divelab/Sys2Bench huggingface dataset:
Question: A contractor undertakes to do a job within 100 days and hires 10 people to do it. After 20 days, he realizes that one fourth of the work is done so he fires 2 people. In how many more days M will the work get over?
Options:
A)60
B)70
C)M=75
D)80
E)100
Rationale: We can also use the concept of man-days here
100 days -->10men so the job includes 100*10=1000 man-days
After 20 days
1/4 of Job is completed so 1/4 X 1000 man-days=250 man-days Job is done
Now the Balance Job=1000-250=750 man-days worth of Job
Since 2 men are fired so B/L men=8
Therefore Total no. of days of Job=750 man-day/8 days = 375/4=94 days (approx.)
Now since this is total and Ques. is asking for additional no. of days,
So 94-20=74 days
The nearest approx. to answer is 75
Ans: C (75 days)
Answer: C
Question: A and B can finish a work in 16 days while A alone can do the same work in 20 days. In how many days B alone will complete the work?
Options:
A)76 days
B)48 days
C)80 days
D)31 days
E)22 days
Rationale: B = 1/16 – 1/20 = 1/80 => 80 days
Answer: C
Answer: C
Question: List L: ABC, BCA, CAB
In list L above, there are 6 positive integers, where each of A, B, and C is a different nonzero digit. Which of the following is the sum of all the positive integers that MUST be factors of the sum of the integers in list L?
Options:
A)47
B)114
C)152
D)161
E)488
Rationale: Let's try to sum the 3 given numbers taking their place values into account:
(100A + 10B + C) + (100B + 10C + A) + (100C + 10A + B)
= 100(A + B + C) + 10(A + B + C) + (A + B + C)
= 111*(A + B + C)
We know 111 = 37 * 3 so the sum will certainly have 1, 3, 37 and 111 as factors. 1 + 3 + 37 + 111 = 152
Note: How do we know that (A + B + C) will not give us a factor that we get every time? Try and take a few cases where A, B and C have different characteristics e.g. case 1: they are all odd, case 2: they are all even with no multiple of 3 etc. We want to see if there are cases where (A+B+C) has no common factors with other cases.
Let's say A, B and C are all odd. 1+3+5 = 9. Factors 3 and 3
A, B and C are all even. 2+4+8 = 14. Factors 2 and 7
Other factors will depend on values of A, B and C. Hence there is no other factor which we MUST get.
E
Answer: E
Question: Robert's salary was decreased by 60% and subsequently increased by 60%. how much percentage does he lose?
Options:
A)10%
B)20%
C)25%
D)36%
E)50%
Rationale: let original salary be $100
Salary after decreasing 60% = 100 - 100 x 60/100 = $40
Salary after increasing 60% on $40 = 40 + 40 x 60/100 = $64
Percentage of loss = 100 - 64 = 36%
Answer : D
Answer: D
Question: If 2x = 3y = 10, then 6xy = ?
Options:
A) 100
B) 200
C) 120
D) 40
E) 20
Rationale: 2x = 10;x=5
3y = 10;y=10/3
Multiply: 6xy=6*5*10/3=100
Answer: A.
Answer: A
Question: In a fuel station the service costs $1.75 per car, every liter of fuel costs 0.65$. Assuming that a company owns 14 cars and that every fuel tank contains 55 liters and they are all empty, how much money total will it cost to fuel all cars?
Options:
A)320$
B)380$
C)525$
D)456$
E)480$
Rationale: Total Cost = ( 1.75*14 ) + ( 0.65 * 14* 55 ) = 24.5 + 500.5 => 525
Hence answer will be (C) 525
Answer: C
Question: An investment of $1000 was made in a certain account and earned interest that was compounded annually. The annual interest rate was fixed for the duration of the investment, and after 12 years the $1000 increased to $4000 by earning interest. In how many years after the initial investment was made the $1000 have increased to $8000 by earning interest at that rate?
Options:
A)16
B)18
C)20
D)24
E)30
Rationale: Amount 1000 is invested for 12 yrs and yields 4000. Amount is compounded annually.
we need number of years it will take to yield 8000.
from 1000 to 4000 = 4 times
from 4000 to 8000 = 2 times.
if compounding is happening at same rate throughout, then
since, time required for 4 times = 12 yrs
=>time required for 2 times = 6 yrs
Total time from initial = 12+6 = 18 yrs
Ans B.
Answer: B
Question: When a merchant imported a certain item, she paid a 7 percent import tax on the portion of the total value of the item in excess of $1,000. If the amount of the import tax that the merchant paid was $111.30, what was the total value of the item?
Options:
A)$2380
B)$2590
C)$2760
D)$2940
E)$3150
Rationale: Let x be the value of the item.
0.07*(x-1000) = 111.30
x = 2590
The answer is B.
Answer: B
Question: If x, y, and z are consecutive positive odd integers, not necessarily in that order, which of the following must be true? I. xy> z^4 II. (x + z)^3 > y III. x+y>z^4
Options:
A)I only
B)II only
C)III only
D)I,II only
E)I,III only
Rationale: Lets suppose that a,b,c can take any one of following three value 1,5,7. Most important point is that the options MUST BE TRUE under any condition.
x+y>z^4
Not necessarily true as 1+5<2401
xz>y^4
Not necessarily true as 1.7<625
We don't need to check option as all the options except B can be discarded.
Thus Answer B
Answer: B
Question: Four of the five parts numbered as (a), (b), (c), (d) and (e)in the following equations are exactly equal. You have to find out the part that is not equal to the other parts. The number of that part is the answer.
Options:
A)a2 + 5ab + 6b2
B)(a + 3b)(a + 2b)
C)a(a + 3b) + 2b(a + 3b)
D)(3a + b)(a + 2b)
E)a(a + 2b) + 3b(a + 2b)
Rationale: The other parts are equal to a2 + 5ab + 6b2.
Answer D
Answer: D
Question: A survey reveals that the average income of a company’s customers is $45,000 per year. If 50 customers respond to the survey and the average income of the wealthiest 10 of those customers is $55,000, what is the average income of the other 40 customers?
Is there a way to solve this using weighted average concept instead of doing tedious calculations?
Options:
A) $27,500
B) $35,000
C) $37,500
D) $42,500
E) $50,000
Rationale: let x be the average of 40 customers
40*x + 10* 55000 = 50*45000
solving this we have x= 42500
Answer is D.
Answer: D
Question: ravi decides to walk from goregaon to andheri .he has reached his destination in 2 hr 15 min by 4 of the distance at 6 kmph and the rest at 8 mph . how far goregaon from andheri?
Options:
A)11.6 km
B)12.6 km
C)13.6 km
D)14.6 km
E)15.6 km
Rationale: covering 3/t1+t2=9/4 hr
(3x/4*6)+(x/4*8*1.609)=9/4
x=15.6 km
ANSWER:E
Answer: E
Question: What is the value of 3x^2 − 1.8x + 0.6 for x = 0.6?
Options:
A)−0.3
B)0.6
C)0.3
D)1.08
E)2.46
Rationale: 3x^2-1.8x+0.6 for x=0.6
=3(0.6*0.6)-3*0.6*(0.6)+0.6
=0+0.6
=0.6
ANSWER:B
Answer: B
Question: A person can row 750 metres against the stream in 11 ¼ minutes and returns in 7 ½ minutes. Then the speed of the person in in still water is :
Options:
A)2 km/hr
B)3 km/hr
C)4 km/hr
D)5 km/hr
E)6 km/hr
Rationale: The speed in upstream = .75 * (4/45 )*60 = 4 kmph
The speed in downstream = .75 *(2/15) *60 = 6 kmph
Speed in still water = ½(4+6) = 5 kmph
ANSWER:D
Answer: D
Question: A person spends 1/5th of his income on the education of his children, and 20% of the remaining on food. If he is left with Rs.576 find his income?
Options:
A)Rs.900
B)Rs.800
C)Rs.500
D)Rs.1000
E)Rs.1200
Rationale: X * 4/5 * 80/100 = 576
X = 14400/16
X = 900
ANSWER:A
Answer: A
Question: If,
1 * 3 * 5 = 16
3 * 5 * 7 = 38
5 * 7 * 9 = 68
Then find,
7 * 9 * 11 =?
Options:
A)106
B)49
C)68
D)38
E)55
Rationale: A
106
(11 * 9) + 7 = 106
Answer: A
Question: Three numbers are in the ratio 1 : 2 : 3 and their H.C.F is 2. The numbers are
Options:
A)12, 24, 30
B)12, 24, 38
C)12, 24, 362
D)2, 4, 6
E)12, 24, 321
Rationale: Explanation:
Let the required numbers be x, 2x, 3x. Then, their H.C.F =x. so, x= 2
\inline \fn_jvn \therefore The numbers are 2, 4, 6
Answer: D) 2, 4, 6
Answer: D
Question: Darcy lives 1.5 miles from work. She can walk to work at a constant rate of 3 miles per hour, or she can ride the train to work at a constant rate of 20 miles per hour. If she rides the train, there is an additional x minutes spent walking to the nearest train station, waiting for the train, and walking from the final train station to her work. If it takes Darcy a total of 10 more minutes to commute to work by walking than it takes her to commute to work by riding the train, what is the value of x?
Options:
A)10.5
B)15
C)15.5
D)30
E)60
Rationale: The time it takes Darcy to walk to work is (1.5/3)*60 = 30 minutes
The time it takes Darcy to take the train is (1.5/20)*60 + x = 4.5 + x minutes
It takes 15 minutes longer to walk, so 30 = 4.5 + x + 10
x=15.5 minutes
Answer: C
Answer: C
Question: In a flower shop there were 7 flowers in each bouquet. If the seller has doubled the number of flowers in each bouquet then the new average of flowers in each bouque is
Options:
A)12
B)11
C)14
D)9
E)None of these
Rationale: Answer
Now required average
= old average x Multiplicand
= 7 x 2 = 14
Correct Option: C
Answer: C
Question: Solution Y is 30 percent liquid X and 70 percent water. If 2 kilograms of water evaporate from 8 kilograms of solution Y and 2 kilograms of solution Y are added to the remaining 6 kilograms of liquid, what percent of this new solution is liquid X?
Options:
A)30%
B)33 1/3%
C)37 1/2%
D)40%
E)50%
Rationale: Initial solution => 8 kg (x:w :: 2.4:5.6)
After evaporation Initial solution => 6 kg (x:w:: 2.4:3.6)
New solution => 2 kg (x:w::0.6:1.4)
Mixing (Initial solution + New solution) => 6 kg (2.4:3.6)+ 2 kg (0.6:1.4) =
= 8 kg [(2.4+0.6) : (3.6+1.4)]
= 8 kg (x : water :: 3kg : 5 kg)
Hence % of x = 3/8 = 37.5%
ANSWER:C
Answer: C
Question: A man can do a piece of work in 7 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)5
B)7
C)15/2
D)21/4
E)18/5
Rationale: Son's 1 day's work = (1/3)-(1/7) = 4/21
The son alone can do the work in 21/4 days
Answer is D
Answer: D
Question: The number of new words that can be formed by rearranging the letters of the word 'NOTE' is ?
Options:
A)118
B)290
C)23
D)120
E)140
Rationale: Number of words which can be formed
= 4! - 1 = 24 - 1
= 23.
Answer:C
Answer: C
Question: Rahul went to a shop and bought things worth Rs. 27, out of which 30 Paise 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)Rs 15
B)Rs 12.10
C)Rs 21.70
D)Rs 16.80
E)None of these
Rationale: Explanation :
Let the cost of the tax items = x
Given that tax rate = 6%
Cost of tax items, x*(6/100) = 30/100
x = 5 rs
Now non taxable item = total cost - cost for taxable item - tax
= 27 - 5 - 0.30
=21.70
Answer : C
Answer: C
Question: Manu, Manju and Maya can do a work in 90, 30 and 45 days respectively. If they work together, in how many days will they complete work?
Options:
A)15
B)10
C)20
D)25
E)30
Rationale: Manu’s one day’s work = 1/90
Manju’s one day’s work = 1/30
Maya’s one day’s work = 1/45
Manu, Manju and Maya together can do the work = 1/90 + 1/30 + 1/45
= (1+3+2)/90
= 1/15
So, They will complete the work in 15 days.
ANSWER:A
Answer: A
Question: X can do a piece of work in 20days. He works at it for 10days and then Y finished it in 12days. How long will Y take to complete the work?
Options:
A)10
B)12
C)24
D)29
E)30
Rationale: Work done by X in 10days = 10*1/20 = 1/2
Remaining work = 1 - 1/2 = 1/2
1/2 work is done by Y in 12days
Whole work will be done by Y in 12*2 = 24days
Answer is C
Answer: C
Question: In one year, the population, of a village increased by 10% and in the next year, it decreased by 10%. If at the end of 2nd year, the population was 7920, what was it in the beginning?
Options:
A)2277
B)8000
C)2688
D)1266
E)1912
Rationale: x*110/100 * 90/100 = 7920
X*0.99=7920
X=7920/0.99
=> 8000
Answer: B
Answer: B
Question: The length of a train and that of a platform are equal. If with a speed of 90 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is:
Options:
A)377
B)267
C)268
D)750
E)271
Rationale: Speed = [90 * 5/18] m/sec = 25 m/sec; Time = 1 min. = 60 sec.
Let the length of the train and that of the platform be x meters.
Then, 2x/60 = 25 è x = 25 * 60 / 2 = 750 .Answer: D
Answer: D
Question: What is the smallest integer k for which 64^k > 4^22?
Options:
A)4
B)5
C)6
D)7
E)8
Rationale: 64^k > 4^22
4^(3k) > 4^22
3k > 22
k = 8
The answer is E.
Answer: E
Question: Out of 10 persons working on a project, 4 are graduates. If 3 are selected, what is the probability that there is at least one graduate among them?
Options:
A)5/7
B)9/6
C)5/9
D)5/6
E)3/6
Rationale: Explanation:
P(at least one graduate) = 1 - P(no graduates) =
1 - ⁶C₃/¹⁰C₃ = 1 - (6 * 5 * 4)/(10 * 9 * 8) = 5/6
Answer: Option D
Answer: D
Question: Laxmi and Prasanna set on a journey. Laxmi moves northwards at a speed of 22 kmph and Prasanna moves southward at a speed of 24 kmph. How far will be Prasanna from Laxmi after 60 minutes ?
Options:
A)44
B)50
C)28
D)27
E)18
Rationale: Explanation:
We know 60 min = 1 hr
Total northward Laxmi's distance = 22kmph x 1hr = 22 km
Total southward Prasanna's distance = 24kmph x 1hr = 24 km
Total distance between Prasanna and Laxmi is = 22 + 24 = 44 km.
Answer: A
Answer: A
Question: GINGER has 3 pairs of pants, 4 different colored dress shirts 3 sports jackets, 9 ties, and 1 pairs of dress shoes in his closet. How many different outfits can he select?
Options:
A)324
B)312
C)290
D)115
E)352
Rationale: no. of ways he can select a pant = 3
no. of ways he can select a shirt= 4
number of ways he can select a pant = 3
number of ways he can select a shirt= 4
similarly, he can select jacket by 3 ways, tie by 9 ways and shoe by 1 way
number of ways to select different outfits = 3*4*3*9*1 =324
Answer:A
Answer: A
Question: In a lottery, there are 10 prizes and 30 blanks. A lottery is drawn at random. What is the probability of getting a prize?
Options:
A)1/10
B)2/5
C)2/7
D)1/4
E)None
Rationale: Solution
P(getting a prize)	= 10 / (10+30)
‹=› 10 / 40
‹=› 1 / 4.
Answer D
Answer: D
Question: James takes a trip and drives 7 hours from Town A to Town C at a rate of 30 miles per hour. On his way back, James drives 60 miles per hour and stops in Town B which is midway between Town A and Town C. How many hours does it take James to drive from Town C to Town B?
Options:
A)1.25
B)1.75
C)1.51
D)1.55
E)2.12
Rationale: distance from A to C =7 hr* 30 mph= 210 miles
hence distance from Y to C= 1/2*210=105
time=105/60=1.75 hrs
IMO: B
Answer: B
Question: The expression (11.98 x 11.98 + 11.98 x x + 0.02 x 0.02) will be a perfect square for x equal to:
Options:
A)0.4
B)0.004
C)0.04
D)0.0004
E)None of them
Rationale: Given expression = (11.98)(power 2) + (0.02)(power 2) + 11.98 x x.
For the given expression to be a perfect square, we must have
11.98 x (x) = 2 x 11.98 x 0.02 or
x = 0.04
Answer is C.
Answer: C
Question: Students at a school were on average 180 cm tall. The average female height was 170 cm, and the average male height was 186 cms. What was the ratio of men to women?
Options:
A) 5:2
B) 5:1
C) 5:3
D) 4:1
E) 3:1
Rationale: We're given a few facts to work with:
1) The average height of the females is 170cm
2) The average height of the males is 186cm
3) The average of the GROUP is 180cm
We're asked for the RATIO of men to women.
W = number of Women
M = number of Men
(170W + 186M)/(W+M) = 180
170W + 186M = 180W + 180M
6M = 10W
3M = 5W
M/W = 5/3
The ratio of men to women is 5 to 3.
C
Answer: C
Question: Find the one which does not belong to that group ?
Options:
A)117
B)121
C)727
D)188
E)122
Rationale: Explanation:
343 = 73, 121 = 112, 1331 = 113, 2197 = 133 and 125 = 53.
343, 1331, 2197 and 125 are perfect cubes, but not 121.
Answer: B
Answer: B
Question: Kamal started a business investing Rs. 9000. After five months, Sameer joined with a capital of Rs. 8000. If at the end of the year, they earn a profit of Rs. 6970, then what will be the share of Sameer in the profit?
Options:
A)2388
B)2380
C)2385
D)2383
E)2381
Rationale: Kamal : Sameer = (9000 * 12) : (8000 * 7)
= 108:56 = 27:14
Sameer's share = 6970 * 14/41 = Rs. 2380.
Answer:B
Answer: B
Question: A cylinder has a diameter of 20 meters and a height of 15 meters. If it is filled to capacity with oil and the content is poured into smaller cylinders of 4 meter radius and 10 meter height, how many smaller cylinders will be filled to capacity?
Options:
A)11
B)5
C)2
D)2
E)3
Rationale: Calculate the volume of the larger cylinder and divide it by the volume of the smaller cylinder.
volume of cylinder =πr2h
larger cylinder volume=1570.8
smaller cylinder volume=502.65
therefore the number of cylinders B that can be filled to capacity=1570.8/502.65=3.1
Answer is E only 3 smaller cylinders can be filled to capacity.
Answer: E
Question: Jamshid and Irwin decided to make up their own version of basketball. In addition to being able to score 2-point baskets, they created ways to score 5-, 11-, and 13-point baskets. If at halftime the product of the point values of Irwin’s baskets was 2,420, how many 11-point baskets did Irwin score?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: First thing I noticed was that all these numbers are prime...
Prime factorization gives the following
Step 1:2*1210
Step 2:2*11*110
Step 4:2*11*11*10
Step 5:2*11*11*2*5
So he scored 2 11-point baskets in my opinion.
Answer C
Answer: C
Question: I had Rs. 10,000 with me. Out of this, money I lent some money to A for 2 years at 15% simple interest. I lent the remaining money to B for an equal number of years at 18% simple interest. After 2 years, I found that A had given me Rs. 360 more as interest as compared to(b) the amount of money which I had lent to B must have been
Options:
A)2,000
B)3,000
C)4,000
D)5,000
E)6,000
Rationale: Explanation:
Total amount = Rs. 10,000
Let money lent A =Rs. x and money lent to B = Rs. (10,000 x)
x = Rs. 6,000. So the amount of money lent to B = Rs. 4,000
Answer: C
Answer: C
Question: A man can row his boat with the stream at 16 km/h and against the stream in 12 km/h. The man's rate is?
Options:
A)8 kmph
B)9 kmph
C)2 kmph
D)4 kmph
E)1 kmph
Rationale: DS = 16
US = 14
S = ?
S = (16 - 2)/2 = 2 kmph
Answer:C
Answer: C
Question: Which of the following integers is a divisor of(15!+10)?
Options:
A)15
B)4
C)3
D)10
E)9
Rationale: When we say 15!, it just means 1*2*3*4*5*...*13*14*15
So you need to find the integer which is a divisor of
(1*2*3*4*5*...*13*14*15 + 10) = 10 (1*2*3*4*5*..*9*11*12*13*14*15 + 1) We obtain this by taking 10 common.
Hence 10 is definitely a divisor of (15! + 10).
Ans D
Answer: D
Question: The cost of producing x tools by a company is given by
C(x) = 1800 x + 5500 (in $)
a) What is the cost of 100 tools?
Options:
A)185500 $
B)185800 $
C)185900 $
D)186500 $
E)182500 $
Rationale: Solution
C(100) = 1800*100 + 5500 = 185500 $
Answer A
Answer: A
Question: The mean of 30 values was 180. It was detected on rechecking that one value 155 was wrongly copied as 135 for the computation of the mean. Find the correct mean.
Options:
A)151
B)149
C)152
D)148
E)180.67
Rationale: Corrected mean = 180×30−135+155/30
= 5400−135+155/30
=5420/30=180.67
Answer E
Answer: E
Question: If x and y are integers, what is the least positive number of 24x+21y?
Options:
A)3
B)5
C)6
D)8
E)9
Rationale: 24x+21y = 3(8x+7y) which will be a minimum positive number when 8x+7y = 1.
8(1) + 7(-1) = 1
Then 3(8x+7y) can have a minimum positive value of 3.
The answer is A.
Answer: A
Question: What is the sum of all possible 3-digit numbers that can be constructed using the digits 1, 2, and 4 if each digit can be used only once in each number?
Options:
A)1210
B)1221
C)1332
D)1443
E)1554
Rationale: There are 6 possible arrangements of the three numbers.
Then each number will be in the hundreds, tens, and ones place two times each.
The sum is 2(111) + 2(222) + 2(444) = 1554
The answer is E.
Answer: E
Question: Find the greatest number that will divide 40, 60 and 120 so as to leave the same remainder in each case.
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: Required number = H.C.F. of (60 - 40), (120 - 60) and (120-40)
= H.C.F. of 20, 60 and 80 = 2.
ANSWER :A
Answer: A
Question: A committee of three people is to be chosen from four married couples. What is the number of different committees that can be chosen if two people who are married to each other cannot both serve on the committee?
Options:
A)16
B)24
C)26
D)30
E)32
Rationale: The committee could have
0 men and 3 women = 4 possibilities ( 4c3 )
1 man and 2 women = 12 possibilities ( no couple should be in the team : 4 * 3c2 )
2 men and 1 woman = 12 possibilities ( no couple should be in the team : 4c2 *2c1 )
3 men and 0 women = 4 possibilities ( 4c3 )
Therefore 4+12+12+4=32
Answer E 32
Answer: E
Question: find out how many positive integers less than 60 are equal to the product of a positive multiple of 5 and an even number?
Options:
A)4
B)5
C)9
D)10
E)11
Rationale: Number of positive multiples of 5 less than 60 = 11
5*1=5
5*2=10
5*3=15
5*4=20
5*5=25
5*6=30
5*7=35
5*8=40
5*9=45
5*10=50
5*11=55
Only 5 of the above are a product of a positive multiple of 5 and an even number - 10,20,30,40,50
Answer B
Answer: B
Question: A side of beef lost 35 percent of its weight in processing. If the side of beef weighed 580 pounds after processing, how many pounds did it weigh before processing?
Options:
A) 191
B) 355
C) 737
D) 892
E) 1,560
Rationale: Let weight of side of beef before processing = x
(65/100)*x = 580
=> x = (580 * 100)/65 = 892
Answer D
Answer: D
Question: Cindy has her eye on a sundress but thinks it is too expensive. It goes on sale for 15% less than the original price. Before Cindy can buy the dress, however, the store raises the new price by 25%. If the dress cost $78.2 after it went on sale for 15% off, what is the difference between the original price and the final price?
Options:
A)$0.00
B)$5.75
C)$3.40
D)$5.00
E)$6.80
Rationale: 0.85*{Original Price} = $78.2 --> {Original Price} = $92.
{Final Price} = $78.2*1.25 = $97.75.
The difference = $97.75 - $92 = $5.75
Answer: B.
Answer: B
Question: The area of a triangle is with base 4m and height 5m?
Options:
A)10
B)20
C)30
D)15
E)11
Rationale: The area of a triangle=1/2*bh
=1/2 * 4 * 5 = 10 m^2
ANSWER:A
Answer: A
Question: Three coworkers P , J , R meet for Dinner. P had 5 sandwiches, J had 3 and R had none. Both PJ share their sandwiches with R such that each one got the same amount. If R paid $ 8 to PJ, how much of $ 8 should P get? Assume both sandwiches and Dollars can be split.
Options:
A)a) 5$
B)b) 3 $
C)c) 7 $
D)d) 4 $
E)e) 5.5 $
Rationale: we got total 8 sandwiches ....we are dividing equally in 3 people.
per person: 8/3
initially
p:8
J:3
r:0
now since r ate 8/3 so he is paying 8 dollars for 8/3 sandwiches.
now p also ate 8/3 of his 5 sandwiches = so he gave 5-8/3 to r ==>7/3 to r
ok we have 8 dollars for 8/3 sandwich
therefore for 7/3 sandwich we will get 7 dollars.
hence p should get 7 dollars.
hence C
Answer: C
Question: A certain league has two divisions. The respective divisions had 7 and 9 teams qualify for the playoffs. Each division held its own double-elimination tournament -- where a team is eliminated from the tournament upon losing two games -- in order to determine its champion. The four division champions then played in a single-elimination tournament -- where a team is eliminated upon losing one game -- in order to determine the overall league champion. Assuming that there were no ties and no forfeits, what is the maximum number of games that could have been played in order to determine the overall league champion?
Options:
A) 30
B) 31
C) 34
D) 36
E) 38
Rationale: Overall, there can be 31 minuses. Tus, it is B.
Answer: B
Question: Jill is dividing her eight-person class into two teams of equal size for a basketball game. If no one will sit out, how many different match-ups between the two teams are possible?
Options:
A)10
B)35
C)126
D)252
E)630
Rationale: With 8 players, the process of figuring out how many groups of 4 can be formed is pretty straight-forward....
8C4 = 8!/(4!4!) = 70 possible groups of 4
Once forming that first group of 4, the remaining 4 players would all be placed on the second team by default.
The 'twist' is that the two teams of 4 canshow upin either order:
B
Answer: B