MU-NLPC/Calc-aqua_rat huggingface dataset:
Machines A and B produce bottles at their respective constant rates. Machine A produces k bottles in 3 hours and machine B produces k bottles in 5 hours. How many hours does it take machines A and B, working simultaneously, to produce 16k bottles?
Pick one: A) 24 B) 26 C) 28 D) 30 E) 32

Solution: A's rate = k/3   B's rate = k/5   k/3 + k/5 = 8k/15   16k / (8k/15) = 30 hours   The answer is 30.16  / (8 /15)= 
16  / (8 /15) = 30
30 hours   The answer is 30.
Answer: D
In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?	Select the correct option:
A) 7/8
B) 4/5
C) 3/2
D) 2/3
E) 1/3

Solution: Total number of balls = (8 + 7 + 6)= 
(8 + 7 + 6) = 21
21.   Let E= event that the ball drawn is neither red nor green   = event that the ball drawn is blue.   n(E) = 7.   P(E) =n(E)/n(S)=7/21=1/3.   Ans: 1/3
Answer: E
A rectangular floor is covered by a rug except fo a strip p meters along each of the four edges. If the floor is m meters by g meteres, What is the area of the rug in square meters?  Choose the correct choice from the following options
A) mn - p(m+n) B) mn – 2p(m+n) C) mn – p^2 D) (m - p)(n - p) E) (m - 2p)(g - 2p)

Solution: The answer must be E.   Plug in M 100   N 50   g 10.
Answer: E
The credit card and a global payment processing companies have been suffering losses for some time now. A well known company recently announced its quarterly results. According to the results, the revenue fell to $48.0 billion from $69.0 billion, a year ago. By what percent did the revenue fall?
Choose one:
A) 29.43
B) 30.43
C) 31.43
D) 32.43
E) 33.43

Solution: $69-$48=21$   (21/69)*10069- 48= 
69- 48 = 21
21$   (21/69)*100=30.434%   ANSWER:30.43
Answer: B
The closest approximation of A(69.28 × 0.004)/0.03 is Pick.
A) 0.092 B) 0.92 C) 9.2 D) 92 E) 920

Solution: A(69.28 × 0.004)/0.03   1. 0.004 = 4 × 10^(-3)   2. 0.03 = 3 × 10^(-2)   3. (a × b)/c = a × (b/c)   4. 0.004/0.03 = 4 × 10^(-3)/ (3 × 10^(-2)) = 4 × 10^( -3 - (-2))/3 = 4 × 10^(-1) / 3 = (4/3) × 10^(-1) = 1.333 × 10^(-1)   Therefore,   (69.28 × 0.004)/0.03 = 69.28 × (0.004/0.03) = 69.28 × 1.33 × 10^(-1) = 69.28 × 1.33/10 = 6.928*1.33   Now,   7 × 2 = 14   7 × 1 = 7   or better:   6.9 × 1 = 6.9   6.9 × 2 = 13.8   hence,   6.9 <6.928 × 1.33 < 13.8   9.2 is the only answer that satisfies this condition.9.2
Answer: C
97 students take part in a test and the median score is 85. Which of the following descriptions must be correct?
I.At least 49 students’ score are less than 85.
II. At least 49 students’ score are equal to or more than 85
III. At most 49 students’ score are equal to or more than 85.	Answers:
A) I  B) II  C) III  D) III  E) IIII

Solution: If we order the scores increasingly, then on the 49th place we have the score of 85. There must be 48 scores (those on the right of the 85 score) greater or equal to 85. So, I is necessarily correct.   The scores on the left of the 49th place, all have to be equal or less than 85. Since we can have the extreme case of all the scores 85, neither II, nor III is correct. The question asks for descriptions thatmustbe correct.   Answer II.
Answer: B
A certain hall contains two cuckoo clocks. If the first clock chirps 20 times per hour and the second clock chirps 9 times per hour, and both clocks chirp for the first time at 2:03 pm, at what time will the first clock have chirped three times as many times as the second clock can chirp per hour?  Select the correct option.
A) 2:42 pm  B) 2:50 pm  C) 3:07 pm  D) 3:21 pm  E) 3:30 pm

Solution: The question is asking when the first clock will have chirped 27 times (3*9 chirps).   The first clock chirps once every 3 minutes.   If the first chirp is at 2:03, then the 27th chirp is at 81 minutes after 2:00.   The answer is 3:21 pm.
Answer: D
Each factor of 200 is inscribed on its own plastic ball, and all of the balls are placed in a jar. If a ball is randomly selected from the jar, what is the probability that the ball is inscribed with a multiple of 40?
Select the correct option
A) 1/6
B) 5/42
C) 1/8
D) 3/16
E) 1/4

Solution: 200=the # of factors 200 has is=12 (see below);   so out of 12 factors only two are multiples of 40: 40 and 200, itself;   So, the probability is 2/12=1/6.   1/6nswer: 1/6.
Answer: A
The flow of water through a drainage pipe was monitored for a 3-hour period. In the second hour, the rate of flow was 24 gallons per hour, which was 50 percent faster than the rate of flow for the first hour. If 25 percent more water flowed through the pipe in the third hour than it did in the second, how many gallons of water flowed through the pipe during the entire three hours?	Choose the correct choice from the following choices
A) 61.25  B) 62.5  C) 63.75  D) 70.0  E) 77.5

Solution: Rate of flow of water in second hour = 24 gallons per hour   Rate of flow of water in first hour = 24/(3/2)= 
24/(3/2) = 16
16 gallons per hour   Rate of flow of water in third hour= (125/100)* 24 = (5/4) * 24= 
(5/4) * 24 = 30
30 gallons per hour   Number of gallons of water that flowed through the pipe during the entire 3 hours= 16+24+30= 
16+24+30 = 70
70 gallons   Answer 70.0
Answer: D
A certain country had a total annual expenditure of $1.2x10^12. If the population of the country was 240 million last year, what was the per capita expenditure?	Select the correct option:
A) $500 B) $1000 C) $2000 D) $3000 E) 5000 dollar

Solution: Explanation:   In scientific notation 240 million is 2.4x10^8. So the per capita expenditure was:   ($1.2x10^12)/(2.4x10^8)=($1.2)/(2.4)x10^12-8=$0.5x10^4=$5000   Answer: Option 5000 dollar
Answer: E
A grocer purchased a quantity of bananas at 3 pounds for $0.50 and sold the entire quantity at 4 pounds for $1.00. How many pounds did the grocer purchase if the profit from selling the bananas was $7.00? Choose the correct answer:
A) 40  B) 84  C) 90  D) 120  E) 240

Solution: Cost price of 1 pound of bananas = 0.5/3 = 1/6   Selling price of 1 pound of bananas = 1/4   Profit per pound = (1/4 - 1/6) = (1/12)   Total profit is given as 7   (1/12)*x = 7   x = 84   Answer: 84
Answer: B
The original price of a certain TV set is discounted by f percent, and the reduced price is then discounted by 2f percent. If P is the original price of the TV Set, which of the following represents the price of the television set after the two successive discounts?  Choose the correct choice from the following choices.
A) P(1 - 0.03x + 0.02x^2) B) P(1 - 0.03f + 0.0002f^2) C) P(1 - 0.03x + 0.002x^2) D) P(1 - 2x^2) E) P(1 - 3x + 2x^2)

Solution: Youcansolve this problem with number plugging.   Say the original price was $10 and f=50. Then after the first reduction the price would become $5 and after the second reduction of   2*50= 
  2*50 = 100
100% the rprice would become $0.   Now, since P is not zero, then the expression in the brackets must be zero for f=50. Only answer choice B works.   Answer: B.   On this problem - number pluggin is not giving me the answer.. I initially used f = 10, then 2f = 20 and P = 100. Answer should after both consecutive discounts = 72. I plug in the respective values and I keep getting 68. Can you double check my math.   100 (1-0.03(10) + 0.0002 (10)^2)   100 (1-0.3 + 0.0002 (100))   100 (0.7 + 0.02)   100 (0.68) = 68????   double check my math. Am I missing something? I also plugged in your numbers and still did not get zero as final answer with choice P(1 - 0.03f + 0.0002f^2)..
Answer: B
A jogger running at 9 km/hr along side a railway track is 200 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?
Pick one.
A) 32	B) 20	C) 36	D) 88	E) 34

Solution: Speed of train relative to jogger = 45 - 9= 
45 - 9 = 36
36 km/hr.= 36 * 5/18= 
36 * 5/18 = 10
10 m/sec.   Distance to be covered= 200 + 120= 
200 + 120 = 320
320 m.   Time taken= 320/10= 
320/10 = 32
32 sec.   32nswer: Option 32
Answer: A
At a conference, the only events scheduled for the day are seminars and breaks. All seminars are the same length and are 10 times as long as each break. A break must be between two consecutive seminars. If the first seminar begins at 9:00 a.m. and the third one ends at 10:40 a.m., how long will the conference last if there are a total of 6 seminars that day?  Choose the correct choice
A) hours and 15 minutes	B) hours and 20 minutes	C) hours and 25 minutes	D) hours and 30 minutes	E) hours and 35 minutes

Solution: Well its like this S B S B S B S B S B S   the interval between 9 am to 10:40 am is 160 min having 3 seminars and 2 breaks .If 1 break is of 5 min than time for 3 seminars = 160 - 2*5= 
160 - 2*5 = 150
150   Time of 1 seminar=150 /3= 
150 /3 = 50
50 min .   So calculating for 6 seminars and 5 breaks ,total time comes out to be 5 hrs and 30 min .   Answer is hours and 30 minutes.
Answer: D
If Sn is the sum of the first n terms of a certain sequence and if Sn = n(n+6) for all positive integers n, what is the third term of the sequence?  Choose the correct option
A) 10	B) 4	C) 6	D) 8	E) 9

Solution: Tn = nth term   T1 = 1st term   T2 = 2nd term   and so on...   Sn = Sum of first n terms of the sequence   Sn = 1st term + 2nd term + 3rd term + ... + nth term   Sn = T1 + T2 + T3 + ....Tn   You are given here thatSn is the SUM of first n terms...So you have   Sn = T1 + T2 + T3 + ....Tn = n(n+1)   So S1 = T1   S2 = T1 + T2   S3 = T1 + T2 + T3   and so on   S1 = T1 = 1*(1+1)= 
1*(1+1) = 2
2   S2= T1 + T2 = 2 + T2 = 2*(2+1)= 
2*(2+1) = 6
6   So T2= 4   S3 = T1 + T2 + T3 = 2 + 4 + T3 = 3*(3+1)= 
3*(3+1) = 12
12   So T3= 10   (This is what we wanted)   The third term is 10.   10
Answer: A
A certain university will select 2 of 5 candidates eligible to fill a position in the mathematics department and 3 of 8 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?
Answers.
A) 42  B) 70  C) 540  D) 565  E) 560

Solution: 5C2*8C3 = 10*56= 
10*56 = 560
560   the answer is (560)
Answer: E
A train moves fast a telegraph post and a bridge 264 m long in 8 sec and 20 sec respectively. What is the speed of the train?  Choose the correct choice from the following answers:
A) 45
B) 46
C) 47
D) 79.2
E) 76

Solution: Let the length of the train be x m and its speed be y m/sec.   Then, x/y = 8 => x = 8y   (x + 264)/20 = y   y = 22   Speed = 22 m/sec = 22 * 18/5= 
22 * 18/5 = 396/5 = around 79.2
79.2 km/hr.   Answer: Option 79.2
Answer: D
A train is 360 meter long is running at a speed of 48 km/hour. In what time will it pass a bridge of 140
meter length.  Choose the correct choice:	A) 27.5 seconds	B) 37.5 seconds	C) 47.5 seconds	D) 57.5 seconds	E) None of these

Solution: Explanation:   Speed = 48 Km/hr = 48*(5/18) m/sec   = 40/3 m/sec   Total distance = 360+140= 
360+140 = 500
500 meter   Time= Distance/speed   =500/40/3 = 37.5 seconds   Answer: 37.5 seconds
Answer: B
In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?	Choose the correct choice:
A) 200	B) 205	C) 209	D) 250	E) 300

Solution: =>1 boy 3 girls or 2 boys 2 girls or 3 boys 1 girl or 4 boys   => (62091 x 42093) + (62092 x 42092) + (62093 x 42091) + (62094)=> 24+90+80+15= 
24+90+80+15 = 209
>209   ANSWER 209
Answer: C
In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together ?	Choose the correct choice from the following answers:
A) 58300	B) 60800	C) 55600	D) 50400	E) 45200

Solution: In the word 'CORPORATION', we treat the two vowels OOAIO as one letter. Thus,we have CRPRTN (OOAIO)   This has 7 letters of which R occurs 2 times and the rest are different.   Number of ways of arranging these letters= 7!/(2!)=2520.   Now 5 vowels in which O occurs 3 times and the rest are different, can be arranged in 5!/3!=20 ways.   Required number of ways =(2520*20)= 
(2520*20) = 50_400
50400.   Answer is 50400
Answer: D
An 11-meter long wire is cut into two pieces. If the longer piece is then used to form a perimeter of a square, what is the probability that the area of the square will be more than 4 if the original wire was cut at an arbitrary point?
Choose the correct choice from the following choices
A) 3/7  B) 5/8  C) 3/10  D) 5/11  E) 6/11

Solution: The longer wire will form a square with an area more than 4 if the wire is cut at a point within three meters of either end. The probability of this is 6/11.   The answer is 6/11.
Answer: E
Krishna bought some wheat at Rs. 10 per kilogram. He buys 2 kg wheat from a ration shop at the rate of Rs. 8 per kilogram. He mixes the two and sells at Rs. 11 per kilogram. He makes 25% profit. What is the ratio of non-ration to ration wheat?
Select:
A) 1:4
B) 1:5
C) 5:1
D) 2:5
E) None of the above

Solution: As the profit is 25% and the selling price is 11, the cost price is 8.8.   Now, to find the ratio between the amount of non-ration and ration rice, we have to find the ratio of (Cost price - Ration price) and (Non-ration price - Cost price)   The required ratio is (8.8-8) : (10- 8.8)   The required ratio is 2:3   ANSWNone of the aboveR:None of the above
Answer: E
20 litres of water are poured into an aquarium of dimensions 50cm length, 20cm breadth, and 40cm height. How high (in cm) will the water rise?
(1 litre = 1000cm³) Pick one:
A) 6	B) 8	C) 10	D) 20	E) 40

Solution: lXbXh= 12000   h= 20000/50*20= 20 cm   '20' is the answer.
Answer: D
A cistern 8m long and 4 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is:
Select the correct option.
A) 62 m2	B) 50 m2	C) 53.5 m2	D) 55 m2	E) 57 m2

Solution: Area of the wet surface	= [2(lb + bh + lh) - lb]   = 2(bh + lh) + lb   = [2 (4 x 1.25 + 8 x 1.25) + 8 x 4] m2   = 62 m2.   62 m2nswer: Option 62 m2
Answer: A
Arrange the words given below in a meaningful sequence.
1. Poverty 2. Population 3. Death 4. Unemployment 5. Disease	Select the correct option:
A) 2, 4, 1, 5, 8	B) 2, 4, 1, 5, 7	C) 2, 4, 1, 5, 3	D) 2, 4, 1, 5, 9	E) 2, 4, 7, 5, 3

Solution: Answer: 2, 4, 1, 5, 3) 2, 4, 1, 5, 3   Explanation:   The correct order is :   Population Unemployment Poverty Disease Death   2 4 1 5 3   Answer:2, 4, 1, 5, 3
Answer: C
What is the least number which when doubled will be exactly divisible by 12, 14, 18 and 22 ? Choose the correct answer: A) 1286 B) 1436 C) 1216 D) 1386 E) 1298

Solution: LCM of 12, 14, 18 and 22 = 2772   Hence the least number which will be exactly divisible by 12, 14, 18 and 22 = 2772   2772 ÷ 2 = 1386   1386 is the number which when doubled, we get 2772 Answer: Option 1386   Hence, 1386 is the least number which when doubled will be exactly divisible by 12, 14, 18 and 22.
Answer: D
A space shuttle orbits the earth at about 9 kilometers per second. This speed is equal to how many kilometers per hour?  Choose the correct choice from the following options
A) 480	B) 2,880	C) 4,800	D) 28,800	E) 32,400

Solution: Seconds in 1 hours:   60s in 1 min   60 min in 1 hr   60*60= 
60*60 = 3_600
3600 sec in 1 hr   9*3600=32,400   Answer: 32,400
Answer: E
The average monthly salary of laborers and supervisors in a factory is Rs.1250 per month; where as the average monthly salary of 6 supervisors is Rs.2450. If the average monthly salary of the laborers is Rs.950 find the number of laborers?  Choose the correct choice from the following answers:
A) 22
B) 42
C) 44
D) 55
E) 77

Solution: 5x 6x 2x   50 25 100   250x + 150x + 200x = 4200   600x = 4200   x = 7 => 6x = 42   Answer: 42
Answer: B
Running at their respective constant rates, machine X takes 2 days longer to produce w widgets than machine Y. At these rates, if the two machines together produce 5/4 w widgets in 3 days, how many days would it take machine X alone to produce 3w widgets?	Options:
A) 4
B) 6
C) 18
D) 10
E) 12

Solution: Let Y produce w widgets in y Days   Hence, in 1 day Y will produce w/y widgets.   Also, X will produce w widgets in y+2 days (given, X takes two more days)   Hence, in 1 day X will produce w/y+2 widgets.   Hence together X and Y in 1 day will produce {w/y + w/y+2} widgets.   Together X and Y in 3 days will produce = 3 * [{w/y + w/y+2}] widgets.   It is given that in 3 days together they produce (5/4)w widgets.   Equating, 3 * [{w/y + w/y+2}] = (5/4)w   Take out w common and move 3 to denominator of RHS   w{1/y + 1/(y+2)} = (5/12)w   Canceling w from both sides   {1/y + 1/(y+2)} = 5/12   2y+2/y(y+2) = 5/12   24y+24=5y^2 + 10y   5y^2-14y-24=0   5y^2-20y+6y-24=0   5y(y-4)+6(y-4)=0   (5y+6)+(y-4)=0   y=-6/5 or y=4   Discarding y=-6/5 as no of days cannot be negative   y=4   hence it takes Y, 4 days to produce w widgets.   Therefore, it will take X  (4+2)= 
 (4+2) = 6
6 days to produce w widgets.   Hence it will take X 3*6= 
3*6 = 18
18 days to produce 3w widgets.   Answer : 18
Answer: C
How many different possible arrangements X can be obtained from the letters G, M, A, T, I, I, and T, such that there is at least one character between both I's?  Choose the most appropriate option.
A) 360  B) 720  C) 900  D) 1800  E) 5040

Solution: Total ways for arranging without restriction = 7!/ (2!2!) { 2! is becoz of two T's and other 2! for two I's)   Restriction : atleast one character between I's = Possible ways - both I's together i.e.o character between I's   _ _ _ _ _ (I I)   Both I's Together = 6! (Assuming 2 I's as one unit) /2!(for 2 T's) * 2! (No of arrangements of 2 I's)/2! (for 2 I's)   =6!/2!   Therefore ans X= 7!/ (2!2!) -6!/2! = 900   HEN900E 900.
Answer: C
Average age of 18 men is decreased by 1 year when one man whose age is 49 years is replaced by a new man. Find age of the new man
Pick one
A) 31
B) 77
C) 88
D) 29
E) 22

Solution: Explanation:   If the replaced persons age is same with the existing average, there is no change in the average. But by replacement overall decrease in the age is 18 × 1 = 18 years. This is the change bought by the new man.   31ge of new man = 31ge of man replaced - Total decrease in age   = 49 - (1 × 18) = 31 years   \   31nswer:31
Answer: A
If a:b=2:5, b:c=3:7 and c:d=1:3 find a:b:c:d?  Options:  A) 6:15:25:115  B) 6:15:35:115  C) 6:15:35:105  D) 6:15:35:125  E) None of these

Solution: Explanation:   a:b = 2:5, b:c = 3:7, c:d = 1:3   2:5   3:7   ( a = 2 × 3 = 6, b = 5 × 3 = 15 and c = 5 × 7 = 35)   (a = a × b, b= b × b and c= b × c)   a:b:c = 6 : 15 : 35   a:b:c = 6 : 15 : 35 and c:d = 1 : 3   (Note: First a,b,c multiplication with c means 1 and last c means 35   multiplication with d means 3   a:b:c:d = 6:15:35:105   Answer: Option 6:15:35:105
Answer: C
How many 5 digit number contain number 3 ?	Choose the correct option
A) 31512 B) 32512 C) 33512 D) 34512 E) 37512

Solution: total 5 digit no. = 9*10*10*10* 10= 
9*10*10*10* 10 = 90_000
90000   not containing 3= 8*9*9*9*9= 
8*9*9*9*9 = 52_488
52488   total 5 digit number contain 3= 90000 - 52488= 
90000 - 52488 = 37_512
37512   ANSW37512R:37512
Answer: E
Which of the following is equal to 1(1/7)%?
Choose the correct option
A) 0.012/100	B) 0.12/100	C) 1.14/100	D) 12/100	E) 12/10

Solution: This notation may be confusing for some, since it looks like we're multiplying 1 and 1/7   How about adding a space:Which of the following is equal to (1 1/7)%   (1 1/7)% = 1.14% = 1.14/100   Answer:   1.14/100
Answer: C
In a college of 525 students, each student takes at least 2 items from among idly, dosa, puri, and chapati for his breakfast. If 375 students take idly, 375 take dosa, 375 students take puri nad 375 students take chapati for their breakfast, the number of students who take all the four items is at most ?
Select the correct option.
A) 275
B) 300
C) 225
D) 325
E) None of these

Solution: Explanation :   Let y students take all four items. Now, y is maximised when all students take either two or exactly four items each (i.e. no student take either three items). Total number of instances = 375 x 4 = 1500, of which 525 x 2 i.e. 1050 are accounted for by all students taking two items each.   Now let y studetns take lla four items (i.e. 2 items more than the initial assumption of 2 items each)   Then 1050 + 2y = 1500 => y = 225   Hence, at most 225 students can take all four items.   Answer : 225
Answer: C
Incomes of two companies A and B are in the ratio of 5 : 8. Had the income of company A been more by 30 lakh, the ratio of their incomes would have been 5 : 4. What is the income of company B?	Choices.
A) 80 lakh  B) 50 lakh  C) 48 lakh  D) 60 lakh  E) None of these

Solution: Let the incomes of two companies A and B be 5x and 8x respectively.   From the question,   5x+30/8x=5/4 ⇒ 20x + 120 = 40x   ∴ x = 6   ∴ Income of company B = 8x = 48 lakh   Answer 48 lakh
Answer: C
How many positive integers less than 5,000 are there in which the sum of the digits equals 5?  Answers.
A) 64
B) 62
C) 63
D) 61
E) 56

Solution: Basically, the question asks how many 4 digit numbers (including those in the form 0XXX, 00XX, and 000X) have digits which add up to 5. Think about the question this way: we know that there is a total of 5 to be spread among the 4 digits, we just have to determine the number of ways it can be spread.   Let X represent a sum of 1, and | represent a seperator between two digits. As a result, we will have 5 X's (digits add up to the 5), and 3 |'s (3 digit seperators).   So, for example:   XX|X|X|X = 2111   ||XXX|XX = 0032   etc.   There are 8C3 ways to determine where to place the separators. Hence, the answer is 8C3 = 56.   56
Answer: E
A man's speed with the current is 17.5 km / hr and the speed of the current is3.5 km / hr. The man's speed against the current is  Choose the correct choice from the following answers:  A) 8.5 km / hr  B) 9 km / hr  C) 10 km / hr  D) 11.5 km / hr  E) None

Solution: Sol.   Man's rate in still in water = (17.5 - 3.5) km / hr = 14 km / hr.   Man's rate against the current = (14 - 3.5) km / hr = 11.5 km / hr.   Answer 11.5 km / hr
Answer: D
Four female friends & four male friends will be pictured in a advertising photo. If the photographer wants to line them up in one row, with men & women alternating. How many possible arrangements may she chose?  Choose the correct choice from the following answers.
A) 40320
B) 1680
C) 1152
D) 576
E) 70

Solution: now any of the alternate 4 places can be filled by 4 male or female in 4!   similarly,   other 4 alternate places can be filled in 4!   hence required probability= 2*4!*4!=1152   hence 1152
Answer: C
In each series, look for the degree and direction of change between the numbers. In other words, do the numbers increase or decrease, and by how much?Look at this series: 95, 10, 75, 20, 55, ... What number should come next? Choose the correct answer
A) 35	B) 40	C) 30	D) 25	E) 90

Solution: C30This is an alternating addition and subtraction series. In the first pattern, 20 is subtracted from each number to arrive at the next. In the second, 10 is added to each number to arrive at the next.
Answer: C
The average of first 35 prime numbers is?	Choose the correct choice from the following.
A) 14.54	B) 15.6	C) 15.8	D) 14.7	E) 14.8

Solution: Explanation:   14.54verage = (2+3+5+7+11+13+17+19+23+29+31)/11= 160/11= 14.54(14.54pprox)   14.54nswer is 14.54
Answer: A
Ben bought 2Q steaks for W dollars. Jerome buys R steaks for a 50% discount, how much will the steaks cost him in cents?	Pick:  A) 50RW/Q.  B) 50QR/W.  C) 25RQ/W.  D) 25RW/Q.  E) RW/(4Q).

Solution: Ben bought 2Q steaks for W dollars, so 1 steak = W/2Q   Jerome buys R steaks for a 50% discount: r* (W/4Q)   in cents the answer will be : r* (100 W/4Q)= 25 RW/Q= 25RW/Q.
Answer: D
calculate the profit loss percentage if a trader bought 7 balloons per rupee and sells the balloons at 6 per rupee.	Choose the correct choice from the following choices: A) 13.7 % B) 12.7 % C) 15.3 % D) 16.7 % E) 13.7 %

Solution: Let he total number of oranges bought by the shopkeeper be 12.   If he buys 7 a rupee, his CP =6   He selling at 6 a rupee, his SP = 7   Profit = SP - CP = 7 - 6= 
7 - 6 = 1
1   Profit Percent= 1/6 * 100 = 16.7 %   Answer: 16.7 %
Answer: D