divelab/Sys2Bench huggingface dataset:
Question: A certain university will select 1 of 6 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?
Options:
A)42
B)270
C)140
D)165
E)315
Rationale: 1 of 6 will be chosen for the math
2 of 10 will be chosen for the computer
None of the 3 chosen people can be in more than one departments.
We can choose any of the 6 candidates for the math dep., which gives as 6 selections.
We can choose 2 of the 10 candidates for the computer dep., which gives us 2 selections and 8 rejections.
So, the way to find how many different selections of 2 candidates we can have for the computer dep., we do:
10! /2!*8!= (9*10) / 2 = 90 / 2 = 45.
We are multiplying our individual selections: 6*45 = 270
In the bolded part, we don't have to multiply all of the numbers, as those in 8! are included in 10!, so we simplify instead.
Ans B
Answer: B
Question: In a certain company, a third of the workers do not have a retirement plan. 50% of the workers who do not have a retirement plan are women, and 40% of the workers who do have a retirement plan are men. If 120 of the workers of that company are men, how many of the workers are women?
Options:
A)80
B)95
C)105
D)156
E)210
Rationale: Set up equation:
x = total number of workers
120 = 0,4 * 2/3 * x + 0,5 * 1/3 * x
120 = 13/30 x
x = 276
276 - 120 = 156
Answer D
Answer: D
Question: The visitors of a modern art museum who watched a certain Picasso painting were asked to fill in a short questionnaire indicating whether they had enjoyed looking at the picture and whether they felt they had understood it. According to the results of the survey, all 130 visitors who did not enjoy the painting also did not feel they had understood the painting, and the number of visitors who enjoyed the painting was equal to the number of visitors who felt they had understood the painting. If 3/4 of the visitors who answered the questionnaire both enjoyed the painting and felt they had understood the painting, then how many visitors answered the questionnaire?
Options:
A)90
B)120
C)160
D)360
E)520
Rationale: If we exclude those cases and take the question at face value, then it seems straightforward.
Group #1 = (didn't like, didn't understand) = 130
Group #2 = (like understood) = 3/4
(1/4)N = 130
N = 520
Answer =(E)
Answer: E
Question: Peter and Tom shared the driving on a certain trip. If Peter and Tom both drove for the same amount of time, but Peter only drove 3/5 of the total distance, what was the ratio of Peter's average speed to Tom's average speed?
Options:
A)1:5
B)3:2
C)1:2
D)3:5
E)2:3
Rationale: The answer is suppose to be B. 3:2. It's from the GMATPrep
Answer:option B
Answer: B
Question: P,Q and R together earn Rs.1620 in 9 days. P and R can earn Rs.600 in 5 days. Q and R in 7 days can earn Rs.910. How much amount does R can earn per day?
Options:
A)Rs.40
B)Rs.70
C)Rs.90
D)Rs.100
E)Rs.120
Rationale: Explanation :
Amount Earned by P,Q and R in 1 day = 1620/9 = 180 ---(1)
Amount Earned by P and R in 1 day = 600/5 = 120	---(2)
Amount Earned by Q and R in 1 day = 910/7 = 130	---(3)
(2)+(3)-(1) => Amount Earned by P , Q and 2R in 1 day
- Amount Earned by P,Q and R in 1 day = 120+130-180 = 70
=>Amount Earned by R in 1 day = 70
Answer : Option B
Answer: B
Question: By selling a house for Rs.45000, it was found that 1/8 of the outlay was gained, what ought the selling to price to have been in order to have lost 5 p.c?
Options:
A)28788
B)38000
C)27992
D)28872
E)29982
Rationale: CP + CP/8 = 45000
CP = 40000
SP = 40000*(95/100) = 38000
Answer: B
Answer: B
Question: if length of a room is three times of its breadth and its area is 12 sq.m.what is perimeter of room?
Options:
A)14 m
B)18 m
C)24 m
D)16 m
E)none of the above
Rationale: let breadth=x m. and length = 3x m.
x*3x=12,x^2=4,x=2.
length=6m,breadth = 2 m.
perimeter=2*(6+2)=16 m
answer D
Answer: D
Question: The curved surface of a sphere is 64 π cm2. Find its radius?
Options:
A)8
B)3
C)4
D)9
E)7
Rationale: Explanation:
4 πr2 = 64 => r = 4
Answer: Option C
Answer: C
Question: A train passes a station platform in 35 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
Options:
A)225
B)279
C)240
D)288
E)231
Rationale: Speed = [54 * 5/18] m/sec = 15 m/sec.
Length of the train = (15 * 20) m = 300 m.
Let the length of the platform be x meters.
Then, x + 300 / 35 = 15
x + 300 = 525
x = 225 m. Answer:A
Answer: A
Question: A school’s annual budget for the purchase of student computers increased by 32% this year over last year. If the price of student computers increased by 20% this year, then the number of computers it can purchase this year is what percent greater than the number of computers it purchased last year?
Options:
A)15%
B)5%
C)10%
D)12%
E)6%
Rationale: Lats year: budget = $100, price = $1 --> the number of computers purchased = 100/1 = 100;
This year: budget = $132, price = $1.2 --> the number of computers purchased = 132/1.2 = 110.
Increase in the number of computers purchased = 10%.
Answer: C
Answer: C
Question: A can give B 60 meters start and C 200 meters start in a kilometer race. How much start can B give C in a kilometer race?
Options:
A)148.94
B)148.13
C)148.22
D)111.0
E)111.12
Rationale: A runs 1000 m while B runs 940 m and C runs 800 m.
The number of meters that C runs when B runs 1000 m,
= (1000 * 800)/940
= 851.06 m.
B can give C = 1000 - 851.06
=148.94m.
Answer:A
Answer: A
Question: The respective ages of father and his son are 47 and 16 years. In how many years will the father be twice as old as his son ?
Options:
A)19 years
B)9 years
C)10 years
D)15 years
E)12 years
Rationale: Suppose x years later the father will be twice as old as his son.
x + 47 = 2 (x + 16)
x = 47 - 32 = 15 years
answer : D
Answer: D
Question: In how many ways a committee consisting of 3 men and 2 women can be formed from 4 men and 3 women?
Options:
A)10
B)15
C)20
D)18
E)21
Rationale: Required number of ways = 4C3*3C2 = 4*3 = 12
Answer is A
Answer: A
Question: What is the greatest positive integer x such that 7^x is a factor of 343^10?
Options:
A)5
B)9
C)10
D)20
E)30
Rationale: 343^10 = (7^3)^10 = 7^30
ANSWER:E
Answer: E
Question: The average age of 8 men increases by 2 years when two women are included in place of two men of ages 20 and 24 years. Find the average age of the women?
Options:
A)5
B)10
C)50
D)40
E)30
Rationale: 20 + 24 + 8 * 2 = 60/2 = 30
Answer: E
Answer: E
Question: The speed of a boat in still water is 70kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?
Options:
A)80,47 kmph
B)80,80 kmph
C)80,42 kmph
D)90,50 kmph
E)83,40 kmph
Rationale: Speed downstream = 70 + 20 = 90 kmph
Speed upstream = 70 - 20 = 50 kmph.Answer:D
Answer: D
Question: If x and y are non-zero integers, and 64x^4 – 4y^4 = 8x^2 + 2y^2, which of the following could be the value of x2 in terms of y?
Options:
A)2y^2
B)2y
C)2y^2/8
D)2y^2-1/8
E)2y^2+1/8
Rationale: 64x^4 – 4y^4 = 8x^2 + 2y^2
(8x^2 + 2y^2) (8x^2 - 2y^2) = 8x^2 + 2y^2
8x^2 - 2y^2 = 1
8x^2 = 2y^2+1
x^2 = 2y^2+1/8
Answer : E
Answer: E
Question: Which of the following is satisfied with |x-4|+|x-3|<3?
Options:
A)1<x<5
B)2<x<5
C)4/3<x<10/3
D)4/3<x<4
E)3<x<4
Rationale: --> If there is addition when there are 2 absolute values, you can just ignore the middle. That is, |x-4|+|x-3|<3 -> |x-4+x-3|<3 -> |2x-7|<3, -3<2x-7<3, 4<2x<10, 2<x<5->
Therefore, the answer is B.
Answer: B
Question: After deducting a commission of 5%, a T.V. set costs $9595. Its market price is ?
Options:
A)10000
B)10100
C)21200
D)21000
E)11000
Rationale: Let the marked price be x
then, x-5% of x = 9595
95% of x = 9595
x = 10100
Answer is B
Answer: B
Question: A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 700 m long?
Options:
A)186 Sec
B)190 Sec
C)279 Sec
D)978 Sec
E)627 Sec
Rationale: L = S*T
S= 1200/120
S= 10 m/Sec.
Total length (D)= 1900 m
T = D/S
T = 1900/10
T = 190 Sec
Answer:B
Answer: B
Question: The length and breadth of a rectangle is increased by 10% and 30% respectively. What is the increase in the area?
Options:
A)43.0
B)44.0
C)43.5
D)45.0
E)42.0
Rationale: 100*100=10000
110*130=14300
----------
4300
10000-------4300
100-------43.00
Answer A
Answer: A
Question: A six-sided die is rolled once. What is the probability that the number rolled is an even number greater than 2?
Options:
A)1/4
B)2/4
C)1/2
D)1/3
E)2/3
Rationale: Out of the 6 possible numbers that may rolled, 3 are even: 2, 4 and 6 BUT only 4 and 6 are greater than 2. Hence the probability that the number rolled is an even number greater than 2 is given by
(number of even numbers greater than 2) / 6 = 2 / 6 = 1 / 3
correct answer D
Answer: D
Question: The average of 10 consecutive integers is 20. Then, 9 is deducted from the first consecutive number, 8 is deducted from the second, 7 is deducted form the third, and so on until the last number which remains unchanged. What is the new average?
Options:
A)14
B)14.5
C)15
D)15.5
E)16
Rationale: The total subtracted is (9+8+...+1) = (9*10) / 2 = 45
On average, each number will be reduced by 45/10 = 4.5
Therefore, the overall average will be reduced by 4.5
The answer is D.
Answer: D
Question: In a two-digit, if it is known that its unit's digit exceeds its ten's digit by 2 and that the product of the given number and the sum of its digits is equal to 144, then the number is:
Options:
A)24
B)26
C)42
D)46
E)48
Rationale: Let the ten's digit be x.
Then, unit's digit = x + 2.
Number = 10x + (x + 2) = 11x + 2.
Sum of digits = x + (x + 2) = 2x + 2.
(11x + 2)(2x + 2) = 144
22x2 + 26x - 140 = 0
11x2 + 13x - 70 = 0
(x - 2)(11x + 35) = 0
x = 2.
Hence, required number = 11x + 2 = 24.
Answer:A
Answer: A
Question: A farmer spent $35 on feed for chickens and goats. He spent 40% money on chicken feed, which he bought at a 20% discount off the full price, and spent the rest on goat feed, which he bought at full price. If the farmer had paid full price for both the chicken feed and the goat feed, what amount would he have spent on the chicken feed and goat feed combined?
Options:
A)$37.80
B)$38.50
C)$39.20
D)$39.50
E)$40.60
Rationale: A farmer spent 40% money on chicken feed, so he spent 0.4*$35=$14 on chicken feed, thus he spent the remaining 35-14=$21 on goat feed.
Now, since he bought chicken feed at a 20% discount then the original price of it was x*0.8=$14 --> x=$17.5.
Therefore if the farmer had paid full price for both the chicken feed and the goat feed, then he would he have spent 17.5+21=$38.5.
Answer: B.
Answer: B
Question: What is the average of xx, 2x2x, and 66?
Options:
A)2x+2
B)x+2x-2
C)x+2x+2
D)x+2
E)x+2x
Rationale: By the definition of an average, we get:
x+2x+63=3x+63x+2x+63=3x+63
=3(x+2)3=x+2.=3(x+2)3=x+2.
Hence, the answer is x+2x+2 or
Option C
Answer: C
Question: A courier charges for packages to a certain destination are 65 cents for the first 250 grams and 10 cents for each additional 100 grams or part thereof. What could be the weight in grams of a package for which the charge is $2.15?
Options:
A)980
B)1120
C)1260
D)1420
E)1670
Rationale: The charge is 65 cents for the first 250 grams.
This leaves a charge of $2.15 - $0.65 = $1.50
The charge for the next 1400 grams is $1.40 which leaves a charge of $0.10
The weight is somewhere between 1650 and 1750.
The answer is E.
Answer: E
Question: If 4 men can colour 48 m long cloth in 2 days, then 6 men can colour 72 m long cloth in
Options:
A)1 day
B)2 days
C)3 days
D)4 days
E)5 days
Rationale: The length of cloth painted by one man in one day = 48 / 4 × 2 = 6 m
No. of days required to paint 36 m cloth by 6 men = 72/ 6 × 6 = 2 day.
B
Answer: B
Question: In a 400 member association consisting of men and women, exactly 20% of men and exactly 25 % women are homeowners. What is the least number of members who are homeowners?
Options:
A)81
B)147
C)145
D)143
E)141
Rationale: Solution simple
Out of 400 20% are male i.e 80 and 25% are female i.e 100 , so total homeowner is 180.
Now min number homeowner is 80 and max is 180 so question ask us to find least and 81 has least value among all option.
So ans is 81.
Answer : A
Answer: A
Question: A can work four times as fast as B. Together they can finish a job in 10 days. In how many days can A complete the job alone?
Options:
A)11.5
B)12.5
C)13.5
D)14.5
E)15.5
Rationale: B's rate is x and A's rate is 4x.
x + 4x = 1/10
x = 1/50
A's rate is 4x = 1/12.5
A can complete the job in 12.5 days.
The answer is B.
Answer: B
Question: On an order of 5 dozen boxes of a consumer product, a retailer receives an extra dozen free. This is equivalent to allowing him a discount of:
Options:
A)15%
B)16 1/6%
C)16 2/3%
D)20%
E)30%
Rationale: Clearly, the retailer gets 1 dozen out of 6 dozens free.
Equivalent discount = 1/6 * 100 = 16 2/3%.
ANSWER:C
Answer: C
Question: An arithemetic sequence of numbers begins p, 2p + 1, 4p + 2... What is the 14th member of this sequence?
Options:
A)A)37
B)B)40
C)+ 13
D)D)53
E)+ 13
Rationale: Common difference of an arithmetic series is constant.
2p+2-p=4p+3-2p-2
p=1
1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37
Ans:B
Answer: B
Question: Tom found a box of 220 baseball cards. Being a thoughtful older brother, he wanted to save at least 50 percent of the cards for himself and split the remaining cards evenly among his 5 younger brothers. What is the lowest possible number of cards that Tom can save for himself that will also allow each of his 5 younger brothers to get an equal number of cards?
Options:
A)110
B)112
C)116
D)118
E)122
Rationale: This question can be easily solved by looking at the options.
Assuming number of cards to be x
We need to find the option for which (1/5)*(x/2) is an integer
Or x/10 is an integer.
Hence we need the lowest multiple of 10 from the given options.
Let us start from the lowest value:
Option A: 110. This is not a multiple of 10. Hence the correct answer.
Correct Option: A
Answer: A
Question: What percentage of numbers from 1 to 60 have 1 or 9 in the unit's digit?
Options:
A)12
B)14.11
C)18.33
D)20
E)21
Rationale: Clearly, the numbers which have 1 or 9 in the unit's digit, have squares that end in the digit 1. Such numbers from 1 to 60 are 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59
Number of such number =11
ANSWER :C
Answer: C
Question: The H.C.F. of two numbers is 5 and their L.C.M. is 150. If one of the numbers is 25, then the other is:
Options:
A)30
B)28
C)24
D)20
E)35
Rationale: Product of two nos = product of HCF and LCM
Let one number = x
=> 25 * x = 5 * 150
x=5*150/25=30
ANSWER A
Answer: A
Question: The amount of an investment will double in approximately 70/ p years, where p is the percent interest, compounded annually. If Thelma invests $ 30,000 in a long-term CD that pays 5 percent interest, compounded annually, what will be the approximate total value of the investment when Thelma is ready to retire 42 years later?
Options:
A)$ 240,000
B)$ 320,000
C)$ 360,000
D)$ 450,000
E)$ 540,000
Rationale: The amount of an investment will double in approximately 70/ p years, where p is the percent interest, compounded annually. If Thelma invests $ 30,000 in a long-term CD that pays 5 percent interest, compounded annually, what will be the approximate total value of the investment when Thelma is ready to retire 42 years later?
The investment gets doubled in 70/p years. Therefore, the investment gets doubled in 70/5= every 14 years. After 42 years, the investment will get doubled 42/14= 3 times.
So the amount invested will get doubled thrice.
So, 30000 *2^3 = 240000
Hence, the answer is A.
Answer: A
Question: x, y, a, and b are positive integers. When x is divided by y, the remainder is 6. When a is divided by b, the remainder is 12. Which of the following is NOT a possible value for y + b?
Options:
A)24
B)21
C)18
D)17
E)15
Rationale: Important note: remainder is ALWAYS less than divisor, thus y>6 and b>12 --> y+b>18.
Answer: C.
Answer: C
Question: 8 men, working 8 hours a day can complete a work in 24 days. How many hours a day must 12 men work to complete the same work in 16 days?
Options:
A)6
B)7
C)8
D)9
E)10
Rationale: The number of hours required to complete the work is 8*8*24 = 1536
12 × 16 × (x) = 1536
x = 8
The answer is C.
Answer: C
Question: I. j; k; m; n; p
II. j - 10; m; m; m; p + 15
III. j + 2; k + 1; m; n - 1; p - 2
If j, k, m, n, and p are consecutive positive integers such that j < k < m < n < p, the data sets I, II, and III above are ordered from greatest standard deviation Z to least standard deviation in which of the following?
Options:
A) I, III, II
B) II, I, III
C) II, III, I
D) III, I, II
E) III, II, I
Rationale: Range of 1st Set = (p-j)
Range of 2nd Set = P+15 - j +10 = (p-j) +25
Range of 3rd Set = P -2 - j - 2 = (p-j) - 4
R2 > R1 > R3 ==> SD2 > SD1 > SD3
Since, Z=Higher the Range -> More Dispersion in the Set -> More Standard Deviation.B
Answer: B
Question: Find the remainder of 1421 x 1423 x 1425 when divided by 12
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: 1421 x 1423 x 1425 / 12
= (12*118+5)*(12*118+7)*(12*118+9)/ 12
=> rem[(5*7*9)/12]
=> rem[(35*9)/12]
=> rem[(36-1)*9/12]
=> rem[(-9)/12]
=> rem = 3
ANSWER:D
Answer: D
Question: 1000 men have provisions for 15 days. If 300 more men join them, for how many days will the provisions last now?
Options:
A)11.5
B)12.5
C)12.6
D)12.2
E)12.1
Rationale: 1000*15 = 1300*x
x = 11.5
Answer: A
Answer: A
Question: 9548 + 7314 = 3362 + (?)
Options:
A)8300
B)8400
C)13500
D)8700
E)9000
Rationale: 9548 16862 = 3362 + x
+ 7314 x = 16862 - 3362
----- = 13500
16862
-----
C)
Answer: C
Question: The distance between A&B is 450km. A person is traveling from A to B at 70km/hr started at 9AM and another person is traveling from B to A at 80km/hr and started at same time. Then at what time they meet together.?
Options:
A)A)12PM
B)B)4PM
C)C)1PM
D)D)3PM
E)E)5PM
Rationale: Let x hours be they will meet together
distance covered by 1st person+distance covered by 2nd person = 450km
70x+80x = 450
x= 3 hr
They will meet = 9AM +3hr = 12PM
Answer is A
Answer: A
Question: In how many ways can you seat 8 people on a bench if one of them, Rohit, does not want to sit on the middle seat or at either end?
Options:
A)720
B)1720
C)25200
D)5040
E)10080
Rationale: Since Rohit does not want to sit on the middle seat or at either end (3 chairs), then he can choose 5 chairs to sit. The remaining 7 people can sit in 7! ways. Thus the # of arrangements is 5*7! = 25,200.
Answer: C.
Answer: C
Question: If 3x−y=27 and 3x+y=243, then find the value of x
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: Explanation:
3x−y=27=33<=>x−y=3... (i)3x+y=243=35<=>x+y=5... (ii) adding (i) and (ii)=>2x=8=>x=4
Option D
Answer: D
Question: John, Mac and Tonny together can do a work in 20 days. John alone can do the work in 80 days and Mac alone can do the same work in 70 days. Find in what time Tonny alone can do that work?
Options:
A)50days
B)43.08days
C)53.80days
D)35days
E)44.50days
Rationale: The required answer is = 20*80*70 / 80*70-20(80+70)
= 112000/2600 = 43.08days
Answer is B
Answer: B
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
Options:
A)120 meters
B)180 meters
C)324 meters
D)150 meters
E)None of These
Rationale: Speed=(60 x(5/18)m/sec	=(50/3)m/sec.
Length of the train = (Speed x Time).
Length of the train =	((50/3)x 9)m = 150 m
D
Answer: D
Question: For any integer k greater than 1, the symbol k* denotes the product of all the fractions of the form 1/t, where t is an integer between 1 and k, inclusive. What is the value of 3*/4* ?
Options:
A)5
B)5/4
C)4/5
D)1/4
E)1/5
Rationale: When dealing with 'Symbolism' questions, it often helps to 'play with' the Symbol for a few moments before you attempt to answer the question that's asked. By understanding how the Symbol 'works', you should be able to do the latter calculations faster.
Here, we're told that K* is the PRODUCT of all the fractions of the form 1/T, where T is an integer between 1 and K, inclusive.
Based on this definition....
IF....
K = 2
K* = (1/1)(1/2) = 1/2
IF....
K = 3
K* = (1/1)(1/2)(1/3) = 1/6
We're asked to find the value of 5*/4*
Now that we know how the Symbol 'works', solving this problem shouldn't be too difficult. You can actually choose to do the math in a couple of different ways....
5* = (1/1)(1/2)(1/3)(1/4)(1/5)
Don't calculate this just yet though....since we're dividing by 4*, many of those fractions will 'cancel out.'
4* = (1/1)(1/2)(1/3)(1/4)
We're looking for the value of:
(1/1)(1/2)(1/3)(1/4)(1/5) / (1/1)(1/2)(1/3)(1/4)
Since the first four fraction in the numerator and denominator cancel out, we're left with just one fraction:
5/4
B
Answer: B
Question: The ratio of the volumes of two cubes is 27 : 125. What is the ratio of their total surface areas?
Options:
A)9 : 25
B)9 : 35
C)81 : 124
D)81 : 126
E)81 : 129
Rationale: Ratio of the sides = 3√27: 3√125 = 3 : 5
Ratio of surface areas = 3^2 : 5^2 = 9:25
Answer: Option A
Answer: A
Question: a+2b=6,ab=4
2/a + 1/b=?
Options:
A)3/2
B)5/2
C)7/2
D)9/2
E)11/2
Rationale: 2/2+1/2=1+1/2=3/2
ANSWER:A
Answer: A
Question: In a competitive examination in State ASS, 3% candidates got selected from the total appeared candidates. State BI had an equal number of candidates appeared and 5% candidates got selected with 12 more candidates got selected than ASS. What was the number of candidates appeared from each State?
Options:
A)500
B)250
C)300
D)1200
E)789
Rationale: State ASS and State BI had an equal number of candidates appeared.
In state ASS, 3% candidates got selected from the total appeared candidates
In state BI, 5% candidates got selected from the total appeared candidates
But in State BI, 12 more candidates got selected than State ASS
From these, it is clear that 1% of the total appeared candidates in State BI = 12
=> total appeared candidates in State BI = 12 x 100 = 1200
=> total appeared candidates in State ASS = total appeared candidates in State BI = 1200
Answer : D
Answer: D
Question: There are 250 female managers in a certain company. Find the total number of female employees in the company, if 2/5 of all the employees are managers and 2/5 of all male employees are managers.
Options:
A)325
B)425
C)625
D)700
E)None of these
Rationale: as per question stem 2/5M (Portion of Men employees who are managers) + 250 (Portion of Female employees who are managers) = 2/5T (Portion of Total number of employees who are managers), thus we get that 2/5M+250 = 2/5T, or 2/5(T-M)=250, from here we get that T-M=625, that would be total number of female employees and the answer (C)
Answer: C
Question: Let the function W(n) represent the product of the first n prime numbers, where n > 0. If x = W(n) + 1, which of the following must be true?
(i) x is always odd
(ii) x is always prime
(iii) x is never the square of an integer
Options:
A)ii only
B)iii only
C)i and ii only
D)i and iii only
E)ii and iii only
Rationale: W(n) is always even, because the first prime is 2 and no matter what n is, 2 always will be a divisor of W(n). Thus, W(n) + 1 = even + 1 = odd. So, (i) is always true.
Now, use logic:
If (ii) is true (so if x is always prime), then (iii) must automatically be true: no prime is the square of an integer. So, the correct answer must be i only; i, ii, and iii only; or i and iii only. since onlyi and iii onlyis among the options, then it must be true.
Or, since (i) is always true, then from options the answer must be either C or D. C cannot be correct because if (ii) is true, then so must be (iii). Thus only D remains.
Answer: D.
Answer: D
Question: What should come in place of the question mark (?) in each of the following questions ?
12 + 22 + 32 + ... + 102 = ?
Options:
A)400
B)625
C)380
D)385
E)370
Rationale: Explanation :
Sum of the squares of first 'n' natural number = n(n+l)(2n+l)/6 Put n = 10. 10x 11x21/6=55x7=385.
Answer : Option D
Answer: D