divelab/Sys2Bench huggingface dataset:
Question: When running a mile during a recent track meet, Nuria was initially credited with a final time of 5 minutes, 40 seconds. Shortly after her run, officials realized that the timing mechanism malfunctioned. The stopwatch did not begin timing her until 11/25 of a minute after she began to run. If the time was otherwise correct, how long did it actually take Nuria to run the mile?
Options:
A)5 minutes, 17.6 seconds
B)5 minutes, 21.8 seconds
C)5 minutes, 43.56 seconds
D)5 minutes, 44.44 seconds
E)6 minutes, 10.4 seconds
Rationale: One approach:
The watch starts to work after Nuria began his running. It means the time should be greater than credited 5 minutes, 40 seconds. The only number is 6 minutes, 10.4 seconds.
Another approach:
11/25 close to 30 second when added to the 5 minutes, 40 seconds, it means it passes 6 minute.
Answer: E
Answer: E
Question: On a sum of money, the S.I. for 2 years is Rs. 660, while the C.I. is Rs. 696.30, the rate of interest being the same in both the cases. The rate of interest is?
Options:
A)22
B)99
C)27
D)11
E)37
Rationale: Difference in C.I. and S.I for 2 years = (696.30 - 660) = Rs. 36.30.
S.I for one year = Rs. 330.
S.I. on Rs. 330 for 1 year = Rs. 36.30
Rate = (100 * 36.30)/(330 * 1) = 11%.Answer: D
Answer: D
Question: In 1990 a total of 100 earthquakes occurred worldwide, some but not all of which occurred in Asia. If 20 of these earthquakes occurred in Asia, which of the following represents the ratio of the number of earthquakes that occurred in Asia to the number that did NOT occur in Asia?
Options:
A)1/7
B)1/6
C)1/2
D)1/4
E)1/3
Rationale: We're given a couple of facts to work with:
1) There were a total of 100 earthquakes
2) Of those earthquakes, 20 of them occurred in Asia
We're asked for the ratio of the number of earthquakes that occurred IN ASIA to the number of earthquakes that DID NOT occur in Asia.
Thus, there were 80 earthquakes that DID NOT occur in Asia....
The answer to the question is 20/80 ie. 1/4
Answer : D
Answer: D
Question: Danya prepared 4 different letters to 4 different addresses. For each letter, she prepared one envelope with its correct address. If the 4 letters are to be put into the four envelopes at random, what is the probability that only one letter will be put into the envelope with its correct address?
Options:
A)1/24
B)1/8
C)1/4
D)1/3
E)3/8
Rationale: Total Danya# of ways - 4! = 24.
Desired:
A-Mapped to the only correct address----------x 1 way only
B-Mapped to other two incorrect addresses - x 2 ways
C-Mapped to other two incorrect addresses - x 2 ways
D-Mapped to other two incorrect addresses - x 2 ways
Therefore, 1*2*2*2/24 = 1/3.?
Answer: D
Question: Excluding stoppages, the speed of a train is 67 kmph and including stoppages it is 51 kmph. Of how many minutes does the train stop per hour?
Options:
A)82
B)17
C)14
D)82
E)18
Rationale: Explanation:
T =16/67 * 60 = 14
Answer: Option C
Answer: C
Question: The mark up between weights of A and B is is 20 percent of the weight of A. The markup is what percent of the weight of B ?
(markup = weight of B - weight of A)
Options:
A) 8%
B) 10%
C) 12 1/2%
D) 15%
E) 16 2/3%
Rationale: A = weight of A
B = weight of B
MP = 0.2 A
B = A + 0.2 A = 1.2 A
hence Markup = B-A = 0.2/1.2 B = 1/6 B. Hence MP is 16.67% of B
Answer E
Answer: E
Question: In the sequence S, each term after the first is twice the previous term. If the first term of sequence S is 3, what is the sum of the 14th, 15th, 16th, 17th, 18th and 19th terms in sequence S?
Options:
A)3(2^16)
B)9(2^15)
C)21(2^14)
D)9(2^14)
E)189(2^13)
Rationale: The terms in the sequence can be shown as
a(n) = 2* a(n-1)
So, the sequence will look like: 3, 2*3, (2^2) *3,...
And the nth term will be given as 2^(n-1) *3
Therefore, a(14) = (2^13)*3, a(15) = (2^14) *3, a(16) = (2^15) *3, a(17) = (2^16) *3 , a(18) = (2^17) *3 and a(19) = (2^18) *3
So, a(14) + a(15) + a(16)+ a(17)+ a(18) = (2^13) *3 + (2^14) *3 + (2^15) *3+ (2^16) *3+ (2^17) *3+ (2^18) *3
= 3* (2^13) *(1+2+4+8+16+32) = 3* (2^13) *63
= 189 * (2^13)
Answer : E
Answer: E
Question: What was the day of the week on 28th May,2006 ?
Options:
A)Thursday
B)Friday
C)Saturday
D)Sunday
E)None of these
Rationale: Solution
28 May,2006 =(2005 years + Period from 1.1.2006 to 28.5.2006)
Odd days in 1600 years = 0
Odd days in 400 years = 0
5 years =(4 ordinary years + 1 leap year)=(4 x 1 + 1 x 2) odd days
=6 odd days
Jan. Feb. March April May
(31 + 28 + 31 + 30 + 28) = 148 days =(21 weeks + 1 day)
= 1 odd day
Total number of odd days = (0 + 0 + 6 + 1)=7 = 0 odd day.
Given day is Sunday. Answer D
Answer: D
Question: Jerry went to a shop and bought things worth Rs. 40, out of which 30 % went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
Options:
A)19
B)19.7
C)21.3
D)31.5
E)34.7
Rationale: Total cost of the items he purchased = Rs.40
Given that out of this Rs.40, 30 % is given as tax
=> Total tax incurred = 30 % = Rs.30/100
Let the cost of the tax free items = x
Given that tax rate = 6%
∴ (40−30/100−x)6/100 = 30/100
⇒ 6(40 −0.3 −x) = 30
⇒ (40 − 0.3 − x) = 5
⇒ x = 40 − 0.3 − 5 = 34.7
E)
Answer: E
Question: Cheese, bologna, and peanut butter sandwiches were made for a picnic in a ratio of 5 to 7 to 8. If a total of 240 sandwiches were made, how many peanut butter sandwiches
were made?
Options:
A)15
B)30
C)38
D)42
E)96
Rationale: For deciding such task we should calculate all parts 5 + 7 + 8 = 20 parts
and we should calculate how many sandwiches holds 1 part:
240 / 20 =12 sandwiches in one part
For peanut butter we have 8 parts so:
8 * 12 = 96
Answer is E
Answer: E
Question: Two goods trains each 250 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
Options:
A)24 sec
B)88 sec
C)48 sec
D)18 sec
E)9 sec
Rationale: Relative speed = 45 + 30 = 75 km/hr.
75 * 5/18 = 125/6 m/sec.
Distance covered = 250 + 250 = 500 m.
Required time = 500 * 6/125 = 48 sec.
Answer:A
Answer: A
Question: If the perimeter of a rectangular park is 1000 m, its length when its breadth is 200 m is?
Options:
A)50
B)100
C)200
D)300
E)400
Rationale: 2(l + 200) = 1000 => l = 300 m Answer: D
Answer: D
Question: Two unbiased coins are tossed. What is probability of getting at most one tail ?
Options:
A)12
B)13
C)32
D)34
E)None of these
Rationale: Explanation:
Total 4 cases = [HH, TT, TH, HT]
Favourable cases = [HH, TH, HT]
Please note we need atmost one tail, not atleast one tail.
So probability = 3/4
Answer: D
Answer: D
Question: Find the area of a parallelogram with base 20 cm and height 10 cm?
Options:
A)290 cm2
B)380 cm2
C)270 cm2
D)280 cm2
E)200 cm2
Rationale: Area of a parallelogram = base * height = 20 * 10
= 200 cm2
Answer:E
Answer: E
Question: A three-digit code for certain locks uses the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 according to the following constraints. The first digit cannot be 0 or 1, the second digit must be 0 or 1, and the second and third digits cannot both be 0 in the same code. How many different codes are possible?
Options:
A)144
B)152
C)160
D)168
E)176
Rationale: The first digit can be filled in 8 ways
For second digit , it can either be 0 or 1
Case 1 -
If second digit is 1 ,Third digit can take 10 values
number of codes = 8 * 1 * 10 = 80
Case 2 -
If second digit is 0,Third digit can take 9 values ( Third digit can't be zero)
number of codes = 8 * 1 * 9= 72
Total number of codes = 152
Answer B
Answer: B
Question: A sun is divided among X, Y and Z in such a way that for each rupee X gets, Y gets 45 paisa and Z gets 30 paisa. If the share of Y is RS. 27, what is the total amount?
Options:
A)178
B)105
C)176
D)159
E)162
Rationale: x:y:z = 100:45:30
20:9:6
9 --- 27
35 --- ? => 105
Answer: B
Answer: B
Question: A monkey ascends a greased pole 10 meters high. He ascends 2 meters in the first minute and then slips down 1 meter in the alternate minute. If this pattern continues until he climbs the pole , in how many minutes would he reach at the top of the pole ?
Options:
A)10th minute
B)21st minute
C)17th minute
D)22nd minute
E)13th minute
Rationale: The money is climbing 1meter in 2min. This pattern will go on till he reaches 10meters. I mean this will continue for first 8*2=16mins. he would have reached 8meters. After that he will climb 2meters and he will reach the pole. So total time taken = 16 + 1 = 17mins.
So, asnwer will be C
Answer: C
Question: Which of the following equations has a solution in common with x^2 - 7x + 10 = 0 ?
Options:
A)x^2 - 3x - 10 = 0
B)4x^2 + 9x + 2 = 0
C)4x^2 + 6x + 2 = 0
D)x^2 + 10x + 25 = 0
E)none of the above
Rationale: Given : x^2 - 7x + 10 = 0 => (x-2) (x-5) = 0 => 2 and 5 are the roots..
A. x^2 - 3x - 10 = 0 => (x+2) (x-5)
B. 4x^2 + 9x + 2 = 0 => (4x+1) (x+2)
C. 4x^2 + 6x + 2 = 0 => (2x+1) (2x+2)
D. x^2 + 10x + 25 = 0 => (x+5) (x+5)
None of the answer equations have exactly both the same roots as the question equation, but at least one of them does share one of the two roots.
So IMO "A" is correct answer... because it shares the one root (part of the solution), 5, from the (x-5) portion of its simplification.
Answer: A
Question: Find the difference between the local value and face value of 5 in the numeral 475240 is
Options:
A)4990
B)4890
C)4995
D)4885
E)4775
Rationale: Explanation:
(Local value of 5) - (Face value of 5)
= (5000 - 5) = 4995
Answer: Option C
Answer: C
Question: In a college, the ratio of the number of boys to girls is 8 : 5. If there are 100 girls, the total number of
students in the college is
Options:
A)420
B)520
C)620
D)260
E)None of these
Rationale: Explanation:
Let the boy are 8x and Girls are 5x
=> 5x = 100
=> x = 20
Total students = 8x+5x = 13x = 13(20) = 260
Answer: D
Answer: D
Question: There are 4 identical pens and 7 identical books. In how many ways can a person select at least one object from this set?
Options:
A)11
B)12
C)39
D)(2^4 - 1)(2^7 -1)
E)2^11 - 1
Rationale: 7 items can be chosen in 8 ways- 0,1,2..7 at a time
similarly 4 items can be chosen way will be 5- choosing 0, choosing 1.. choosing 4
total ways = 8*5=40..
But we are looking for AT LEAST 1, so subtract 1 way when both are 0..
ans 40-1=39.
ANSWER:C
Answer: C
Question: x, y, and z are three positive integers whose average is 10. If x≤y≤z and z-x=3, which of the following could be the median R of x, y, and z?
I. 9
II. 10
III. 11
Options:
A)I only
B)II only
C)III only
D)I and II only
E)I and III only
Rationale: Average gives us an idea that 3 nos. are close to 10.
so 10, 10, 10 is an unacceptable option because (z-x =3), but it helps in getting other combinations.
Let us see options.
If 9 has to be median R.
1st term has to less than 9 or equal to 9. (also maintain z-x = 3)
9 9 12 --> satisfies all conditions so 9 can be a median value.
If 11 has to be a median
3rd term has to be 11 or more than 11. (also maintain z-x = 3)
8 11 11 -->satisfies all conditions so 9 can be a median value.
Now for 10 to be median.
z+ x = 20 and z-x = 3, we wont have integer values of z.
10 cannot be a median
E is the answer.
Answer: E
Question: An article is bought for Rs.765 and sold for Rs.1000, find the gain percent?
Options:
A)30.6%
B)30.5%
C)30.7%
D)30.8%
E)30.9%
Rationale: 765 ---- 235
100 ---- ? => 30.7%
Answer:C
Answer: C
Question: If x/y = 2 and (a - x)/(3b - y) = 2, then the value of a/b is?
Options:
A) –3
B) -2
C) 6
D) 2
E) 3
Rationale: x = 2y
a - 2y = 2(3b - y)
a - 2y = 6b - 2y
a = 6b
a/b = 6
Answer: C
Answer: C
Question: At what rate percent on simple interest will Rs.750 amount to Rs.900 in 5 years?
Options:
A)5%
B)3 1/2%
C)4%
D)5 1/2 %
E)6 1/2 %
Rationale: Explanation:
150 = (750*5*R)/100
R = 4%
ANSWER IS C
Answer: C
Question: A can give B 100 meters start and C 200 meters start in a kilometer race. How much start can B give C in a kilometer race?
A. 111.12 m
Options:
A)111.12 m
B)221.12 m
C)271.12 m
D)611.12 m
E)191.12 m
Rationale: Explanation:
A runs 1000 m while B runs 900 m and C runs 800 m.
The number of meters that C runs when B runs 1000 m,
= (1000 * 800)/900 = 8000/9 = 888.88 m.
B can give C = 1000 - 888.88 = 111.12 m.
Answer:A
Answer: A
Question: A money lender lends Rs.2000 for six months at 20% p.a. rate. It the interest is reckoned quarterly than find the amount given after time limit.
Options:
A)2205
B)3387
C)2882
D)2997
E)1278
Rationale: A = 2000(21/20)2 = 2205
Answer: A
Answer: A
Question: A number whose fifth part increased by 4 is equal to its fourth part diminished by 4 is ?
Options:
A)160
B)180
C)200
D)220
E)None
Rationale: Answer
Let the number be N.
Then, (N/5) + 4 = (N/4) - 4
â‡’ (N/4) - (N/5) = 8
â‡’ (5N - 4N)/20 = 8
âˆ´ N = 160
Option: A
Answer: A
Question: In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 4 boys when a boy gets any no. of prizes?
Options:
A)53
B)58
C)64
D)69
E)72
Rationale: Ans.(C)
Sol. In this case, repetitions are allowed, so all the three prizes can be given in 4 ways, i.e. (4 x 4 x 4) ways = 43 ways = 64 ways Or nr ways = 43 ways = 64 ways
Answer: C
Question: A bullet train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the bullet train is 54 km/hr, what is the length of the platform?
Options:
A)240 m
B)220 m
C)260 m
D)224 m
E)239 m
Rationale: A
240 M
Speed = 54 x 5/18 = 15 m/s
Length of the bullet train = (15 x 20)m = 300 m.
Let the length of the platform be x metres.
Then, (x + 300)/36 = 15
--> x + 300 = 540
x = 240m.
Answer: A
Question: The timing of a college is from 12 p.m to 5.00 p.m. Five lectures are held in the given duration and a break of 5 minutes after each lecture is given to the students. Find the duration of each lecture.
Options:
A)56 minutes
B)45 minutes
C)30 minutes
D)48 minutes
E)44 minutes
Rationale: Explanation:
Total time a student spends in college = 5 hours 00 minutes = 300 minutes
As there are 5 lectures, the number of breaks between lectures is 4. Total time of the break = 20 minutes
Hence, the duration of each lecture is = (300 â€“ 20)/5
= 56 minutes
ANSWER A
Answer: A
Question: If n is a positive integer and the product of all the integers from 1 to n, inclusive, is a multiple of 8, what is the least possible value of n?
Options:
A)7
B)4
C)5
D)3
E)6
Rationale: We need 3 factors of 2, so n must be at least 4. Therefore, the answer is B.
Answer: B
Question: A third of Paul's marks in Mathematics exceeds a half of his marks in English by 30. If he got 240 marks in the two subjects together, how many marks did he get in English?
Options:
A)50
B)40
C)45
D)60
E)55
Rationale: Let Paul's marks in Mathematics and English be x and y respectively.
Then, x/3 - y/2 = 30, the LCM of 3,2 is 6 by cross multiplying we get 2x - 3y = 180 -- (I)and we know (x + y = 240) * 2 ==>
2x +2y = 480 --(II)
subtract (I) from (II) we get 5y = 300 ==> y = 60.
so Paul's marks in English is 60.
The correct answer is option D) 60.
Answer: D
Question: If A : B : C = 3 : 4 : 7, then what is the ratio of (A / B) : (B / C) : (C / A)?
Options:
A)63 : 48 : 196
B)66 : 49 : 190
C)56 : 40 : 186
D)46 : 38 : 160
E)43 : 20 : 170
Rationale: EXPLANATION:
Hint: If a = kb for some constant k, then we can say that a is directly proportional to b.
A : B : C = 3 : 4 : 7
Assume, A = 3 k, B = 4 k, C = 7 k
Therefore,
A/B	=	(3k)/(4K)	,	B/C	=	(4k)/(7K)	,	C/A	=	(7k)/(3K)
A/B	=	(3)/(4)	,	B/C	=	(4)/(7)	,	C/A	=	(7)/(3)
L.C.M of 3, 4, 7 is 84
(3 x 84) / 4 = 63
(4 x 84) / 7 = 48
(7 x 84) / 3 = 196
Ratio of (A/B) : (B/C) : (C/A) = 63:48:196
ANSWER IS A
Answer: A
Question: In how many ways 4 boys and 1 girls can be seated in a row so that they are alternate.
Options:
A)144
B)288
C)24
D)256
E)None
Rationale: Solution: Let the Arrangement be,
B B B B G
4 boys can be seated in 4! Ways.
Girl can be seated in 1! Ways.
Required number of ways,
= 4!*1! = 24.
Answer: Option C
Answer: C
Question: How long will it take for a sum of money to grow from Rs.5000 to Rs.20,000, if it is invested at 10% p.a simple interest?
Options:
A)30 years
B)64 years
C)72 years
D)56 years
E)None
Rationale: In this case, Rs. 5000 has become Rs.20,000.
Therefore, the interest earned = 20,000 – 5000 =15000
Interest for Rs 5000 @ 10% for 1 year = 500
500 - 1
15000 - ? => 30 years
Answer : A
Answer: A
Question: Find the area of the quadrilateral of one of its diagonals is 20 cm and its off sets 9 cm and 6 cm?
Options:
A)128 cm2
B)150 cm2
C)172 cm2
D)177 cm2
E)167 cm2
Rationale: 1/2 * 20(9 + 6)
= 150 cm2
Answer:B
Answer: B
Question: By selling an article for $100 a man gains $20 then his gain%?
Options:
A)25%
B)30%
C)50%
D)20%
E)10%
Rationale: S.P. = $100
Gain = $20
C.P. = 100-20 = 80
Gain% = 20/80 * 100 = 25%
Answer is A
Answer: A
Question: 1, 2, 9, 24, 120, 36,?
Options:
A)4040
B)5040
C)3040
D)2040
E)556
Rationale: 1!=1
2!=2
3^2=9
4!=24
5!=120
6^2=36
and according to the sequence now
7!=5040
ANSWER:B
Answer: B
Question: A cab driver 5 days income was $200, $150, $750, $400 , $500. Then his average income is?
Options:
A)$420
B)$410
C)$400
D)$390
E)$380
Rationale: avg = sum of observations/number of observations
avg income=(200+150+750+400+500)/5 = 400
Answer is C
Answer: C
Question: At a school, three-fifths of the male students and two-thirds of the female students speak a foreign language. If the number of males is equal to the number of females, what fraction of the students speak a foreign language?
Options:
A)17/30
B)19/30
C)11/15
D)7/15
E)2/5
Rationale: Let x be the number of students in the school.
The number of males who speak a foreign language is (3/5)(1/2)x = (3/10)x
The number of females who speak a foreign language is (2/3)(1/2)x = (1/3)x
The total number of students who speak a foreign language is (3/10)x + (1/3)x = (19/30)x
The answer is B.
Answer: B
Question: In a urban village of india named "owlna" , 90% people have refrigerator , 86% people have television , 80% people got computers and 80% got Air-conditionor. how many people(minimum) got all these luxury.
Options:
A)23%
B)36%
C)30%
D)34%
E)42%
Rationale: B
10%
100 - [ (100-90)+(100-86)+(100-80) +(100-80)]
=100-(10+14+20+20)
=100-64
Answer: B
Question: If a man lost 1% by selling oranges at the rate of 16 a rupee at how many a rupee must he sell them to gain 44%?
Options:
A)12
B)14
C)7
D)11
E)10
Rationale: 99% ---- 16
144% ---- ?
99/144* 16 = 11
Answer: D
Answer: D
Question: A man purchased 2 blankets @ Rs.100 each, 5 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.150. Find the unknown rate of two blankets?
Options:
A)A)300
B)B)350
C)C)450
D)D)470
E)E)550
Rationale: Explanation:
10 * 150 = 1500
2 * 100 + 5 * 150 = 950
1500 – 950 = 550
E
Answer: E
Question: If a farmer wants to plough a farm field on time, he must plough 340 hectares a day. For technical reasons he ploughed only 85 hectares a day, hence he had to plough 2 more days than he planned and he still has 40 hectares left. What is the area of the farm field and how many days the farmer planned to work initially?
Options:
A)280
B)490
C)720
D)435
E)679
Rationale: Let x be the number of days in the initial plan. Therefore, the whole field is 340â‹…x hectares. The farmer had to work for x+2 days, and he ploughed 85(x+2) hectares, leaving 40 hectares unploughed. Then we have the equation:
340x=85(x+2)+40
255x=210
x=0.823
So the farmer planned to have the work done in 6 days, and the area of the farm field is 340(0.823)=280 hectares
correct answer A
Answer: A
Question: What percent is 120 of 90?
Options:
A)133 1/3 %
B)132 1/3%
C)132 2/3%
D)132 2/5%
E)131 1/5%
Rationale: 120/90 = 4/3
4/3 × 100 = 400/3 = 133 1/3 %
A)
Answer: A
Question: The average age of students of a class is 15.8 years. The average age of boys in the class is 16.5 years and that of the girls is 15.4 years. The ration of the number of boys to the number of girls in the class is:
Options:
A)2:5
B)2:3
C)2:4
D)2:1
E)4:7
Rationale: Let the ratio be k : 1. Then,
k * 16.5 + 1 * 15.4 = (k + 1) * 15.8
= (16.5 - 15.8)k = (15.8 - 15.4)
= k = 0.4/0.7 = 4/7
Required ratio = 4/7 : 1 = 4:7.
Answer:E
Answer: E
Question: A boy sells a horse for Rs.800 and loses something, if he had sold it for Rs.980, his gain would have been double the former loss. Find the cost price of the horse?
Options:
A)860
B)880
C)900
D)920
E)940
Rationale: CP = SP + 1CP = SP - g
800 + x = 980 - 2x
3x = 180 => x = 60
CP = 800 + 60 = 860
A
Answer: A
Question: If the cost price of 50 articles is equal to the selling price of 40 articles, then the gain or loss percent is?
Options:
A)27%
B)75%
C)95%
D)35%
E)25%
Rationale: Given that, cost price of 50 article is equal to selling price of 40 articles.
Let cost price of one article = Rs. 1
Selling price of 40 articles = Rs. 50
But Cost price of 40 articles = Rs. 40
Therefore, the trader made profit.\Percentage of profit = 10/40 * 100
= 25%
Answer: E
Answer: E
Question: How many bricks each measuring 25cm x 11.25cm x 6cm, will be needed to build a wall 8m x 6m x 22.5m
Options:
A)5600
B)600
C)6400
D)7200
E)None of these
Rationale: Explanation:
no. of bricks= volume of the wall/volume of 1 brick = (800 x 600 x 22.5) / (25 x 11.25 x 6) = 6400
Answer: C
Answer: C
Question: 79 laboratories raise the bacterium, the laboratory have 48 culture dishes on average, which has about 25,070 bacteria each. How many bacteria are there approximately?
Options:
A)10^7
B)10^8
C)10^9
D)10^10
E)10^11
Rationale: 79 laboratories raise the bacterium, the laboratory have 48 culture dishes on average, which has about 25,070 bacteria each. How many bacteria are there approximately?
A. 10^7
B. 10^8
C. 10^9
D. 10^10
E. 10^11
-> Due to approximately, 79=80, 48=50, 25,070=25,000 are derived, which makes (79)(48)(25,075)=(80)(50)(25,000)=10^8. The answer is B.
Answer: B
Question: A and B can do a piece of work in 10 days, while B and C can do the same work in 15 days and C and A in 25 days. they started working together, after 4 days A left. After another 4 days B left. In how many days C can finish the remaining work?
Options:
A)16
B)32
C)64
D)96
E)None of These
Rationale: Let the rates of A, B and C be a, b, and c respectively.
A and B can do a piece of work in 10 days: a + b = 1/10;
B and C can do the same work in 15 days: b + c = 1/15;
C and A can do the same work in 25 days: c + a = 1/25.
Sum the above 3 equations: 2(a + b + c) = 31/150 --> a + b + c = 31/300
Subtract a + b = 1/10 from above to get c = 1/300.
For 4 days all 3 worked and completed 4*(a + b + a) = 124/300 of the work.
For the next 4 days B and C worked and they completed 4(b + c) = 4/15 = 80/300 of the work.
So, by the time C is left alone 1 - (124/300 + 80/300) = 96/300 of the work is left to be completed by C alone.
Time = Job/Rate = (96/300)/(1/300) = 96 days.
Answer: D
Answer: D
Question: What is the smallest integer k for which 64^k > 4^16?
Options:
A)4
B)5
C)6
D)7
E)8
Rationale: 64^k > 4^16
4^(3k) > 4^16
3k > 16
k = 6
The answer is C.
Answer: C
Question: Find the average of all prime numbers between 30 and 50?
Options:
A)24.7
B)39.8
C)12.3
D)41.3
E)15.8
Rationale: There are five prime numbers between 30 and 50.
They are 31,37,41,43 and 47.
Therefore the required average=(31+37+41+43+47)/5 = 199/5 = 39.8.
Ans: B
Answer: B
Question: The average of first six prime numbers greater than 3 is?
Options:
A)16
B)10
C)12
D)19
E)17.8
Rationale: 5 + 7 +11 + 13 + 17 + 19 = 72/6 = 12
Answer: C
Answer: C
Question: The average expenditure of a man for the first five months is Rs.60 and for the next seven months it is Rs.130. If he saves Rs.290 in that year, his monthly average income is :
Options:
A)Rs.125
B)Rs.150
C)Rs.165
D)Rs.170
E)none
Rationale: Explanation:
Total income = Rs.(60Ã—5+130Ã—7+290)=Rs.1500
Average monthly income
= Rs. (1500/12)=Rs.125
Correct Option: A
Answer: A
Question: A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 50 sq. feet, how many feet of fencing will be required?
Options:
A)34
B)40
C)25
D)88
E)78
Rationale: We have: l = 20 ft and lb = 50 sq. ft.
So, b = 2.5 ft.
Length of fencing = (l + 2b) = (20 + 5) ft = 25 ft.
ANSWER:C
Answer: C
Question: In how many different number of ways 4 boys and 3 girls can sit on a bench such that girls always sit together?
Options:
A)720
B)740
C)760
D)780
E)800
Rationale: Option 'A'
Answer: A