divelab/Sys2Bench huggingface dataset:
Question: Find the no.of ways of arranging the boy and 10 guests at a circular table so that the boy always sits in a particular seat?
Options:
A)10!
B)9!
C)8!
D)6!
E)7!
Rationale: Ans.(A)
Sol. Total number of persons = 10 Host can sit in a particular seat in one way. Now, remaining positions are defined relative to the host. Hence, the remaining can sit in 8 places in 10P10 = 10! Ways ... The number of required arrangements = 10! x 1=10! = 10! ways
Answer: A
Question: Jill, who lives in City C, plans to visit 6 different cities, M,N,O,P, L, and S. She plans to visit each city exactly once and return to City C after the 6 visits. She can visit the cities in any order. In how many different orders can she visit the 6 cities?
Options:
A) 3
B) 720
C) 800
D) 900
E) 12
Rationale: 6! = 720=B
Answer: B
Question: What number has a 4:1 ratio to the number 100?
Options:
A)40
B)200
C)400
D)800
E)4000
Rationale: 4:1 = x: 100
x = 4*100
x=400
ANSWER:C
Answer: C
Question: If cement, gravel and sand are to be mixed in 7:10:13 and 6 tons of cement is available how many tons of mixture can be produced assuming that sufficient gravel and sand is readily available.
Options:
A)25 5/7
B)36
C)34 2/7
D)34 5/7
E)34 6/7
Rationale: Cement:Gravel:Sand = 7:10:13 --> total of 7+10+13 = 30 parts.
If we use 6 tons of cement, then we'll get 6/7*30 = 25 5/7 tons of mixture.
Answer: A.
Answer: A
Question: If a truck is traveling at a constant rate of 108 kilometers per hour, how many seconds will it take the truck to travel a distance of 600 meters? (1 kilometer = 1000 meters)
Options:
A)20
B)24
C)30
D)36
E)48
Rationale: Speed = 108 Km/hr =>108,000 m/hr
In one minute => 108000/60 = 1800 meters
In one sec => 1800/60 = 30 meters
Time = Total distance need to be covered / Avg. speed
=> 600/ 30 =20 and hence the Answer : A
Answer: A
Question: Find the value of y from (12)^3 x 6^4 ÷ 432 = y?
Options:
A)6434
B)4673
C)7684
D)7658
E)5184
Rationale: Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184
432 12 x 62
E
Answer: E
Question: The probability of pulling a black ball out of a glass jar is 1/V. The probability of pulling a black ball out of a glass jar and breaking the jar is 1/Y. What is the probability of breaking the jar?
Options:
A)1/(XY)
B)V/Y
C)Y/X
D)1/(X+Y)
E)1/(X-Y)
Rationale: P of pulling a black ball out of a glass jar AND breaking the jar = 1/Y
P of pulling a black ball out of a glass jar is 1/V
Lets say P of breaking the jar = n
That means 1/V*n=1/Y
n= V/Y
B is the answer
Answer: B
Question: The two lines y = x and x = -7 intersect on the coordinate plane. If z represents the area of the figure formed by the intersecting lines and the x-axis, what is the side length of a cube whose surface area is equal to 6z?
Options:
A)16
B)8√2
C)8
D)7/√2
E)(√2)/3
Rationale: 800score Official Solution:
The first step to solving this problem is to actually graph the two lines. The lines intersect at the point (-7, -7) and form a right triangle whose base length and height are both equal to 4. As you know, the area of a triangle is equal to one half the product of its base length and height: A = (1/2)bh = (1/2)(7 × 7) = 49/2; so z = 49/2.
The next step requires us to find the length of a side of a cube that has a face area equal to 49/2. As you know the 6 faces of a cube are squares. So, we can reduce the problem to finding the length of the side of a square that has an area of 49/2. Since the area of a square is equal to s², where s is the length of one of its side, we can write and solve the equation s² = 49/2. Clearly s = √49/2 = 7/√2 , oranswer choice (D).
Answer: D
Question: How many integers between 100 and 200, inclusive, cannot be evenly divided by 3 nor 5?
Options:
A)46
B)48
C)50
D)52
E)54
Rationale: The total numbers between 100 and 200, inclusive, is 101.
3*34=102 and 3*66=198 so the number of multiples of 3 is 33.
5*20=100 and 5*40=200 so the number of multiples of 5 is 21.
However, the multiples of 15 have been counted twice.
15*7=105 and 15*13=195 so the number of multiples of 15 is 7.
Thus the total number is 101-33-21+7=54.
The answer is E.
Answer: E
Question: At a certain conference, 150 students spoke one or more of the following languages: Spanish, English, and French. If 63 students spoke Spanish, 90 spoke English, 65 spoke French, and 32 spoke only 2 languages, how many students spoke three different languages?
Options:
A)7
B)9
C)12
D)15
E)18
Rationale: 150=63+90+65-32-2x
x=18
E. 18
Answer: E
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 back. What is the total distance traveled by the man ?
Options:
A)4.58 kms
B)6.35 kms
C)5.76 kms
D)5.24 kms
E)5 kms
Rationale: Explanation:
Speed in still water = 6 kmph
Stream speed = 1.2 kmph
Down stream = 7.2 kmph
Up Stream = 4.8 kmph
x/7.2 + x/4.8 = 1
x = 2.88
Total Distance = 2.88 x 2 = 5.76 kms
ANSWER IS C
Answer: C
Question: Find the simple interest on Rs.945 for 5 months at 4 paisa per month?
Options:
A)s.325
B)s.500
C)s.200
D)s.189
E)s.211
Rationale: Explanation:
I = (945*5*4)/100 = 189
Answer: Option D
Answer: D
Question: A jogger running at 9 km/hr along side a railway track is 240 m ahead of the engine of a 120 m long train running at 27 km/hr in the same direction. In how much time will the train pass the jogger?
Options:
A)76 sec
B)72 sec
C)98 sec
D)36 sec
E)23 sec
Rationale: Speed of train relative to jogger = 27 - 9 = 18 km/hr.
= 18 * 5/18 = 5 m/sec.
Distance to be covered = 240 + 120 = 360 m.
Time taken = 360/5 =72 sec.
Answer:B
Answer: B
Question: Five people are running in a race. The first one to finish wins a gold medal, the second wins a silver medal and the third wins a bronze medal. How many different arrangements of medal winners, in order from first to third, are possible?
Options:
A)5
B)10
C)60
D)120
E)125
Rationale: Assuming no ties in the race :
The Gold Medal can be given in 5 ways
The Silver Medal can be given in 4 ways
The Bronze Medal can be given in 3 ways
So total number of ways = 5 * 4 * 3 = 60
Answer - C
Answer: C
Question: The average age of a husband and a wife is 23 years when they were married five years ago but now the average age of the husband, wife and child is 20 years(the child was born during the interval). What is the present age of the child?
Options:
A)6 years
B)9 years
C)9 years
D)4 years
E)3 years
Rationale: 28 * 2 = 56
20 * 3 = 60
-----------
4 years
Answer: D
Answer: D
Question: In how many ways the word "KIT" can be arranged?
Options:
A)6
B)8
C)18
D)21
E)24
Rationale: Explanation :
The required number of ways = 3!
= 6
Answer : A
Answer: A
Question: A letter lock consists of three rings each marked with seven different letters. The number of distinct unsuccessful attempts to open the lock is at the most?
Options:
A)342
B)269
C)215
D)177
E)123
Rationale: Since each ring consists of seven different letters, the total number of attempts possible with the three rings is
= 7*7*7 = 343. Of these attempts, one of them is a successful attempt.
Maximum number of unsuccessful attempts = 342- 1
= 342
Answer:A
Answer: A
Question: interest, but he includes the interest every six months for calculating the principal. If he is charging an interest of 10%, the effective rate of interest becomes:
Options:
A)10%
B)10.25%
C)10.6%
D)10.75%
E)11%
Rationale: Let the sum be Rs. 100. Then,
S.I. for first 6 months= Rs. (100x10x1) / ( 100x2 ) –Rs. 5
S.I. for last 6 months =Rs. (105x10x1)/(100x2) =Rs.5.25
So amount at the end of 1 year =Rs.(100+5+5.25) = Rs. 110.25
Effective = (110.25-100) =10.25%
answer :B
Answer: B
Question: What is the remainder when 1031*1047*1050*1053 is divided by 33?
Options:
A)3
B)24
C)30
D)21
E)18
Rationale: take the remainder from each of 1031/33, 1047/33 and so on..
1031/33 gives remainder = 8
1047/33 gives remainder = 24
1050/33 gives remainder = 27
1053/33 gives remainder = 30
the net remainder is the product of above individual remainders. i.e =8*24*27*30
break them into pairs 8*24/33 gives remainder 27
and 27*30/33 gives remainder 18
so 27*18/33 gives remainder 24.
B
Answer: B
Question: If k is an integer and 0.0010101 x 10^k is greater than 10, what is the least possible value of k?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: 0.0010101 * 10^k > 10
We need to move the decimal point to the right 4 places to get 10.101
This is equivalent to multiplying by 10^4.
The answer is C.
Answer: C
Question: Find the number of square tiles to cover the floor of a room measuring 4 m * 9 m leaving 0.25 m space around the room. A side of square tile is given to be 10 cms?
Options:
A)187
B)476
C)268
D)2975
E)276
Rationale: Area of the room =3.5 * 8.5 = 29.75
Area of the tile = 0.1 *0.1=0.01
No. of tiles = 29.75/0.01 = 2975
Answer : D
Answer: D
Question: In the interior of a forest, a certain number of apes equal to the square of one-fifthhth of the total number are playing and having great fun. The remaining four apes are on a hill and the echo of their shrieks by the adjoining hills frightens them. They came and join the apes in the forest and play with enthusiasm. What is the total number of apes?
Options:
A)48
B)16
C)5 or 20
D)80
E)16 or 48
Rationale: Let total number be x
No in the interior = (x/5)^2
No outside = 4
So : x - (x/5)^2=4
x^2-25x+100=0
(x-20)(x-5)=0
So either x=5 or x=20
C
Answer: C
Question: If a : b = 2 : 3 and b : c = 5 : 7, then find a : b : c
Options:
A)12 : 15 : 9
B)10 : 15 : 21
C)14 : 12 : 21
D)2 : 15 : 7
E)3 : 16 : 9
Rationale: EXPLANATION:
a : b : c = (2 x 5) : ( 3 x 5) : (3 x 7) = (10) : (15) : (21)
ANSWER IS B
Answer: B
Question: Alex is shuffling a pack of cards (54 cards in total) and after some time, he takes out a joker card.
Now, he splits the remaining cards into two piles. Can you find out the probability where one of the piles has a sequence of card from A to K in order?
Options:
A)5/6227020800
B)4/6227020800
C)3/6227020800
D)1/6227020800
E)2/6227020800
Rationale: Solution:
1/6227020800
This can be solved through a simple mathematical equation.
N cards have n! permutations.
Therefore, the probability of obtaining a specific one by chance is 1/n!
Now, in this particular case, n = 13
Therefore, the required probability is 1/6227020800
Answer D
Answer: D
Question: 30^10 / 90^5=?
Options:
A)6^5
B)5^6
C)3^6
D)10^5
E)15^3
Rationale: 30^10 / 90^5=?
A. 6^5
B. 5^6
C. 3^6
D. 10^5
E. 15^3
-> 30^10 / 90^5=(30^10)/(3^5)(30^5)=(30^5)/(3^5)=(3^5)(10^5)/(3^5)=10^5.
Thus, D is the answer.
Answer: D
Question: Last Sunday a certain store sold copies of Newspaper A for $1.00 each and copies of Newspaper B for $1.25 each, and the store sold no other newspapers that day. If r percent of the store’s revenues from newspaper sales was from Newspaper A and if p percent of the newspapers that the store sold were copies of newspaper A, which of the following expresses r in terms of p?
Options:
A)100p/(125-p)
B)150p/(250-p)
C)300p(375-p)
D)400p(500-p)
E)500p/(625-p)
Rationale: This problem can be easily solved by picking numbers. The explanation given in the OG can be very laborious.
Lets say the number of newspaper A sold = 20, so revenue from A = 20 and the number of newspaper sold from B = 80, so revenue from B = 100. Now total revenue =120 out of which 20 came from A. So
r = 20/120 = 1/6 = 16.7% and p = 20
A) 100*20/(125-20) -> Incorrect
B) 150*20/(250-20) -> Incorrect
C) 300*20/(375-20) -> Incorrect
D) 400*20/(500-20) = 8/48 = 1/6*100 = 16.7% - > Correct
E) 500*20/(625-20) -> Incorrect
So Ans D
Answer: D
Question: A is thrice as good work than as B. Together they can finish a work in 6 days.In how many days A alone do the work?
Options:
A)6 days
B)10 days
C)13 days
D)2 days
E)5 days
Rationale: Explanation:
Ratio of their work = 1:3
1x+3x=6
4x=6
X=24
24/4=6
6:18
Answer: Option A
Answer: A
Question: A bowl was filled with 10 ounces of water, and 0.008 ounce of the water evaporated each day during a 50-day period. What percent of the original amount of water evaporated during this period?
Options:
A)0.004%
B)0.04%
C)0.40%
D)4%
E)40%
Rationale: Total amount of water evaporated each day during a 50-day period = .008 * 50
=.008 * 100/2
= .8/2
= .4
percent of the original amount of water evaporated during this period = (.4/10) * 100%
= 4 %
Answer D
Answer: D
Question: The sale price sarees listed for Rs.450 after successive discount is 20% and 15% is?
Options:
A)321
B)276
C)306
D)265
E)162
Rationale: Explanation:
450*(80/100)*(85/100) = 306
Answer: C
Answer: C
Question: Machine A and machine B process the same work at different rates. Machine C processes work as fast as Machines A and B combined. Machine D processes work three times as fast as Machine C; Machine D’s work rate is also exactly four times Machine B’s rate. Assume all four machines work at fixed unchanging rates. If Machine A works alone on a job, it takes 7 hours and 20 minutes. If all four machines work together on the same job simultaneously, how many minutes will it take all of them to complete it?
Options:
A)20
B)22
C)24
D)26
E)28
Rationale: C = A + B
D = 3C = 3(A+B) = 4B
Then B = 3A and C = 4A
The combined rate of the four machines is A + 3A + 4A + 12A = 20A
Machine A can complete the work in 440 minutes, so its rate is 1/440 of the work per minute.
The combined rate is 20/440 = 1/22 so the work will be completed in 22 minutes.
The answer is B.
Answer: B
Question: Susan rolls 4 six-sided dice at once to win a bet with her neighbour Jeff. If all 4 dice return the same number after only one roll, Susan wins her bet. What is the probability that Susan LOSES the bet?
Options:
A)Less than 50%
B)Between 50% and 70%
C)Between 70% and 90%
D)Between 90% and 99%
E)Greater than 99%
Rationale: The acceptable rolls are all of the Quad-tuples: 1111, 2222, 3333, 4444, 5555, 6666. Thus there are six possibilities. The four dice can roll 6*6*6*6 (6^4) number of ways. The probability that Susan wins the bet is: 6/6^4 = 1/6^3 = 0.0046 = 0.46%.
Therefore probability that Susan loses is 1 - probability of Susan winning:
1 - 0.46% = 99.5% > 99%
Answer: E.
Answer: E
Question: First column specifies the No of Days prior to departure information. Second column specifies the Percentage discount offered.
0 - 6 days ==> 0%
7 - 13 days ==> 10%
14 - 29 days ==> 25%
30 days or more ==> 40%
The table above shows the discount structure for advanced purchase of tickets at a particular airline. A passenger bought a ticket at this airline for $ 1050. The ticket agent informed her that, had she purchased the ticket one day later, she would have paid $210 more. How many days before her departure did she purchase her ticket.
Options:
A)6
B)7
C)13
D)14
E)29
Rationale: First I figured out the percentage change from the immediate previous amount for each of the period.Thus it comes-
0 - 6 days ==> 0%
7 - 13 days ==> 10% (90% of the price)
14 - 29 days ==> 17% (approx) (went from 90% to 75%)
30 days or more ==> 20% (went from 75% to 60%)
If the passenger had to pay the extra amount, she had to pay=(210+1050)=1260
now 210 is somehow between 10% and 20% of 1260. So 17% is the choice here.
correct ans: 14 days
ANSWER:D
Answer: D
Question: A man 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)227
B)267
C)128
D)860
E)179
Rationale: CP = SP + 1CP = SP - g
800 + x = 980 - 2x
3x = 180 => x = 60
CP = 800 + 60 = 860
Answer: D
Answer: D
Question: The ratio of the amount of the oil bill for the month of February to the amount of the oil bill for the month of January was 3:2. If the oil bill for February had been $20 more, the corresponding ratio would have been 5:3. How much was the oil bill for January?
Options:
A)$100
B)$120
C)$140
D)$160
E)$180
Rationale: 3:2 = 9:6 and 5:3 = 10:6.
An increase in $20 increases the ratio by 1:6.
Therefore, January's bill was 6($20) = $120.
The answer is B.
Answer: B
Question: A rectangular tank can hold k litres of water.How many litres of water can tank hold if all dimensions doubles.
Options:
A)8k liters
B)7k litrs
C)9k litrs
D)5k litrs
E)6k litrs
Rationale: let dimensions of tank are x*y*z=xyz
so xyz can hold k litres of water
now dimensions are doubled i.e 2x*2y*2z=8xyz
as xyz holds k litres,so 8xyz will hold 8*k=8k litres of water
ans 8k litrs
ANSWER:A
Answer: A
Question: A bank pays interest to its customers on the last day of the year. The interest paid to a customer
is calculated as 10% of the average monthly balance maintained by the customer. John is a
customer at the bank. On the last day, when the interest was accumulated into his account, his
bank balance doubled to $4680. What is the average monthly balance maintained by John in his
account during the year?
Options:
A) 2840
B) 5680
C) 23400
D) 7540
E) 28400
Rationale: bank balance is doubled with accumulation of interest tp 4680..
this means INTEREST is 4680/2=2340 for entire year..
although since interest is 10% of avg MONthly balance, it becomes 23400..
C
Answer: C
Question: A train crosses a bridge of length 150 m in 7.5 seconds and a lamp post on the bridge in 2.5 seconds. What is the length of the train in metres?
Options:
A)37.5 m
B)75 m
C)25 m
D)80 m
E)30 m
Rationale: Let Length of Train = L
Case-1: Distance = 150+L (While crossing the bridge)
Time = 7.5 Seconds
i.e. Speed = Distance / Time = (150+L)/7.5
Case-2: Distance = L (While passing the lamp post)
Time = 2.5 Seconds
i.e. Speed = Distance / Time = (L)/2.5
But Since speed has to be same in both cases so
(150+L)/7.50 = (L)/2.5
i.e. 3L = L + 150
i.e. 2L = 150
i.e. L = 75
Answer: option B
Answer: B
Question: John invested $ 10,000 in a savings bank account that earned 2% simple interest. Find the interest earned if the amount was kept in the bank for 4 years.
Options:
A)600
B)800
C)850
D)900
E)950
Rationale: Principle P = $ 10,000 Time Period T =4 years and Rate of Interest = 2% = 0.02
Plugging these values in the simple Interest formula,
I = PX T X R
= 10,000 X 4 x 0.02
= $ 800
Interest earned for the investment = $ 800
answer :B
Answer: B
Question: A man sold 20 articles for $60 and gained 20%. How many articles should he sell for $80 to incur a loss 20%?
Options:
A)45
B)36
C)40
D)50
E)48
Rationale: Production cost per article: $60*(100%-20%) / 20 = $2.40
Required production costs for a loss of 20%: $80*(100% + 20%) = $96
Number of articles to be sold for $96 to incur a 20% loss: $96/ $2.40 = 40
Thus, solution C is correct.
Answer: C
Question: The sum of five numbers is 655. The average of the first two numbers is 85 and the third number is 125. Find the average of the two numbers?
Options:
A)180
B)170
C)190
D)175
E)200
Rationale: P + Q + R + S + T = 655.
(P + Q)/2 = 85 and R = 125
P + Q = 170 and R = 125
P + Q + R = 295
S + T = 655 - (P + Q + R) = 360
Average of the last two numbers = (S + T)/2 = 180.
ANSWER A
Answer: A
Question: Tomy's age 20 years hence will be thrice his age four years ago. Find Tomy's present age?
Options:
A)12 years
B)16 years
C)15 years
D)17 years
E)18 years
Rationale: Let MTomy's present age be 'x' years.
x+ 20 = 3(x- 4)
=> 2x = 32 => x = 16 years.
B
Answer: B
Question: Each week, Harry is paid X dollars per hour for the first 30 hours and 1.5X dollars for each additional hour worked that week. Each week, James is paid X dollars per hour for the first 40 hours and 2X dollars for each additional hour worked that week. Last week James worked a total of 47 hours. If Harry and James were paid the same amount last week, how many hours did Harry work last week?
Options:
A)35
B)36
C)37
D)38
E)46
Rationale: Amount earned by James = 40*x + 7*2x = 54x
Therefore, Amount earned by Harry = 54x
But we know the amount Harry earned assuming working y hours (y>30) is 30*x + (y-30)*1.5x
[[We know y>30 because in 30h the most Harry could earn is 30x, but he has earned 54x]]
So x*(1.5y -45 +30) = 54x
Or x*(1.5y - 15) = 54x
So 1.5y - 15 = 54
So 1.5y = 69
So y = 46
Answer is E
Answer: E
Question: The surface of a cube is 24sq cm. Find its volume?
Options:
A)8cc
B)9cc
C)2cc
D)4cc
E)6cc
Rationale: 6a2 = 24
a = 2 => a3 = 8cc
Answer: A
Answer: A
Question: The age of man is three times the sum of the ages of his two sons. Eight years hence,his age will be double of the sum of the ages of his sons.The fatherâ€™s present age is :
Options:
A)40 years
B)45 years
C)50 years
D)55 years
E)72 years
Rationale: Solution
Let the sum of present ages of the two sons be x years.
Then,father's present age = 3x years.
âˆ´ (3x + 8)=2 (x +16) â‡” 3x + 8 = 2x + 32 â‡” x =24.
Hence,father's present age = 72 years. Answer E
Answer: E
Question: An investor purchased 100 shares of stock X at 6 1/8 dollars per share and sold them all a year later at 18 dollars per share. If the investor paid a 2 percent brokerage fee on both the total purchase price and the total selling price, which of the following is closest to the investor's percent gain on this investment?
Options:
A)189%
B)240%
C)280%
D)300%
E)380%
Rationale: If the purchase price was 6$ per share then the investor would have made a profit of 200%.
Since the purchase price is slightly more than 6$ the profit would be slightly less than 200%.
Also a 2% brokerage is negligible and it brings down the profit percentage only by a small value. Approximation is very useful to solve these kind of problems as the answer choices are far apart.
Answer: A
Answer: A
Question: If 10 litres of an oil of Rs.50 per litres be mixed with 5 litres of another oil of Rs.66 per litre then what is the rate of mixed oil per litre?
Options:
A)Rs.49.17
B)Rs.51.03
C)Rs.54.17
D)Rs.55.33
E)None of the above
Rationale: 50*10 = 500
66*5 = 330
830/15 = 55.33
ANSWER:D
Answer: D
Question: In a certain quiz that consists of 10 questions, each question after the first is worth 4 points more than the preceding question. If the 10 questions on the quiz are worth a total of 300 points, how many points is the third question worth?
Options:
A)22
B)24
C)26
D)20
E)28
Rationale: x
x+4
x+8
x+12
x+16
x+20
x+24
x+28
x+32
x+36
10x+180=300
10x=120
x=12
3rd question = x+8 = 12+8 = 20
Answer D
Answer: D
Question: There are 85 doors marked with numbers 1 to 85. And there are 85 individuals marked 1 to 85.
An operation on a door is defined as changing the status of the door from open to closed or vice versa. All doors are closed to start with.
Now one at a time one randomly picked individual goes and operates the doors. The individual however operates only those doors which are a multiple of the number he/she is carrying. For e.g. individual marked with number 5 operates the doors marked with the following numbers: 5, 10, 15 ... 85.
If every individual in the group get one turn then how many doors are open at the end?
Options:
A)0
B)1
C)2
D)8
E)9
Rationale: Let us start with 1.
When 1 goes, all the doors are open since every number is a multiple of 1.
Also 1 will remain opened since 1 is not a multiple of any number.
Prime numbers can only be operated by people with prime numbers.
So 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59, 61,67,71,73,79,83 will be closed when people with respective numbers perform operations on them.
From the other numbers, only those numbers will remain opened on which even number of operations are performed including the operation performed by number 1.
This is possible only for perfect squares which are 4,9 ... 81.
So our numbers are 1,4,9,16,25,36,49,64,81.
Answer:- E
Answer: E
Question: A 12 month project had a total budget of $42,000. After eight months, the project had spent $23,700. At this point, how much was the project under budget?
Options:
A)$4100
B)$4300
C)$4500
D)$4700
E)$4900
Rationale: Each month, the project should spend $42,000 / 12 = $3500.
In 8 months, the project should spend 8*$3500=$28,000.
The project is under budget by $28,000 - $23,700 = $4300.
The answer is B.
Answer: B
Question: If M is the least positive integer that is divisible by every integer from 4 to 12 inclusive, then M/11 is =
Options:
A) 40320
B) 27720
C) 20160
D) 6720
E) 2520
Rationale: The integer should be divisible by: 4, 5, 6, 7, 8, 9, 10, 11 and 12, that is 2^2, 5, 2*3, 7, 2^3, 3^2, 2*5, 11, 3*2^2. The least common multiple of these integers is the product of 11, 7, 5, 3^2 and 2^3. Then, M/11 is (11 * 7 * 5 * 3^2 * 2^3)/11 = 7*5*9*8 = 2520.
Answer: E.
Answer: E