mathewhe/aqua_rat huggingface dataset:
Question: There are 11 baskets numbered from 1 to 11 and filled with apples. 10 children are asked to pick apples one by one from each basket such that the number of apples picked by each child from each basket is equal to the number marked on the basket. If there were 1000 apples in total and the baskets were filled in such a way that none of the basket became empty in the process, how many apples were left in the end?
(A) 180
(B) 220
(C) 260
(D) 300
(E) 340
Rationale: Each child takes a total of 1+2+3+4+5+6+7+8+9+10+11 = 11*12/2 = 66 apples.
The total number of apples taken by 10 children is 10*66 = 660
The number of apples left in the end is 1000 - 660 = 340 apples.
The answer is E.
Answer: (E) 340
Question: John want to buy a $100 Trouser at the store, but he think itâ€™s too expensive. Finally, it goes on sale for $80. What is the percent decrease?
(A) 20%
(B) 30%
(C) 40%
(D) 50%
(E) 60%
Rationale: The is always the difference between our starting and ending points. In this case, itâ€™s 100 â€“ 80 = 20. The â€œoriginalâ€ is our starting point; in this case, itâ€™s 100. (20/100)*100 = (0.2)*100 = 20%.
A
Answer: (A) 20%
Question: Suppose you have three identical prisms with congruent equilateral triangles as the end-polygons. Suppose you attach them by the rectangular faces so they are perfectly aligned. There will be some large faces created by two or more co-planar faces of the individual prisms: count each such large face as one. Given that, how many faces does the resultant solid have
(A)  4
(B)  9
(C) 6
(D)  10
(E)  12
Rationale: To arrange them as described I did as follows on my scratch paper (see the file attached), where I counted 4 sides and added top and bottom, hence 4+2 = 6.
C
Answer: (C) 6
Question: Two identical machines have the ability to produce both nuts and bolts. However, it takes 1 second to produce a bolt but 2 seconds to produce a nut. What is the fastest the two machines, working together, can produce 1,200 nuts and 1,200 bolts?
(A) 1,250 seconds
(B) 1,500 seconds
(C) 1,800 seconds
(D) 2,000 seconds
(E) 3,000 seconds
Rationale: I used the Rate formula (R=\frac{1}{T})
Rate of 1st machine = Rate of making 1 bolt + Rate of making 1 nut = 1 + \frac{1}{2}
Rate of 1st machine = Rate of 2nd machine
After this I got lost.
Please can you help how to approach using algebra?
I wouldn't complicate:
1 machine needs 1,200*1 seconds to produce 1,200 bolts, so 2 need half of that, so 1,200/2 seconds.=600 sec
1 machine needs 1,200*2 seconds to produce 1,200 nuts, so 2 need half of that, so 1,200*2/2 seconds.=1200 sec
total = 1800
C
Answer: (C) 1,800 seconds
Question: The number of boys in a class is three times the number of girls. Which one of the following numbers cannot represent the total number of children in the class ?
(A) 48
(B) 44
(C) 42
(D) 40
(E) 4
Rationale: remaining are divisible by 4
ANSWER:C
Answer: (C) 42
Question: Find the number of ways of arranging the letters of the word "MATERIAL" such that all the vowels in the word are to come together?
(A) 6775 ways
(B) 1440 ways
(C) 1345 ways
(D) 1324 ways
(E) 1688 ways
Rationale: In the word, "MATERIAL" there are three vowels A, I, E.
If all the vowels are together, the arrangement is MTRL'AAEI'.
Consider AAEI as one unit. The arrangement is as follows.
M T R L A A E I
The above 5 items can be arranged in 5! ways and AAEI can be arranged among themselves in 4!/2! ways.
Number of required ways of arranging the above letters = 5! * 4!/2!
= (120 * 24)/2 = 1440 ways.
Answer: B
Answer: (B) 1440 ways
Question: A company has 14 equally qualified applicants for 4 open positions. How many different groups of 4 applicants can be chosen by the company to fill the positions if the order of selection does not matter?
(A) 881
(B) 921
(C) 961
(D) 1001
(E) 1041
Rationale: 14C4=1001
The answer is D.
Answer: (D) 1001
Question: A goods train leaves a station at a certain time and at a fixed speed. After ^hours, an express train leaves the same station and moves in the same direction at a uniform speed of 90 kmph. This train catches up the goods train in 4 hours. Find the speed of the goods train.
(A) 26
(B) 16
(C) 36
(D) 46
(E) 13
Rationale: Let the speed of the goods train be x kmph.
Distance covered by goods train in 10 hours= Distance covered by express train in 4 hours
10x = 4 x 90 or x =36.
So, speed of goods train = 36kmph.
ANSWER C
Answer: (C) 36
Question: Ten people are planning to share equally the cost of a rental van. If one person withdraws from the arrangement and the others share equally the cost of the rental van, then the share of each of the remaining people will increase by...?
(A) 1/9
(B) 1/8
(C) 1/7
(D) 7/8
(E) 8/7
Rationale: Let P = total cost of the rental van.
The original share per person is P/10.
The new share per person is P/9.
P/9 = P/10 * 10/9 = (1 + 1/9)*original share
The answer is A.
Answer: (A) 1/9
Question: 3+3.3+333+33.33=?
(A) 362.33
(B) 372.63
(C) 702.33
(D) 702
(E) None of them
Rationale: 3
3.3
333
33.33
----------
372.63
----------
Answer is B
Answer: (B) 372.63
Question: How many ways are there to select a subcommittee of 6 members from among a committee of 17?
(A) 22888
(B) 19448
(C) 28791
(D) 27711
(E) 12376
Rationale: Explanation:
Since it does not matter what order the committee members are chosen in, the combination formula is used.
Committees are always a combination unless the problem states that someone like a president has higher hierarchy over another person. If the committee is ordered, then it is a permutation.
C(17,6)= 12,376
Answer: E
Answer: (E) 12376
Question: A, B and C rents a pasture for Rs.870. A put in 12 horses for 8 months, B 16 horses for 9 months and 18 horses for 6 months. How much should C pay?
(A) 270
(B) 278
(C) 792
(D) 267
(E) 721
Rationale: 12*8 :16*9 = 18*6
8: 12: 9
9/29 * 870 = 270
Answer: A
Answer: (A) 270
Question: Martha has 4 dogs and 4 cats. She takes each animal separately for a daily walk. She can take the animals for a walk to the park or to the barber shop. How many different options for a walk with a single animal does Martha have?
(A) 8
(B) 9
(C) 16
(D) 18
(E) 20
Rationale: 4 dogs, 4 cats; park/barber shop
1 dog - 2 options - either park or barber shop, so, 4 dogs - 8 options and 4 dogs - 8 options.
Total = 16 options.
C
Answer: (C) 16
Question: The fourth proportional to 3, 8, 18 is:
(A) 42
(B) 44
(C) 46
(D) 48
(E) 50
Rationale: Let the fourth proportional to 3, 8, 18 be x.
Then, 3 : 8 : 18 : x
3x = (8 x 18)
x =	(8 x 18)/3
x=144/3 =48
Answer: Option D
Answer: (D) 48
Question: The length of a rectangular landscape is 4times its breadth. There is a playground in it whose area is 1200 square mtr & which is 1/3rd of the total landscape. What is the length of the landscape?
(A) 100
(B) 110
(C) 120
(D) 140
(E) 150
Rationale: Sol. x * 4x = 3 * 1200
x = 30
Length = 4 * 30 = 120
C
Answer: (C) 120
Question: Simple interest on a certain sum of money for 3 years at 10% per annum is half the compound interest on Rs. 6500 for 2 years at 14% per annum. The sum placed on simple interest is
(A) Rs.6500
(B) Rs.1947.4
(C) Rs.973.7
(D) Rs.2000
(E) None
Rationale: Solution
C.I.	=Rs[6500x(1+14/100)Â²-6500]
Rs.(6500x114/100x114/100-6500)	= Rs.1947.4.
Sum	=Rs. [973.7x100 /3x10]
= Rs.3245.67.
Answer E
Answer: (E) None
Question: two houses of the same type were advertised to be let in a locality. Three men made separate applications for a house. What is the probability that each of them applied for the same house.
(A) 1/3
(B) 2/27
(C) 3/27
(D) 4/27
(E) 2/9
Rationale: Since each of the house has same probability of getting selected so for each men proability of selecting a house out of 2 houses 1/2
Let us consider case where all 3 men choose House no 1
So for First men it will be 1/2,second men 1/2 and third men also 1/2
So probability of selecting house no 1 is 1/2*1/2*1/2= 1/8
And since there are 2 such house so probability that each men select the same house is 2*1/27
Ans is B
Answer: (B) 2/27
Question: R is the set of positive odd integers less than 100, and S is the set of the squares of the integers in R. How many elements does the intersection of R and S contain ?
(A)  None
(B)  Two
(C)  Four
(D)  Five
(E)  Seven
Rationale: R is the set of positive odd integers less than 100, and S is the set of the squares of the integers in R.
How many elements does the intersection of R and S contain?
R=1,3,5,7,9,11,13,15...
S=1,9,25,49,81...
Numbers: 1, 9, 25, 49, and 81 are odd integers (less than 100) that are in both sets.
Solution: Five
Answer: D
Answer: (D)  Five
Question: If XY denotes X is raised to the power Y, Find the last two digits of 19413846+ 19614181
(A) 67
(B) 74
(C) 82
(D) 98
(E) 34
Rationale: 1941^3846
unit digit= 1^4=1
10th digit=4*6=24=2 means last two digit =41
and 1972^4181
unit digit=1
10th digit=7*2=14 mean last two digit= 41
hence,
41+41= 82
Answer: (C) 82
Question: How many digits are in (8×10^14)(10×10^10)?
(A) 24
(B) 25
(C) 26
(D) 27
(E) 28
Rationale: he question simplifies to (8×10^14)(10^11)
=> 8*10^25
=> Will contain 25 zeros +1 digit 8
=>26
Ans C
Answer: (C) 26
Question: A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. How far is the place?
(A) 2.89
(B) 2.88
(C) 2.89
(D) 2.82
(E) 2.12
Rationale: M = 6
S = 1.2
DS = 6 + 1.2 = 7.2
US = 6 - 1.2 = 4.8
x/7.2 + x/4.8 = 1
x = 2.88
Answer:B
Answer: (B) 2.88
Question: Anthony and Cindy were each given X dollars in advance for each day they were expected to perform at a community festival. Anthony eventually performed on all 15 days of the festival, while Cindy performed on 5 fewer days than Anthony performed. If Cindy gives Anthony y dollars of her advance payment so that they would have each received the same daily rate, what was Anthony paid in advance, in terms of Y?
(A) 6Y
(B) 10Y
(C) 8Y
(D) 5Y
(E) 7Y
Rationale: Both of them were given X $ each
Cindy to adjust Y $ in advance to Anthony
So Cindy now has (X-Y)$ and Anthony has (X+Y) $ such that their daily rate becomes same
So Rate of CIndy= Rate of Anthony
Also , Cindy works for 10 days and ANthony works for full 15 days
(X-Y) / 10 = (X+Y) / 15
Solving 15x-15y=10x+10y =>5x=25y => x=5y
X= 5Y
Answer : D
Answer: (D) 5Y
Question: Last year Department Store X had a sales total for December that was 2 times the average (arithmetic mean) of the monthly sales totals for January through November. The sales total for December was what fraction of the sales total for the year?
(A) 1/4
(B) 4/15
(C) 2/13
(D) 4/11
(E) 4/5
Rationale: Let avg for 11 mos. = 10
Therefore, Dec = 20
Year total = 11*10 + 20 = 130
Answer = 20/130 = 2/13 = C
Answer: (C) 2/13
Question: The area of a rectangular field is equal to 750 square meters. Its perimeter is equal to 110 meters. Find the width of this rectangle.
(A) 5
(B) 10
(C) 15
(D) 20
(E) 25
Rationale: L * W = 750 : area , L is the length and W is the width.
2 L + 2 W = 110 : perimeter
L = 55 - w : solve for L
(55 - W) * W = 750 : substitute in the area equation
W = 25 and L = 30
correct answer E
Answer: (E) 25
Question: A number is said to be a “digifac” if each of its digits is a factor of the number itself. What is the sum M of the missing digits of the following five-digit digifac: 9, 5, 3 _ _ ?
(A)  5
(B)  7
(C)  9
(D)  10
(E)  14
Rationale: Here, the term “digifac” should look intimidating. You probably haven’t studied digifacs before, so how should you approach this problem? Well, keep in mind that digifacs aren’t being tested; in fact, the author of this question just made that term up, and then defined it for you. What makes this question hard is that the non-challenge-seeker (I think I just made that term up, too…) will see the unfamiliar term “digifac” and lose faith immediately. “I don’t know what that is!” She who finds the challenge in the GMAT fun, however, will read the definition and think “got it – I need to find the two digits that ensure that 9, 5, and 3 are both factors of the overall number, and that the remaining two digits are also factors”. And work from there. The number must be divisible by 5, so the only units digits that work are 0 or 5. And the number must be divisible by 9 (and also 3), so we need the sum M of all digits to be a multiple of 9. 9 + 5 + 3 = 17, so our only options are to get the sum to 18 (by adding 1) or to 27 (by adding 10). A quick glance at the answer choices shows that 0 1 isn’t an option. Why not? That would require 0 to be one of the digits…and 0 isn’t a factor of anything. So the units digit must be 5, making the tens digit 5, and we have 95,355. That number is a multiple of 5, 3, and 9, so it works:the correct answer is D, and more importantly this fun challenge required no “trivial” information about digifacs…that term only existed to obscure the link between the given information and the path to the answer.D
Answer: (D)  10
Question: The food in a camp lasts for 35 men for 40 days. If ten more men join, how many days will the food last?
(A) 40 days
(B) 20 days
(C) 31 days
(D) 50 days
(E) 45 days
Rationale: one man can consume the same food in 35*40 = 1400 days.
10 more men join, the total number of men = 45
The number of days the food will last = 1400/45 = 31 days.
ANSWER:C
Answer: (C) 31 days
Question: If an amount of Rs 42,240 is distributed equally
amongst 22 persons, how much amount would each
person get?
(A) Rs 1905
(B) Rs 1920
(C) Rs 745
(D) Rs 765
(E) None
Rationale: Required amount =42240/22 = Rs 1920
Answer B
Answer: (B) Rs 1920
Question: A 160 meter long train crosses a man standing on the platform in 18 sec. What is the speed of the train?
(A) 96 kmph
(B) 94 kmph
(C) 32 kmph
(D) 56 kmph
(E) 76 kmph
Rationale: S = 160/18 * 18/5 = 32 kmph
ANSWER:C
Answer: (C) 32 kmph
Question: If negative integers k and p are NOT both even, which of the following must be odd?
(A) kp
(B) 4(k + p)
(C) k – p
(D) k + 1 – p
(E) 2(k + p) – 1
Rationale: If negative integers k and p are NOT both even, which of the following must be odd?
(A) kp --> can be even if either k or p is even.
(B) 4(k + p) --> always even.
(C) k – p --> can be even as well as odd. For example consider k-p=odd-odd=even and k-p=odd-even=odd.
(D) k + 1 – p --> can be even as well as odd. For example consider, k+1-p=odd+odd-odd=odd and k+1-p=odd+odd-even=even.
(E) 2(k + p) – 1 --> always odd, because: 2(k+p)-1=2*integer-odd=even-odd=odd.
Answer: E.
Answer: (E) 2(k + p) – 1
Question: Difference between the length &breadth of a rectangle is 30 m. If its perimeter is 300 m, then its area is?? We have: (l - b) = 30 and 2(l + b) = 300 or (l + b) = 150?
(A) 5425 m^2
(B) 5250 m^2
(C) 5300 m^2
(D) 5200 m^2
(E) 5400 m^2
Rationale: Solving the two equations, we get: l = 90 and b = 60.
Area = (l x b) = (90 x 60) m2 = 5400 m^2
E
Answer: (E) 5400 m^2
Question: An athlete runs 200 metres race in 24 seconds. What is his speed?
(A) 20 km/hr
(B) 30 km/hr
(C) 25 km/hr
(D) 27.5 km/hr
(E) None of these
Rationale: Explanation:
Speed = Distance/Time = 200/24 m/s=200/24 × 18/5 km/hr
= 40×34 km/hr = 10×3 km/hr = 30 km/hr
Answer: Option B
Answer: (B) 30 km/hr
Question: A reduction of 25% in the price of oil enables a house wife to obtain 5kgs more for Rs.800, what is the reduced price for kg?
(A) 72
(B) 27
(C) 40
(D) 28
(E) 20
Rationale: 800*(25/100) = 200 ---- 5
? ---- 1 => Rs.40
Answer:C
Answer: (C) 40
Question: A train crosses a bridge of length 2500 m in 120 seconds and a lamp post on the bridge in 30 seconds. What is the length of the train in metres ?
(A) 375 m
(B) 750/3 m
(C) 2500/3 m
(D) 800 m
(E) 300 m
Rationale: Let Length of Train = L
Case-1: Distance = 2500+L (While crossing the bridge)
Time = 120 Seconds
i.e. Speed = Distance / Time = (2500+L)/120
Case-2: Distance = L (While passing the lamp post)
Time = 30 Seconds
i.e. Speed = Distance / Time = (L)/30
But Since speed has to be same in both cases so
(2500+L)/120 = (L)/30
i.e. 4L = 2500 + L
i.e. 3L = 2500
i.e. L = 2500/3
Answer: option C
Answer: (C) 2500/3 m
Question: Tough and Tricky questions: Combinations.
Eight students - 4 boys and 4 girls - are to sit side by side for a makeup exam. How many ways could they arrange themselves given that no two boys and no two girls can sit next to one another?
(A) 12
(B) 36
(C) 72
(D) 240
(E) 1152
Rationale: We can have 2 arrangements:
BGBGBGBG or GBGBGBGB
4!*4!*2 = 24*24*2 = 1152 ways.
Ans. E) 1152
Answer: (E) 1152
Question: In what time will a railway train 60 m long moving at the rate of 54 kmph pass a telegraph post on its way?
(A) 4 sec
(B) 7 sec
(C) 2 sec
(D) 6 sec
(E) 9 sec
Rationale: T = 60/54 * 18/5
= 4 sec
Answer:A
Answer: (A) 4 sec
Question: A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes. How long will it take to go 5 km in stationary water?
(A) 1 hr 15 min
(B) 1 hr 30 min
(C) 1 hr
(D) 2 hr
(E) 2 hr 30 min
Rationale: Upstream speed = u-v;
Downstream speed=u+v;.
According to formula, s=d/t.
u-v = 2/1, and
u+v = 60/10.
On solving these equations, we get.
u=4 and v=2.
Therefore, speed of boatman = 4 km/hr.
Hence, t=d/s.
t=5/4.
We get 1hr 15min is answer.
answer:A
Answer: (A) 1 hr 15 min
Question: A train 90 meters long completely crosses a 270-meter long bridge in 36 seconds. What is the speed of the train in km/h?
(A) 28 km/h
(B) 32 km/h
(C) 36 km/h
(D) 40 km/h
(E) 44 km/h
Rationale: speed = distance / time = (90 + 270)/36 = 360/36 (m/s) * 3600/1000 = 36 km/h
The answer is C.
Answer: (C) 36 km/h
Question: 36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work?
(A) 26
(B) 22
(C) 12
(D) 24
(E) 20
Rationale: Explanation:
Let the required number of days be x
More men, less days (indirect proportion)
Hence we can write as
(men) 36 : 27 :: x : 18
⇒36×18=27 × x
⇒12×18=9 × x
⇒12×2=x
⇒x=24
Answer: Option D
Answer: (D) 24
Question: In your classes you counted 122 hands. How many students were at the class?
(A) 60
(B) 61
(C) 85
(D) 86
(E) 88
Rationale: Total number of hands = 122
We have 2 hands.
To find how many students were at the class, divide the total number of hands by the number of hands we have.
We get, divide 122 by 2
122 ÷ 2 = 61
Therefore, there were 61 students at the class.
ANSWER IS B
Answer: (B) 61
Question: The distance between West-Town to East-Town is 20 kilometers. Two birds start flying simultaneously towards one another, the first leaving from West-Town at a speed of 4 kilometers per minute and the second bird, leaving from East-Town, at a speed of 1 kilometers per minute. What will be the distance, in kilometers, between the meeting point and West-Town?
(A) 3.
(B) 7.
(C) 10.
(D) 16.
(E) 15.
Rationale: Time taken by the birds to meet = 20/(4 + 1) = 4 mins
Distance traveled by the bird traveling from West-Town = 4 *4= 16
Answer: D
Answer: (D) 16.
Question: In how many different number of ways 4 boys and 2 girls can sit on a bench?
(A) 700
(B) 710
(C) 720
(D) 730
(E) 740
Rationale: npn = n!
6p6 = 6 × 5 × 4 × 3 × 2 × 1 = 720
C
Answer: (C) 720
Question: Two sides of a triangle have lengths x and w and meet at a right angle. If the perimeter of the triangle is 4x, what is the ratio of x to w ?
(A) a) 2 : 3
(B) b) 3 : 4
(C) c) 4 : 3
(D) d) 3 : 2
(E) e) 2 : 1
Rationale: Ahhhh....my bad. Thank you, you're correct. 8x = 6w --> x/w = 3/4.
Actually B is the right answer.
Answer: (B) b) 3 : 4
Question: In how many ways, a committee of 10 members can be selected from 8 men and 6 ladies, consisting of 5men and 5 ladies?
(A) 336
(B) 298
(C) 315
(D) 283
(E) 159
Rationale: (5 men out 8) and (5 ladies out of 6) are to be chosen
Required number of ways = (8C5 * 6C5) = 336
Answer is A
Answer: (A) 336
Question: Two trains are traveling on parallel tracks in the same direction. The faster train travels at 130 miles per hour, while the slower train travels at 100 miles per hour. At 3 o’clock the faster train is 15 miles behind the slower one. How far apart are the two trains at 5 o'clock?
(A) 45 miles
(B) 80 miles
(C) 90 miles
(D) 120 miles
(E) 400 miles
Rationale: Answer = A. 45 miles
Relational speed = 130 - 100 = 30 miles per hour
In 2 hours, difference = 30 * 2 = 60 miles
Fast train trailing 15 miles, so effective difference = 60 - 15 = 45 miles
Answer: (A) 45 miles
Question: If m and n are whole numbers such that mn = 121, the value of (m – 1)n + 1 is:
(A) 1
(B) 10
(C) 121
(D) 1000
(E) 131
Rationale: EXPLANATION
We know that 112 = 121.
Putting m = 11 and n = 2, we get:
(m – 1)n + 1 = (11 – 1)(2 + 1) = 10(3) = 1000.
Answer D
Answer: (D) 1000
Question: What is the remainder when 123456789101112131415161718192021222324252627282930313233343536373839404142434481 is divided by 45?
(A) 26
(B) 36
(C) 16
(D) 06
(E) 40
Rationale: Explanation :
Let's call : A = 123456789101112131415161718192021222324252627282930313233343536373839404142434481
=> A = B * 100 + 81 [with B = 1234567 ..... 424344]
We have:
B x 100 is divisible by 45
Because:
- Sum of all digits in B
= 1+2+3 + .... +44 = (1+44) + (2+43) + ....+ (22+23) (22 pairs)
= 22*45 => B divisible for 9
Since B is divisible by 9, B * 100 will be divisible by 9*5 = 45
81 divided 45 gives a remainder of 36
Therefore, A divided by 45 reminder 36
Answer : B
Answer: (B) 36
Question: Abel can complete a work in 8 days, Ben in 12 days and Carla in 15 days. All of them began the work together, but Abel had to leave after 2 days and Ben 3 days before the completion of the work. How long did the work last?
(A) 4
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: Abel in the 2 days that he worked completed 1/4 of the job = 3/4 remains
Then if Ben had to leave 3 days before the completion, this means that Carla had to work alone for these 3 days in which she completed 1/5 of the job.
Now together, Ben and Carla completed the job in (1/12 + 1/15)(t) = 3/20
3/20 (t) = 3/20 ---> t = 1
Therefore, these 1 day worked plus the 3 days that Carla had to work by herself add to 4 days
Answer: A
Answer: (A) 4
Question: The diameter of a wheel of cycle is 21 cm. It moves slowly along a road. How far will it go in 500 revolutions?
(A) 260 m
(B) 290 m
(C) 320 m
(D) 330 m
(E) 380 m
Rationale: In revolution, distance that wheel covers = circumference of wheel Diameter of wheel = 21 cm
Therefore, circumference of wheel = πd
= 22/7 × 21
= 66 cm
So, in 1 revolution distance covered = 66 cm
In 500 revolution distance covered = 66 × 500 cm
= 33000 cm
= 33000/100 m
= 330 m
Answer : option D
Answer: (D) 330 m
Question: The value of 1 + [1/(8 x 2)] + [1/(8 x 2²)] + [1/(8 x 2³)] is :
(A) 71/64
(B) 1/16
(C) 1/4
(D) 1/3
(E) None of these
Rationale: (8 x 2³ + 2² + 2 + 1)/(8 x 2³) = (64 + 4 + 2 + 1)/ 64
= 71/64.
ANSWER:A
Answer: (A) 71/64
Question: How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated?
(A) 5
(B) 10
(C) 51
(D) 15
(E) 20
Rationale: Since each desired number is divisible by 5, so we must have 5 at the unit place. So, there is 1 way of doing it.
The tens place can now be filled by any of the remaining 5 digits (2, 3, 6, 7, 9). So, there are 5 ways of filling the tens place.
The hundreds place can now be filled by any of the remaining 4 digits. So, there are 4 ways of filling it.
Required number of numbers = (1 x 5 x 4) = 20.
Option E
Answer: (E) 20
Question: A and B began business with Rs.3000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.714 find the share of A.
(A) 240
(B) 272
(C) 379
(D) 277
(E) 122
Rationale: Explanation:
(3*8 + 2*4):(4*8 + 5*4)
8:13
8/21 * 714 = 272
Answer: B
Answer: (B) 272
Question: The average mark of a class of twenty five students is 66. If five students whose marks are 32,28, 30, 26 and 34 are removed , then find the average mark of the remaining students of the class.
(A) 75
(B) 74
(C) 57
(D) 70
(E) 80
Rationale: Exp. Total mark of 25 students = 66*25 = 1650,
Total mark after the removal of 5 students = 1650 –(32 +28+30+26+34 )
= 1650 – 150 = 1500
Average mark = 1500/(25-5) = 1500/ 20 = 75
Answer: A
Answer: (A) 75
Question: If 40% of a number is 28, then the number is
(A) number is 60
(B) number is 70
(C) number is 90
(D) number is 80
(E) None of these
Rationale: Solution:
Let "a" be the number we seek. We get
40% × a = 28
2 × 40% × a = 2 × 28 = 56
80% × a = 56
10% × a = 56 : 8 = 7
100% × a = 7 × 10 = 70
a = 70
Answer B
Answer: (B) number is 70