answer: D
Question: If x > 0.7, which of the following could be the value of x?
Options:
A)√0.06
B)√0.07
C)√0.7
D)√0.05
E)√0.04
Rationale: Answer : C
Answer: C
Question: (64 - 12)^2 + 4 x 64 x 12 = ?
Options:
A)5246
B)4406
C)5776
D)5126
E)5128
Rationale: Explanation :
(a + b)^2 = a^2 + 2ab + b^2
(a - b)^2 = a^2 - 2ab + b^2
Here, the given statement is like (a - b)^2 + 4ab where a= 64 and b = 12
(a - b)^2 + 4ab = (a^2 - 2ab + b^2) + 4ab = a^2 + 2ab + b^2 = (a + b)^2
Hence (64 - 12)^2 + 4 x 64 x 12 = (64 + 12)^2 = 76^2 = 5776
Answer is C
Answer: C
Question: There is a sequence ni such, in which i is a positive integer, ni+1=2ni.
If n1=1, n2=2, n3=4, n4=8, what is the scope including n11?
Options:
A)10~100
B)1,000~10,000
C)10,000~100,000
D)100,000~1,000,000
E)1,000,000~
Rationale: -> ni=2^(i-1) -> 2^10=1,024>1,000=10^3 -> n11=2^10=(2^10)>(10^3)=10^3
Thus, the answer is B.
Answer: B
Question: A and B can do a job in 15 days and 10 days, respectively. They began the work together but A leaves after some days and B finished the remaining job in 5 days. After how many days did A leave?
Options:
A)2 days
B)3 days
C)1 day
D)4 days
E)None of these
Rationale: A’s one day’s work = 1⁄15 th work.
B’s one day’s work = 1⁄10 th work.
(A + B)’s one day’s work = 1⁄15 + 1⁄10 = 1⁄6 th work.
Let A left after x days.
∴ (A + B)’s x days’ work = x⁄6 th work.
Remaining work = 1 - x⁄6 = (6 - x)⁄6 th work.
Now, in 5 days, work done by B = (6 - x)⁄6 th work.
∴ in 1 day work done by B = (6 - x)⁄30 th work.
and (6 - x)⁄30 = 1⁄10
∴ x = 3 days
Answer B
Answer: B
Question: If Q = x% of y and B = y% of x, then which of the following is true?
Options:
A)1) Q is smaller than B.
B)2) A is greater than B
C)3) Relationship between A and B cannot be determined.
D)4) If x is smaller than y, then Q is greater than B.
E)5) None of the above
Rationale: Basically Q = B = xy/100
None of the options mentions this; hence E.
Answer: E
Question: A and B undertake to do a piece of work for Rs. 600. A alone can do it in 6 days while B alone can do it in 8 days. With the help of C, they finish it in 3 days. !find the share of each.
Options:
A)25
B)50
C)75
D)80
E)None of them
Rationale: C's 1 day's work = 1/3-(1/6+1/8)=24
A : B : C = Ratio of their 1 day's work = 1/6:1/8:1/24= 4 : 3 : 1.
A’s share = Rs. (600 *4/8) = Rs.300, B's share = Rs. (600 *3/8) = Rs. 225.
C's share = Rs. [600 - (300 + 225») = Rs. 75.
Answer is C
Answer: C
Question: A grocer is storing soap boxes in cartons that measure 25 inches by 42 inches by 60 inches. If the measurement of each soap box is 7 inches by 12 inches by 5 inches, then what is the maximum number of soap boxes that can be placed in each carton?
Options:
A)210
B)150
C)280
D)300
E)420
Rationale: however the process of dividing the volume of box by the volume of a soap seems flawed but it does work in this case due to the numbers
Dimensions of the box =25*42*60
Dimensions of the soap = 5*12*7
placing the 7 inch side along 42 inch side we get 6 soaps in a line and in a similar way 5 along 25 and 6 along 60
we get = 5x6x5 = 150
so the question is why this particular arrangement, in order to maximize number of soaps we need to minimize the space wasted and this is the only config where we dont waste any space so we can expect the maximum number
the answer is (B)
Answer: B
Question: Find the value of 72515 x 9999 = m?
Options:
A)456578972
B)725077485
C)653658791
D)725117481
E)357889964
Rationale: 72515 x 9999 = 72515 x (10000 - 1)
= 72515 x 10000 - 72515 x 1
= 725150000 - 72515
= 725077485
B
Answer: B
Question: The rate of a certain chemical reaction is directly proportional to the square of the concentration of chemical A present and inversely proportional to the concentration of chemical T present. If the concentration of chemical T is increased by 100 percent, which of the following is closest to the percent change in the concentration of chemical A required to keep the reaction rate unchanged?
Options:
A)100% decrease
B)50% decrease
C)40% decrease
D)40% increase
E)50% increase
Rationale: Let A and T be the concentratrations of the individual chemicals.
Rate of chemical reaction = A^2/T
Since new T is increased by 100%
Rate = A^2/(2T)
For the rate to be constant, new value of A should be square root(2)
So new value of A = 1.414A
That means A is increased by 41.4%
Nearest solution is D
Answer: D
Question: How many of the following numbers are divisible by 132?
264, 396, 462, 792, 968, 2178, 5184, 6336,528,1320
Options:
A)4
B)5
C)6
D)7
E)8
Rationale: Explanation:
A number is divisible by 132, if it is divisible by each one of 11, 3 and 4.
Clearly, 968 is not divisible by 3. None of 462 and 2178 is divisible by 4.
Also, 5184 is not divisible by 11.
Each one of remaining 6 is divisible by each one of 11, 3 and 4 and therefore, by 132.
Answer: C
Answer: C
Question: Rs.160 contained in a box consists of one rupee, 50 paisa and 25 paisa coins in the ratio 4:5:6. What is the number of 25 paisa coins?
Options:
A)120
B)130
C)140
D)150
E)200
Rationale: 4x 5x 6x
100 50 25
400x + 350x + 150x = 16000
x = 20
6x = 120
ANSWER A
Answer: A
Question: If x is an integer and 2.134 × 10^x is less than 2,200,000, what is the greatest possible value for x?
Options:
A)7
B)6
C)5
D)4
E)3
Rationale: x is an integer and 2.134 × 10x is less than 2,200,000, what is the greatest possible value for x?
for 2.134 × 10x is less than 2,200,000 to remain true, the greatest number is 2,134,000, which makes x=6
B. 6
Answer: B
Question: Population of a city in 20004 was 1000000. If in 2005 there isan increment of 15% , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45%, then find the population of city atthe end of the year 2007
Options:
A)986431
B)964347
C)946778
D)934656
E)1083875
Rationale: Required population = P (1 + R1/100)(1 - R2/100)(1 + R3/100)
= P (1 + 15/100)(1 - 35/100)(1 + 45/100)
= 1083875
E
Answer: E
Question: A jar holds 10 pink candies and 30 yellow candies. One candy is drawn at random. What is the probability that the candy drawn is yellow?
Options:
A)1
B)1/2
C)3/5
D)3/4
E)None of these
Rationale: Explanation:
Total cases = 10 + 30 = 40
Favourable cases = 30
So probability = 30/40 = 3/4
Answer: D
Answer: D
Question: The annual interest rate earned by an investment increased by 10 percent from last year to this year. If the annual interest rate earned by the investment this year was 12 percent, what was the annual interest rate last year?
Options:
A)1%
B)1.1%
C)9.1%
D)10%
E)10.9%
Rationale: 12=1.1*x
X=10.90%
Answer E)
Answer: E
Question: If square-root of 15 is 3.87. Then find the value of square-root of (5/3)
Options:
A)1.29
B)1.39
C)1.49
D)1.59
E)1.69
Rationale: => root 5/ root 3 = (root 5/ root 3)*(root 3/ root 3)
= root 15/ root 9
= 3.87/3
= 1.29
ANSWER:A
Answer: A
Question: A boat covers a certain distance downstream in 1 hour, while it comes back in 1½ hours. If the speed of the stream be 3 kmph, what is the speed of the boat in still water?
Options:
A)12 kmph
B)13 kmph
C)14 kmph
D)15 kmph
E)None
Rationale: Sol.
Let the speed of the boat in still water be x kmph. Then,
Speed downstream = (x + 3) kmph, Speed upstream = (x - 3)kmph.
∴ (x + 3) * 1 = (x -3) * 3/2 ⇔ 2x + 6 = 3x - 9 ⇔ x = 15 kmph.
Answer D
Answer: D
Question: What is the product of the greatest 2 digit multiple of 9 and the greatest 2 digit prime number?
Options:
A)9,312
B)9,408
C)9,603
D)9,603
E)9,702
Rationale: the greatest 2 digit multiple of 9: 99
the greatest 2 digit prime numebr: 97
97*99.
9603
C
Answer: C
Question: a,b,c,d,e,f,g sitting in a row what is the probability that a & c sitting adjacent.
Options:
A)6/7
B)5/7
C)4/7
D)3/7
E)2/7
Rationale: total number of arrangement is= 7!= 5040
Favorable event i.e a and b can be arranged in 2! and the remaining can be arranged in 6! since ab can be in any of the four positions.
so 6!*2!/7! = 2/7
ANSWER:E
Answer: E
Question: The least number which when divided by 5, 6 , 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder, is:
Options:
A)1677
B)2523
C)1683
D)3363
E)3567
Rationale: L.C.M. of 5, 6, 7, 8 = 840.
Required number is of the form 840k + 3
Least value of k for which (840k + 3) is divisible by 9 is k = 2.
Required number = (840 x 2 + 3) = 1683. Answer: Option 'C'
Answer: C
Question: Joe’s average (arithmetic mean) test score across 4 equally weighted tests was 90. He was allowed to drop his lowest score. After doing so, his average test score improved to 95. What is the lowest test score that was dropped?
Options:
A)20
B)25
C)55
D)75
E)80
Rationale: The arithmetic mean of 4 equally weighted tests was 90. So what we can assume is that we have 4 test scores, each 90.
He dropped his lowest score and the avg went to 95. This means that the lowest score was not 90 and other three scores had given the lowest score 5 each to make it up to 90 too. When the lowest score was removed, the other 3 scores got their 5 back. So the lowest score was 3 *5 = 15 less than 90.
So the lowest score = 90 - 15 = 75
Answer (D)
Answer: D
Question: What is the units digit of 28! + 50! + 3! + 4!?
Options:
A)0
B)2
C)4
D)6
E)8
Rationale: For all N greater than 4, the units digit of N! is 0.
The sum of the four units digits is 0 + 0 + 6 + 4 = 10
The units digit is 0.
The answer is A.
Answer: A
Question: On a certain baseball team, 1 out of 5 batters hit the ball. If 2 out of every 10 batters who hit the ball score a home-run, and there are 20 batters who've hit home-runs, how many players have been up to bat?
Options:
A)500
B)50
C)100
D)5,0000
E)2,000
Rationale: Proportions: Let B = batters, and Bh = batters hit the ball, and Bhr = batters hit the ball and home-run.
20Bhr/xBh = 2Bhr/10Bh
xBh = 100Bh
1Bh/5B = 100Bh/yB
yB = 500B
Answer: A
Answer: A
Question: The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 2000 resolutions?
Options:
A)1187 m
B)1704 m
C)2816 m
D)2827 m
E)2897 m
Rationale: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 2000 resolutions.
= 2000 * 2 * 22/7 * 22.4
= 281600 cm
= 2816 m
Answer:C
Answer: C