MU-NLPC/Calc-aqua_rat huggingface dataset:
A certain list has an average of 6 and a standard deviation of d (d is positive). Which of the following pairs of data when added to the list, must result in a list of 102 data with standard deviation less than d?	Choose the correct choice from the following answers.
A) (-6;0)  B) (0;0)  C) (0;6)  D) (0;12)  E) (6;6)

Solution: Standard deviation shows how much variation there is from the mean. A low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values.   So when we add numbers , which are far from the mean we are stretching the set making SD bigger and when we add numbers which are close to the mean we are shrinking the set making SD smaller.   According to the above adding two numbers which are closest to the mean will shrink the set most, thus decreasing SD by the greatest amount.   Closest to the mean are 6 and 6 (actually these numbers equal to the mean) thus adding them will definitely shrink the set, thus decreasing SD.   Answer: (6;6).
Answer: E
Integer X represents the product of all integers between 1 to 28 (inclusive). The smallest prime factor of (x+1) must be  Choose the correct choice:  A) Between 1 to 10  B) Between 11 to 15  C) Between 15 to 20  D) Between 20 to 28  E) Greater than 28

Solution: Answer = E = Greater than 28   This problem is asking smallest prime factor of (28!+1)   28! already have there prime factors 2,3,5,7,11,13.......... so on upto 23 (1 cannot be considered prime factor)   Just adding 1 to 28! will remove all the factors stated above;   so the smallest possible prime factor has to be greater than 28   Answer = Greater than 28
Answer: E
45 men working 8 hours per day dig 30 m deep. How many extra men should be put to dig to a depth of 50 m working 6 hours per day?  Choose one:
A) 74 B) 55 C) 44 D) 75 E) 72

Solution: 55   55   (45 * 8)/30 = (x * 6)/50 => x =100   100 – 45 = 55
Answer: B
In a division, a student took 48 as divisor instead of 36. his answer was 24 . The correct answer is-	Choose one.
A) 42
B) 32
C) 48
D) 28
E) 38

Solution: X/48 = 24.   X = 24 *48.   So correct answer would be,   (24 *48) /36= 
(24 *48) /36 = 32
32.   ANSWER : 32
Answer: B
Find the odd man out. 187, 264, 316, 473, 682, 781  Choose the most appropriate option: A) 187 B) 316 C) 781 D) 682 E) 473

Solution: In all numbers except 316, the middle digit is the sum of other two digits.Answer is 316
Answer: B
A windmill is taking advantage of strong air currents in order to produce electrical energy. On a typical day the wind speed is around 20 mph and in that speed the windmill produces 500 kw/h (kilowatts per hour). On a stormy day a windmill produces 20% more energy. How much kw/h can three windmills produce in two hours on a stormy day?  Pick one
A) 2880.  B) 3600.  C) 5780  D) 5760  E) 6380.

Solution: Normal Day = 500 kw/h   Stormy Day = 500*1.2= 
500*1.2 = 600
600 kw/h   3 windmills for 2 hours on stormy day     600*3*2= 
  600*3*2 = 3_600
3600   Answer: 3600.
Answer: B
John works at a resort from the beginning of March to the end of September. During the month of August this past year, he made 6 times the average (arithmetic mean) of his monthly totals in tips for the other months. His total tips for August were what fraction of his total tips for all of the months he worked?	Choose the correct choice:
A) 1/8
B) 1/7
C) 1/2
D) 1/4
E) 1/6

Solution: First notice the number of months for which he worked - March to Sept i.e. 7 months   Avg of monthly totals in tips for months other than August = x   Tips in August = 6x   Total tips for all months = 6*x + 6x = 12x   Tips for August/Total tips for all months = 6x/12x = 1/2   Answer : 1/2
Answer: C
When the airplane moves at an average speed of 450 kmph it reaches its destination on time. When its average speed becomes 400 kmph, then it reaches its destination 30 minutes late. Find the length of journey.	Choose the correct choice from the following
A) 1250 km
B) 1500 km
C) 1100 km
D) 1800 km
E) None

Solution: Sol.   Difference between timings = 30 min = 1/2 hr.   Let the length of journey be x km.   Then, x/400 - x/450 = 1/2   â‡” 9x - 8x = 1800   â‡” x = 1800 km.   Answer 1800 km
Answer: D
A 250 m long train is running at a speed of 55 Km/hr. It crossed a platform of length 520 m in?
Choose the correct choice from the following:
A) 30.4 sec B) 40.4 sec C) 60.4 sec D) 50.4 sec E) 80.4 sec

Solution: 50.4 sec   50.4 sec   Speed = 55 Km/hr   (to convert km/hr in to M/s)   = 55 x 5/18 M/s   50.4 secistance = 250 m + 520 m ( If questions is about train crossing a post you need to consider only the length of Train, )   = 770 m   Time = 50.4 secistance / Speed   = 770 x 18 / (5 x 55)   = 50.4 sec
Answer: D
An order was placed for supply of carpeat of breadth 3 metres the length of carpet was 1.44 times of breadth. Subsequently the breadth and length were increased by 25 and 40 percent respectively. At the rate of Rs.45 per square metre, what would be the increase in the cost of the carpet?	Choose the correct choice:
A) Rs.1020.6 B) Rs.398.8 C) Rs.437.4 D) Rs.583.2 E) Rs.354.6

Solution: Explanation:   Initial area of the carpet = 3 x 3 x 1.44 = 12.96 sq.metres.   Increased area = 3 + 3 x 25/100 x 3 x 1.44/100 + 3 x 1.44 x 40/100   = 375 x 604.8/ 100 x 100 = 22.68 sq.metre   :. Increase in area = 22.68 – 12.96 = 9.72 sq.metre.   Rs.437.4ost of 9.72 sq.metre = 9.72 x 45 = Rs.437.40   Answer: Option Rs.437.4
Answer: C
Annie and Sam set out together on bicycles traveling at 15 and 12 km per hour respectively. After 40 minutes, Annie stops to fix a flat tire. If it takes Annie 35 minutes to fix the flat tire and Sam continues to ride during this time, how many minutes will it take Annie to catch up with Sam assuming that Annie resumes riding at 15 km per hour?  Choose the most appropriate option:
A) 20  B) 40  C) 60  D) 80  E) 100

Solution: Annie gains 3 km per hour (or 1 km every 20 minutes) on Sam.   After 40 minutes Annie is 2 km ahead.   Sam rides 1 km every 5 minutes.   In the next 35 minutes, Sam rides 7 km so Sam will be 5 km ahead.   It will take Annie 100 minutes to catch Sam.   The answer is 100.
Answer: E
A dishonest shopkeeper professes to sell pulses at the cost price, but he uses a false weight of 930gm. for a kg.His gain is …%.
Choose the correct answer:
A) 5.26%
B) 5.36%
C) 4.26%
D) 6.26%
E) 7.53%

Solution: His percentage gain is 100*7/930 as he is gaining 70 units for his purchase of 930 units.   so 7.53%.   ANSW7.53%R:7.53%
Answer: E
6 men and 8 women can complete a work in 10 days. 26 men and 48 women can finish the same work in 2 days. 15 men and 20 women can do the same work in - days.
Options.
A) 4 B) 5 C) 6 D) 7 E) 8

Solution: Let work done by 1 man in 1 day = m and work done by 1 woman in 1 day = b   Work done by 6 men and 8 women in 1 day = 1/10   => 6m + 8b = 1/10   => 60m + 80b = 1 --- (1)   Work done by 26 men and 48 women in 1 day = 1/2   => 26m + 48b = ½   => 52m + 96b = 1--- (2)   Solving equation 1 and equation 2. We get m = 1/100 and b = 1/200   Work done by 15 men and 20 women in 1 day   = 15/100 + 20/200 =1/4   => Time taken by 15 men and 20 women in doing the work = 4 days   4nswer is 4.
Answer: A
A watch was sold at a loss of 36%. If it was sold for Rs.140 more, there would have been a gain of 4%. What is the cost price?
Choose the correct choice:
A) 350	B) 288	C) 799	D) 778	E) 901

Solution: 64%   104%   --------   40% ---- 140   100% ---- ? => Rs.350   350nswer: 350
Answer: A
Three people took GMAT practice tests in which the minimum and maximum possible scores are 200 and 800, respectively. They each took a test 3 times, and no one scored below 510 or over 780. If the individual ranges of the three people's scores in those 3 practice tests were 20, 90 and 130, what is the difference between the maximum and minimum possible ranges of all their scores put together. Choose the correct choice:
A) 70	B) 80	C) 90	D) 140	E) 170

Solution: According to the information in the question the maximum range would be between 510 and 780(270). The minimum range would be the greatest range for any one individual, which is listed in the problem as 130. So the difference between these would be 270-130 or 140.   Answer: 140
Answer: D
The speed of the boat in still water in 12 kmph. It can travel downstream through 48 kms in 3 hrs. In what time would it cover the same distance upstream?  Choose the correct choice:
A) 8 hours  B) 6 hours  C) 4 hours  D) 5 hours  E) 6 hours

Solution: Still Water=12km/hr   Downstream=48/3= 
48/3 = 16
16km/hr   Upstream=>> still water=(u+v/2) =>> 12=u+16/2= 
+16/2 = 8
8km/hr   So time taken in upstream= 48/8= 
48/8 = 6
6hrs   ANSW6 hoursR:6 hours
Answer: E
Sonika deposited Rs.8000 which amounted to Rs.9200 after 3 years at simple interest. Had the interest been 2% more. She would get how much?
Choose the correct answer:  A) 9680  B) 2288  C) 7799  D) 1777  E) 2991

Solution: (8000*3*2)/100= 
(8000*3*2)/100 = 480
480   9200   --------   9680   9680nswer:9680
Answer: A
A car dealer sold x used cars and y new cars during May. If the number of used cars sold was 10 greater than the number of new cars sold. Which of the following expresses this relationship ? Choose the correct choice from the following choices:  A) x > 10y  B) x > y + 10  C) x > y – 10  D) x = y + 10  E) x = y – 10

Solution: Given: x used cars and y new cars   Number of used cars (x) sold was 10 greater than the number of new cars (y) sold   So, x is 10 greater than y   To show their relative sizes let's write x LARGER than y to get: x and y   Our goal is to create an EQUATION. So, how do we make these two values EQUAL?   Well, we need to make the smaller value (y) bigger. 10 bigger to be exact.   So, we get x = y + 10   Answer: x = y + 10
Answer: D
A teacher prepares a test. She gives 5 objective type questions out of which 4 have to be answered. Find the total ways in which they can be answered if the first 2 questions have 3 choices and the last 3 have 4 choices. Choose the correct choice from the following options:	A) 255	B) 816	C) 192	D) 100	E) 144

Solution: Two cases.   First Case: 2 Questions - 3 Choices, 2 Questions - 4 Choices   2C2 * 3C2 ways to select the questions   3C1 * 3C1 * 4C1 * 4C1 ways to answer the questions   = 1 * 3 * 3 * 3 * 4 * 4   = 27 * 16= 
27 * 16 = 432
432   Second Case: 1 Question - 3 Choices, 3 Questions - 4 Choices   2C1 * 3C3 ways to select the questions   3C1 * 4C1 * 4C1 * 4C1 ways to answer the questions= 2 * 1 * 3 * 4 * 4 * 4   = 6 * 64= 
6 * 64 = 384
384   Total= 384 + 432= 
384 + 432 = 816
816   ANS:816
Answer: B
How many unique positive odd integers less than 70 are equal to the product of a positive multiple of 5 and an odd number? Choose the correct option:
A) 4	B) 7	C) 11	D) 12	E) 15

Solution: The Question basically asks how many positive odd integers less than 70 are odd multiples of 5   So we have 5,15,25,35,45,55 and 65   =7   Ans 7
Answer: B
if m<0 and x is m percent of y, then, in terms of m, y is what percent of x?	Choose the correct choice from the following options:  A) a)10^4m  B) b)1/100m  C) c)1/m  D) d)10/m  E) e)10,000/m

Solution: Given (m*y)/100=x   to find (y/x)*100   Rearranging first equation   y/x*100 = 100*100/m   =10000/m   a)10^4mnswer a)10^4m
Answer: A
A cyclist rides a bicycle over a route which is 1/3 uphill, 1/3 level, and 1/3 downhill. If the cyclist covers the uphill part of the route at the rate of 14 km per hour and the level part at the rate of 21 km per hour, what rate in km per hour would the cyclist have to travel the downhill part of the route in order to average 21 km per hour for the entire route?  Choose the correct choice.
A) 28 B) 35 C) 42 D) 49 E) 56

Solution: Let V be the speed on the downhill section.   Let D be the distance of each of the three equal sections.   Total time T = T1+T2+T3 and 3D/T = 21 km/hour   3D / (D/14 + D/21 + D/V) = 21   1/7 = 1/14 + 1/21 + 1/V   1/V = 1/42 and so V = 42 km/h   The answer is 42.
Answer: C
A and B enter into partnership with capital as 7:9. At the end of 8 months, A withdraws. If they receive the profits in the ratio of 8:9 find how long B's capital was used?	Choose the correct choice from the following choices
A) 6 B) 5 C) 9 D) 7 E) 2

Solution: 7 * 8 : 9 * x = 8:9   => x= 7   Answer:7
Answer: D
Fine the volume of cuboid 15 m length, 9 m breadth and 2 m height. Choose one
A) 1440	B) 1540	C) 1140	D) 1220	E) 1330

Solution: l × b × h => 15 × 12 × 8 = 1440 m(power3)   1440nswer is 1440
Answer: A
If all of the telephone extensions in a certain company must be even numbers, and if each of the extensions uses all four of the digits 1, 2, 4, and 5, what is the greatest number of four-digit extensions that the company can have? Pick:	A) 4	B) 6	C) 12	D) 16	E) 24

Solution: Since the phone number must be even, the unit's digit can be either 2 or 4.   When the unit's digit is 2 --> number of possibilities is 3! = 6   When the unit's digit is 4 --> number of possibilities is 3! = 6   Largest number of extensions = 6 + 6= 
6 + 6 = 12
12   Answer:12
Answer: C
Divide Rs.118000 among three persons A, B and C such that the ratio of the shares of A and B is 3:4 and that of B:C is 5:6?
Choose the correct choice from the following options:
A) 30000 B = 40000 C = 48000
B) 30060 B = 40800 C = 49000
C) 33000 B = 40000 C = 48600
D) 30000 B = 40000 C = 48000
E) 30000 B = 43000 C = 48060

Solution: Compound ratio of A:B:C   A:B = 3:4   B:C = 5:6   ----------   A:B:C = 15:20:24   We can divide Rs.118000 in this ratio.   Share of 30000 B = 40000 C = 48000 = 15/59 * 118000= 
15/59 * 118000 = 30_000
30000   Share of B= 20/59 * 118000= 
20/59 * 118000 = 40_000
40000   Share of C= 24/59 * 118000= 
24/59 * 118000 = 48_000
48000   30000 B= 40000 C = 48000nswer:30000 B = 40000 C = 48000
Answer: A
If (n+2)!/n!=156, n=?
Choose one
A) 2/131 B) 9 C) 10 D) 11 E) 12

Solution: (n+2)!/n!= 156   Rewrite as:[(n+2)(n+1)(n)(n-1)(n-2)....(3)(2)(1)]/[(n)(n-1)(n-2)....(3)(2)(1)]= 132   Cancel out terms: (n+2)(n+1) = 156   From here, we might just TEST the answer choices.   Since (13)(12) = 156, we can see that n = 11   11
Answer: D
What is the length of a bridge (in meters), which a train 156 meters long and travelling at 45 km/h can cross in 30 seconds?  Choose the correct choice from the following answers.
A) 203
B) 211
C) 219
D) 227
E) 235

Solution: speed = 45 km/h = 45000 m / 3600 s = 25/2 m/s   In 30 seconds, the train can travel  25/2 * 30= 
 25/2 * 30 = 375
375 meters   375= length of train + length of bridge   length of bridge = 375 - 156= 
375 - 156 = 219
219 meters   The answer is 219.
Answer: C
There are 18 balls in a jar. You take out 3 blue balls without putting them back inside, and now the probability of pulling out a blue ball is 1/5. How many blue balls were there in the beginning?	Choose the correct choice from the following choices:  A) 12  B) 9  C) 8  D) 7  E) 6

Solution: There are 18 balls in a jar. You take out 3 blue balls without putting   3 blue balls + 15 / 5 =6   Answer:6
Answer: E
In how many ways can six different rings be worn on four fingers of one hand?
Choose the correct choice.
A) 10
B) 12
C) 15
D) 16
E) 18

Solution: Required number of ways = ways of selecting 4 objects out of 6 given objects   = 6154 = 6x 5/2= 15   Answer 15
Answer: C
How long does a train 110 metres long running at the speed of 72 km / hr take to cross a bridge 132 metres in length? Pick one:
A) 9.8 sec
B) 12.1 sec
C) 12.42 sec
D) 14.3 sec
E) None

Solution: Solution   Speed	= (72 x 5/18 )m/sec   = 20 m/ sec   Total Distance covered	= (110 + 132)= 
(110 + 132) = 242
242 m   Required time= (242 / 60) sec   = 12.1 sec   Answer 12.1 sec
Answer: B
Each student is given a four-character identification code. The first character is a number from 0 to 9 inclusive, and the last three characters are selected from the 26 letters of the alphabet. If characters may be repeated and the same characters used in a different order constitute a different code, how many different identification codes can be generated following these rules?	Choose the correct choice from the following
A) 175,760  B) 163,120  C) 152,340  D) 143,590  E) 132,670

Solution: The number of possible codes is 10*26*26*26=175,760.   The answer is 175,760.
Answer: A
If a and b are prime numbers and one the value of them is 2, which of the following CANNOT be the value of ab? Choices:
A) 9 B) 14 C) 21 D) 24 E) 25

Solution: Here one the prime number is 2,so the answer should be the double of a prime number,which is14=7/2..   ans 14
Answer: B
-20 , -16 , -12 , -8 ....
In the sequence above, each term after the first is 4 greater than the preceding term. Which of the following could not be a term in the sequence?	Select the correct option:
A) 0	B) 200	C) 440	D) 668	E) 762

Solution: Simplifying the question into easier words we just need to find which of the numbers is not divisible by 4   clearly the answer is 762 because if we divide 762 by 4 we get a remainder of 2   Correct answer - 762
Answer: E
If m and n are positive integers, and m=2n and k=m, then - Options.
A) m/2 is a factor of k. B) 2m is a factor of k. C) 3m is a factor of k/2. D) k is a factor of m. E) k is a factor of m/2.

Solution: m=2n --> m is even.   k=m --> m is factor of k, thus m/2 = integer must also be a factor of k.   m/2 is a factor of k.nswer: m/2 is a factor of k..
Answer: A
Rodrick mixes a martini that has a volume of 'n' ounces having 35% Vermouth and 60% Gin by volume. He wants to change it so that the martini is 25% Vermouth by volume. How many ounces of Gin must he add?
Choose one
A) n/6	B) n/3	C) 2n/5	D) 5n/6	E) 8n/5

Solution: total V G   1 ounce 0.35 0.6   n ounce 0.35n 0.6n -------------initial expression   lets say g ounces of gin is added to this mixture   n+g 0.35n 0.6n+g --------------final expression   given that after adding g ounces of gin , V should become 25% of the total volume.   =>Volume of V/total volume = 25/100   => 0.35n /n+g = 1/4   => 1.4n = n+g   => g = 2n/5   Answer is C.   Note that after we add pure Gin, the volume of Vermouth will remain the same. Based on this set the equation:   0.35n=0.25(n+g) --> g=2n/5   Answer: 2n/5.
Answer: C
A boat moves upstream at the rate of 1 km in 20 minutes and down stream 1 km in 15 minutes. Then the speed of the current is : Answers.
A) 1 kmph B) 0.5 kmph C) 3 kmph D) 2.5 kmph E) 3.5 kmph

Solution: Rate upstream = (1/20 *60)= 
(1/20 *60) = 3
3 kmph   Rate down stream= 1/15 * 60= 
1/15 * 60 = 4
4 kmph   Rate of the current= ½ (4-3) = 0.5 kmph   ANSWER:0.5 kmph
Answer: B
The cost of.275 kgs. of sugar is Rs.26. What is the cost of 6 kgs. of sugar?
Choose the correct choice from the following choices:
A) Rs.68
B) Rs.67
C) Rs.572
D) Rs.567.275
E) Rs.75

Solution: Explanation:   The cost of 6 kgs. of sugar = 26X6/0.275 = Rs.567.275   Answer: Option :Rs.567.275
Answer: D
Ms. Samantha sold two properties, X and Y, for $45,500 each. She sold property X for 30 % more than she paid for it and sold property Y for 30% less than she paid for it. If expenses are disregarded , what was her total net gain or loss, if any, on the two properties ?  Choose the correct choice from the following answers: A) $9500 B) $9000 C) $9600 D) $9700 E) $9800

Solution: There is a property to solve such questions withCommon Selling PriceandCommon %gain and loss. such cases always result in a loss and...   Total %Loss = (Common Gain% or Loss%/10)^2   Hence Here Loss% = (30/10)^2 = 9%   which means he recovered only 91% of his investment which amount to a total revenue = 45500 + 45500= 
45500 + 45500 = 91_000
91000   i.e. 91% of cost= 91000   therefore, 9% of cost (Loss) = $9000   Answer: $9000
Answer: B
A motorcyclist made 3 roundtrips to the park until he ran out of gas back at home. Te park is 1500 meters away from his home. His speedometer was broke and he wanted to calculate his speed. It took him two and half hours to complete the journey. How fast was the motorcyclist traveling?
Select the correct option.
A) 25 B) 60 C) 36 D) 45 E) 32

Solution: The distance from the park to the motorcyclist home was 15000 meters.   He made the trip 3 times in total with each trip being 30000 meters.   multiply 3 by 30000 to get 90000 meters or 90km in total.   D= ST   90000/2.5= 
90000/2.5 = 36_000
T which comes to 36000 meters or 36 km per hour   36orrect answer= 36
Answer: C
In the accounting branch of a commercial institute, the percentage of male and female workers is 48% and 52% respectively. In this branch, 40% of males and 20% of females are age 25 or older. If one of the workers is selected at random, what is the probability W that the worker is under 25 years old?	Choose the correct option
A) 0.30	B) 0.25	C) 0.45	D) 0.70	E) 0.90

Solution: Percentage of male worker = 48   Percentage of female worker = 52   Let total number of workers = 1000   number of male workers= 480   number of female workers = 520   Number of male age 25 or older = (4/10)*480= 
(4/10)*480 = 192
192   Number of female age 25 or older=(2/10)*520= 
(2/10)*520 = 104
104   Total number of workers 25 or older= 192+104= 
192+104 = 296
296   Total number of workers under 25= 1000 - 296= 
1000 - 296 = 704
704   Probability that a worker randomly selected is under 25 years old= 704/1000= 
704/1000 = 88/125 = around 0.704
.704   Alternatively , since the answer options are not close , we can use estimation here .   Percentage of male worker 25 or older= (4/10)*48 = 20 % approx   Percentage of female worker 25 or older = (2/10)*52 = 10 % approx   Percentage of total worker 25 or older = 30 %   Percentage of total worker under 25 = 70 %   Probability that a worker randomly selected is under 25 years old W= .7   Answer 0.70
Answer: D
Jayant opened a shop investing Rs. 30,000. Madhu joined him 2 months later, investing Rs. 45,000. They earned a profit of Rs. 60,000 after completion of one year. What will be Madhu's share of profit?
Choose the correct choice from the following:
A) Rs. 27,000	B) Rs. 24,000	C) Rs. 30,000	D) Rs. 36,000	E) None of these

Solution: 30,000 *12=45,000*8   1:1   Madhu's share=1/2*60,000   i.e. Rs. 30,000   ANSWER:Rs. 30,000
Answer: C
A table is bought for Rs.900/- and sold at Rs.810/- find the loss percentage
Choose one.
A) 5% B) 10% C) 15% D) 20% E) 22%

Solution: Formula = (Selling price ~ Cost price)/Cost price * 100   = (810 ~ 900)/900 = 10% Loss   10%
Answer: B
The average of 5 numbers is 6.8. If one of the numbers is multiplied by a factor of 3, the average of the numbers increases to 12.8. What number is multiplied by 3?
Pick one:
A) 15.0  B) 13.0  C) 13.9  D) 10.0  E) 6.0

Solution: The average of 5 numbers is 6.8   The sum of 5 numbers will be 6.8 x 5 = 34   The average of 5 number after one of the number is multiplied by 3 is 12.8   The sum of the numbers will now be 12.8 x 5 = 64   So the sum has increased by  64-34= 
 64-34 = 30
30   Let the number multiplied by 3 be n   Then,   3n= n+30   or 2n = 30   or n = 15   15.0nswer:- 15.0
Answer: A
Some of the workers at a hedge fund are analysts; the others are not analysts. There are a total of 2x/3 analysts at the hedge fund. A total of x hedge fund workers have an MBA. Furthermore, x/3 analysts have an MBA, y/4 of the hedge fund workers are neither analysts nor have an MBA, and 60 workers are not analysts. If there are y total workers at the hedge fund, x is equal to which of the following? Choose the correct choice from the following answers
A) 45  B) 54  C) 60  D) 75  E) 80

Solution: AnalystsNot AnalystsTotal   MBAx/32x/3x   No MBAy/4   Total2x/350y   We are asked for the value of x.   From the table: 2x/3 = y - 60   y - 60 + (y/4) = 60   5y/4 = 120   y = 96   2x/3 = 96 - 60= 
96 - 60 = 36
36   x= 108/2= 
108/2 = 54
54   Answer: 54
Answer: B
In how many ways, a committee of 5 members can be selected from 8 men and 5 ladies, consisting of 3 men and 2 ladies?
Options: A) 75 B) 152 C) 175 D) 560 E) 612

Solution: (3 men out 8) and (2 ladies out of 5) are to be chosen   Required number of ways = (8C3 * 5C2) = 560   Answer is 560
Answer: D