MU-NLPC/Calc-aqua_rat huggingface dataset:
A committee is composed of w women and m men. If 3 women and 4 men are added to the committee, and if one person is selected at random from the enlarged committee, then the probability that a woman is selected can be represented by  Choose the correct choice from the following choices.
A) w/m  B) w/(w+m)  C) (w+3)/(m+4)  D) (w+3)/(w+m+3)  E) (w+3)/(w+m+7)

Solution: The number of women is w+3.   The total number of people is w+m+7.   P(a woman is selected) = (w+3) / (w+m+7)   The answer is (w+3)/(w+m+7).
Answer: E
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 2 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?
Pick
A) 10.5 B) 15 C) 25.5 D) 30 E) 23.5

Solution: The time it takes Darcy to walk to work is (1.5/3)*60= 
(1.5/3)*60 = 30
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 + 2   x=23.5 minutes   Answer: 23.5
Answer: E
What is the least possible product of 4 different integers, each of which has a value between –3 and 10, inclusive? Select the correct option
A) –5040  B) –3600  C) –2160  D) –600  E) –120

Solution: Maximize the total product with a -ve sign   so -3 * 10 * 9 * 8 = 720 * -3 = -2160   Answer is –2160.
Answer: C
P is a prime number. If 6p is between 15 and 95, which of the following can be a value of 7p + 2?
Choices
A) 15  B) 79  C) 121  D) 65  E) 21

Solution: We see that the format we are looking for is 7p + 2.   When you subtract 2 from option A, you get 13 - not a multiple of 7. Ignore.   When you subtract 2 from option B, you get 77. It is a multiple of 7. Let's check it. p = 11 which is prime. Good. 6p = 66 which is between 15 and 95. Very good.   ANSWER:65
Answer: D
Shekhar started a business investing Rs.25,000 in 1999.In 2000,he invested an additional amount of Rs.10,000 and Rajeev joined him with an amount of Rs.35,000.In 2001,Shekhar invested another additional amount of Rs.10,000 and Jatin joined them with an amount of Rs.35,000.What will be Rajeev’s share in the profit of Rs.2,70,000 earned at the end of 3 years from the start of the business in 1999 ?  Choose the correct choice from the following:
A) Rs.45,000 B) Rs.50,000 C) Rs.90,000 D) Rs.75,000 E) None of these

Solution: Solution   Shekhar : Rajeev : Jatin   = (25000x12+35000x12+45000x12) :(35000x24) : (35000x12)   = 1260000 : 840000 : 420000 = 3 : 2 : 1.   ∴ Rajeev’s share = Rs.(27000x2/6) = Rs. 90,000. Answer Rs.90,000
Answer: C
The speed of a boat in upstream is 90 kmph and the speed of the boat downstream is 190 kmph. Find the speed of the boat in still water and the speed of the stream?	Choose the correct choice from the following options
A) 10 kmph	B) 76 kmph	C) 12 kmph	D) 97 kmph	E) 50 kmph

Solution: Speed of the boat in still water   = (90+190)/2= 
(90+190)/2 = 140
140 kmph. Speed of the stream= (190-90)/2= 
(190-90)/2 = 50
50 kmph.   Answer:50 kmph
Answer: E
Arun purchased 30 kg of wheat at the rate of Rs. 11.50 per kg and 20 kg of wheat at the rate of 14.25 per kg. He mixed the two and sold the mixture. Approximately what price per kg should be sell the mixture to make 15% profit? Choose the correct choice from the following options: A) 14.49 B) 16.33 C) 16.35 D) 16.3 E) 16.32

Solution: C.P. of 50 kg wheat = (30 * 11.50 + 20 * 14.25) = Rs. 630.   S.P. of 50 kg wheat = 115% of Rs. 630 = 115/100 * 630 = Rs. 724.5   S.P. per kg = 724.5/50= 
724.5/50 = 14.49
14.49   14.49
Answer: A
Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:
Select the correct option.
A) 3/9
B) 3/2
C) 3/1
D) 3/7
E) 3/4

Solution: Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train   = 27 x meters, and length of the second train = 17 y meters. (27 x + 17 y) / (x + y) = 23   ==> 27 x + 17 y = 23 x + 23 y ==> 4 x   = 6 y ==> x/y = 3/2.   Answer:3/2
Answer: B
The probability of picking 2 red balls one after another without replacement from a bag containing only red and white balls is 14/33. What will be the probability of picking 2 white balls one after another w/o replacement from that bag, given that it can hold at the most 20 balls?	Pick.
A) 1/33	B) 3/33	C) 5/33	D) 9/33	E) 19/33

Solution: Probability of picking 2 red balls = 14/33   (R/R+W)*(R-1)/(R+W-1) = 14/33 = (2*7)/(3*11) = (2/3)*(7/11) --> Once the value is reduced to this level, it should be easy to find out the number of red balls.   1) Considering the above expression, both numerator and denominator must be consecutive.   2) Lets multiply both numerator and denominator with the same integer so that the value remains unaffected.   3) We can't multiply 7/11 as we need a consecutive term in both numerator and denominator. So lets multiply (2/3) to make the numerator and denominator consecutive.   (2/3)*(2/2) = 4/6 --> 4*7/6*11 --> Numerator and denominator not consecutive   (2/3)*(3/3) = 6/9 --> 6*7/9*11 --> Only numerator is consecutive   (2/3)*(4/4) = 8/12 --> 8*7/12*11 --> Numerator and denominator are consecutive here   Number of red balls, R = 8.   Total number of balls, R + W = 12 (This value is < 20, satisfying the condition)   Number of white balls, W = 12 - 8= 
12 - 8 = 4
4   Probability of picking 2 white balls w/o replacement= (W/R+W)*(W-1)/(R+W-1) = (4/12)*(3/11) = 3/33   Answer: 3/33
Answer: B
Worker W produces n units in 5 hours. Workers V and W, workers independently but at thesame time, produce n units in 2 hours.how long would it take V alone to produce n units?	Choose the correct choice from the following:
A) 1 hr 26 min  B) 1 hr 53 min  C) 2 hr 30 min  D) 3 hr 30 min  E) 3 hr 20 min

Solution: V and W produce n units in 2 hours. So they produce n/2 units in 1 hour.   W produces n units in 5 hrs. So he alone produce n/5 units in 1 hr.   So V produces in 1 hr. = n/2 - n/5 = 3 n/10 units.   V produces n units in 10/3 hrs. which is 3 hrs 20 min.   ANSW3 hr 20 minR:3 hr 20 min
Answer: E
The average of 11 results is 50, if the average of first five results is 49 and that of the last seven is 52. Find the fifth result?  Options:
A) 55
B) 56
C) 57
D) 58
E) 59

Solution: 1 to 11 = 11 * 50= 
11 * 50 = 550
550   1 to 5= 5 * 49= 
5 * 49 = 245
245   5 to 11= 7 * 52= 
7 * 52 = 364
364   5th= 245 + 364 – 550 = 59   ANSW59R:59
Answer: E
Find the rank of the word GOOGLE if all the words which can be formed by permuting letters of this word without repitition are arranged in dictionary in alphabetical order???
Choose one:
A) 86 B) 67 C) 88 D) 89 E) 69

Solution: EGGLOO arranging in alphabetiaccal order   E - - - - - 5!/(2!*2!)=30   GE- - - - 4!/2!=12 30+12=42   GG- - - - 4!/2!=12 42+12=54   GL- - - - 4!/2!=12 54+12=66   GOE - - - 3!=6 66+6=72   GOG- - - 3!=6 72+6=78   GOL- - - 3!=6 78+6=84   GOOE - - 2= 
 - - 2 = 2
2 84+2=86   GOOGE - 1!=1 86+1=87   GOOGLE 1!=1 87+1=88   So, 88 th no, is GOOGLE   ANSWER:88
Answer: C
The surface of a cube is 54sq cm. Find its volume?	Choices: A) 8cc B) 27cc C) 2cc D) 4cc E) 6cc

Solution: 6a2 = 54 = 6*9   a = 3 => a3 = 27cc   Answer: 27cc
Answer: B
A firm has 3 senior partners and 5 junior partners. How many different groups of 3 partners can be formed in which at least one member of the group is a senior partner? (Note that two groups are considered different if at least one group member is different.) Choices
A) 42	B) 46	C) 50	D) 54	E) 58

Solution: The number of ways to form a group of 3 is 8C3 = 56   The number of groups with no senior partner is 5C3 = 10   The number of groups with at least one senior partner is 56-10= 
56-10 = 46
46   The answer is 46.
Answer: B
Fresh grapes contain 75% by weight while dried grapes contain 25% water by weight. What is the weight of dry grapes available from 200 kg of fresh grapes? Pick one:
A) 40.00 kg B) 45.50 kg C) 66.67 kg D) 80.56 kg E) 90.00 kg

Solution: From the question we know: 200kg * 75% = 150kg of water in the fresh grapes   200kg - 150kg of water = 50kg of non-water mass   We are looking for the weight of the dry grapes (X).   Since the question tells us that 25% of the weight of the dry graps is water and we know that 50kg is non-water mass we can set up the following equation:   X = 1/4(X) + 50kg   3/4(X) = 50kg   X = 66.67 kg   Answer- 66.67 kg
Answer: C
A woman has five blouses of different colors, three skirts of different colors, and two different pairs of shoes. She refuses to wear her pink blouse with her green skirt. How many different blouseskirt-shoe combinations could she wear?  Pick
A) 8	B) 12	C) 28	D) 17	E) 18

Solution: total ways = 5*3*2=30..   now its better to find the ways in which the pink blouse and green skirt are together and subtract from total to get the answer..   the ways in which the pink blouse and green skirt are together=1*1*2=2..   total ways =30-2=28..   ANSWER:28
Answer: C
The value of 0.1 x 0.1 x 0.1 + 0.02 x 0.02 x 0.02/ 0.2 x 0.2 x 0.2 + 0.04 x 0.04 x 0.04	is:  Choices:
A) 0.125 B) 0.135 C) 0.145 D) 0.155 E) 0.165

Solution: Given expression   =(0.1)(power 3) + (0.02)(power 3) /2(power 3) [(0.1)(power 3) + (0.02)(power 3)]   =1/8= 
1/8 = 1/8 = around 0.125
0.125   0.125nswer is 0.125
Answer: A
A man standing at a point P is watching the top of a tower, which makes an angle of elevation of 30° with the man’s eye. The man walks some distance towards the tower to watch its top and the angle of the elevation becomes 60°. What is the distance between the base of the tower and the point P?	Select the correct option.
A) 4 units B) 8 units C) 12 units D) Data inadequate E) None of these

Solution: Explanation:   One of AB, AD and CD must have been given.So, the data is inadequate.   Answer: Data inadequate
Answer: D
The sum of the fourth and twelfth term of an arithmetic progression is 20. What is the sum of the first 10 terms of the arithmetic progression?
Choose the correct choice from the following answers:  A) 300  B) 100  C) 150  D) 170  E) 270

Solution: n th term of A.P. is given by a+(n-1)d   4 th term = a+3d   12 th term = a+11d   Given a+3d+a+11d=20 --> 2a+14d=20 --> a+7d = 10   Sum of n term of A.P = n/2[2a+(n-1)d]   subsitiuing n = 10 ...we get 10/2[ 2a + 14d] = 10 [a+7d] = 10*10 = 100...   Answer is 100...
Answer: B
In a division sum, the divisor is 10 times the quotient and 5 times the remainder. If the remainder is 46, the divident is Choose the correct choice from the following answers:
A) 4236
B) 4306
C) 4336
D) 5336
E) None

Solution: Solution   Divisor	= (5×46)   = 230.   Also. 10×Q	= 230   ‹=› Q=23.   And, R= 46.   Dividend	= (230×23+46)   = 5336.   Answer 5336
Answer: D
A line that passes through (–1, –4) and (3, k) has a slope = k. What is the value of k?  Choose the correct answer.
A) 3/4
B) 1
C) 4/3
D) 2
E) 7/2

Solution: This is a considerably more difficult one, which will involve some algebra. Let’s say that the “first” point is (–1, –4) and the “second,” (3, k). The rise = k + 4, which involves a variable. The run = 3 – (–1) = 4. There the slope is (k + 4)/4, and we can set this equal to k and solve for k.   {{k + 4}/4} = k   k + 4= 
+ 4 = 4
4k   4= 3k   k = 4/3   Answer = 4/3
Answer: C
If the function f(x) is defined for all real numbers x as the maximum value of 4x + 4 and 12 + 3x, then for which one of the following values of x will f(x) actually equal 4x + 4 ?  Choices:
A) 4
B) 5
C) 6
D) 7
E) 9

Solution: Since f(x) defines maximum of 4x + 4 and 12 + 3x,   to find those x when 4x+4 has greater value,   4x + 4 > 12 + 3x   or x < 8   Only value that satisfy this is 7.   Answer is (7),
Answer: D
A train 250 m long is running at a speed of 58 kmph. How long does it take to pass a man who is running at 8 kmph in the same direction as the train?	Select the correct option:
A) 5 sec B) 9 sec C) 12 sec D) 18 sec E) 15 sec

Solution: Answer : D.   Speed of the train relative to man = (58 - 8) kmph   = (50* 5/18) m/sec = (125/9)m/sec   Time taken by the train to cross the man   = Time taken by It to cover 250 m at 125/9 m / sec = 250 *9/ 125= 
250 *9/ 125 = 18
18sec
Answer: D
A is a working and B is sleeping partners in a business. A puts in Rs. 5000 and B puts in Rs.6000. A receives % of the profit for managing the business and the rest is divided in proportion to their capital. What does each get out of a profit of Rs. 880?
Choose the correct answer.
A) 770 B) 266 C) 297 D) 260 E) 277

Solution: Total profit = Rs. 880   A's share for managing the business i.e   \inline 12\frac{1}{2} % = \inline \frac{25\times 880}{200}=Rs.110   Remaining profit of A and B as per their capital = 880 - 110 = Rs. 770   Ratio of amounts = 5000 : 6000 = 5 : 6   Sum of ratios = 5 + 6= 
5 + 6 = 11
11   A's share= \inline 770\times \frac{5}{11}= Rs.350   A's total share = 350 + 110 = Rs. 460   B's share = \inline 770\times \frac{6}{11}=Rs.420   770nswer:770
Answer: A
Ten cards numbered 1 to 10 are placed in a box, mixed up thoroughly and then one card is drawn
randomly. If it is known that the number on the drawn card is more than 3, what is the probability
that it is an even number?  Choose the correct choice from the following choices
A) 1/3 B) 1/5 C) 4/7 D) 3/5 E) 4/9

Solution: Let A be the event ‘the number on the card drawn is even’ and B be the   event ‘the number on the card drawn is greater than 3’. We have to find P(A|B).   Now, the sample space of the experiment is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}   Then A = {2, 4, 6, 8, 10}, B = {4, 5, 6, 7, 8, 9, 10}   and A n B = {4, 6, 8, 10}   Also P(A) = 5/2, P(B) = 7/10 and P(A n B) = 4/10   Then P(A|B) = P(A n B)/P(B) = (4/10)/(7/10)	= 4/7   4/7)
Answer: C
A contract is to be completed in 56 days if 104 persons work, each working at 8 hours a day. After 30 days, 2/5 of the work is completed. How many additional persons should be deployed so that the work will be completed in the scheduled time, each person’s now working 9 hours a day.	Choose the correct choice
A) 160	B) 150	C) 24	D) 56	E) 75

Solution: Explanation:   Persons worked = 104   Number of hours each person worked per day = 8   Number of days they worked = 30   Work completed =25   Remaining days = 56 - 30= 
56 - 30 = 26
26   Remaining Work to be completed=1−2/5=3/5   Let the total number of persons who do the remaining work =x   Number of hours each person needs to be work per day = 9   More days, less persons (indirect proportion)   More hours, less persons (indirect proportion)   More work, more persons (direct proportion)   Hence we can write as   (days)30:26   (hours)8:9   (work)35:25 }::x:104   ⇒30×8×35×104 =26×9×2/5 × x   ⇒x=30×8×3/5×104/26×9×2/5   =30×8×3×104/26×9×2   =30×8×104/26×3×2   =30×8×4/3×2   =5×8×4=160   Number of additional persons required = 160 - 104= 
160 - 104 = 56
56   Answer: Option 56
Answer: D
A Ball is dropped from 8 m height.it rebounds to half the height when it hits the ground. What is the distance travelled by the ball before it hits the ground?	Pick one:
A) 20m
B) 21m
C) 22m
D) 24m
E) 28m

Solution: distance travelled by the ball before coming to rest = 8+4+4+2+2+1+1+(1/2)+(1/2)+(1/4)+(1/4)+...upto infinity   =8+2*[4+2+1+(1/2)+(1/4)+...]   =8+2*[4/(1-1/2)]   =8+2*8= 
8+2*8 = 24
24 m   ANSWER:24m
Answer: D
Raviraj invested an amount of 1000000000 at compound interest rate of 10 pcpa for a period of three years. How much amount will Raviraj get after three years? Choose the correct choice from the following answers
A) 12,310000	B) 13,210	C) 13,3200000	D) 13,120	E) 1331000000

Solution: Amount = 1000000000(1 + 10⁄100)3   = 1000000000 × 11⁄10 × 11⁄10 × 11⁄10   = 1331000000   Answer 1331000000
Answer: E
If at least 150 dollar is to be divided equally among 12 beneficiaries, how much more the donor needs to add to his dollar balance in order to meet the equal distribution criteria. Pick one.
A) 5
B) 6
C) 7
D) 8
E) 9

Solution: The donor when left with 150 dollar can either distribute either 12 dollar (12x12=144) or 13 dollar (13x12=156) meeting criteria of equal distribution. As the donor has to distribute at least 150 dollar, he or she needs to add 6 dollar more to the balance. Answer: 6
Answer: B
What number would replace the question mark in this quite difficult number sequence ?
21 32 54 87 131 ?  Choose the correct choice from the following answers
A) 300	B) 125	C) 450	D) 340	E) 186

Solution: 186   186   186xplanation :   21+11*1= 
21+11*1 = 32
> 32   32+11*2= 
32+11*2 = 54
> 54   54+11*3= 
54+11*3 = 87
> 87   87+11*4= 
87+11*4 = 131
> 131   131+11*5= 
131+11*5 = 186
> 186
Answer: E
A car started running at a speed of 30 km/hr and the speed of the car was increased by 2 km/hr at the end of every hour. Find the total distance covered by the car in the first 10 hours of the journey.	Choose the correct choice from the following options.
A) 390 km
B) 340 km
C) 380 km
D) 360 km
E) 320 km

Solution: 390 km   390 km   The total distance covered by the car in the first 10 hours = 30 + 32 + 34 + 36 + 38 + 40 + 42 + 44 + 46 + 48 = sum of 10 terms in 390 kmP whose first term is 30 and last term is 48 = 10/2 [30 + 48] = 390 km
Answer: A
In a sports club with 30 members, 17 play badminton and 19 play tennis and 2 do not play either. How many members play both badminton and tennis?	Choose the most appropriate option.
A) 3 B) 5 C) 6 D) 7 E) 8

Solution: 17+19= 
17+19 = 36
36   but where as total number is   30-2= 
  30-2 = 28
28   therefore answer is   36-28= 
  36-28 = 8
8   Hence Answer is 8
Answer: E
A basket has 5 apples and 4 oranges. Three fruits are picked at random. The probability that at least 2 apples are picked is?	Pick
A) 25/42 B) 25/47 C) 25/17 D) 25/19 E) 25/98

Solution: Total fruits = 9   Since there must be at least two apples,   (⁵C₂ * ⁴C₁)/⁹C₃ + ⁵C₃/⁹C₃   = 25/42.   25/42nswer: 25/42
Answer: A
If two projectiles are launched at the same moment from 1386 km apart and travel directly towards each other at 445 km per hour and 545 km per hour respectively, how many minutes will it take for them to meet?	Choose the correct answer
A) 80  B) 82  C) 84  D) 86  E) 88

Solution: The projectiles travel a total of 990 km per hour.   The time to meet is   1386/990= 
  1386/990 = 7/5 = around 1.4
1.4 hours= 84 minutes   The answer is 84.
Answer: C
Two trains are running at 40km/hr and 20km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 5 seconds. What is the length of the fast train?	Choose the correct choice from the following:	A) 23 m	B) 23 2/9 m	C) 27 7/9 m	D) 29 m	E) 28 m

Solution: SOLUTION:   Relative speed =(40-20)km/hr=(20*5/18)m/sec=(50/9)m/sec.   Therefore length of faster train = ((50/9)*5)m=250/9 m = 27 7/9 m.   Answer: 27 7/9 m
Answer: C
Ravi and sunil are partners in a business. Ravi invests Rs.9,000 for 8 months and Sunil invested Rs.12000 for 9 months then after one year ratio of their profits will be  Pick:  A) 1:3  B) 2:3  C) 3:2  D) 3:1  E) 3:4

Solution: =(9000*8):(15000*8)   =72000:108000   =2:3   ANSWER:2:3
Answer: B
Rs. 120 are divided among A, B, C such that A's share is Rs. 20 more than B's and Rs. 20 less than C's. What is B's share Choose the correct option:
A) Rs 10
B) Rs 20
C) Rs 24
D) Rs 28
E) Rs 29

Solution: Explanation:   Let C = x. Then A = (x—20) and B = (x—40).   x + x - 20 + x - 40 = 120 Or x=60.   A:B:C = 40:20:60 = 2:1 :3.   B's share = Rs. 120*(1/6) = Rs. 20   Option Rs 20
Answer: B
A tourist purchased a total of $1,200 worth of traveler’s checks in $10 and $50 denominations, During the trip the tourist cashed 7 checks and then lost all of the rest. If the number of $10 checks cashed was one more or one less than the number of $50 checks cashed, what is the minimum possible value of the checks that were lost?  Choose one.
A) $1,430  B) $1,310  C) $1,290  D) $1,270  E) $970

Solution: since total cashed checks = 7 ans $10 check cashed = one less or more than $50 checks   Therefore either $10 checks = 3 and $50 checks = 4 OR $10 checks = 4 and $50 checks = 3   using this information 1st option gives us the maximum cashed value therefore if we negate this value from total value we will get minimum value of which checks have lost   Therfore   1200 - 230= 
  1200 - 230 = 970
970 hence answer is $970
Answer: E
You are having 31kg of rice. You are provided with a 1kg stone for weighing. In how many weights the 31kg of rice can be weighed. ?	Choose the correct choice from the following:  A) 3  B) 4  C) 5  D) 6  E) 7

Solution: in 1st weight 1kg stone and 1 kg rice.. rice weighed = 1kg.   2nd weighing 2kg of (stone +rice) and 2 kg of rice.. rice weighed = 3kg.   3rd weighing 4kg of (stone +rice) and 4 kg of rice.. rice weighed = 7kg.   4th weighing 8kg of (stone +rice) and 8 kg of rice.. rice weighed = 15kg.   5th weighing 16kg of (stone +rice) and 16 kg of rice.. rice weighed = 31kg.   Therefore 5 weights   ANSWER:5
Answer: C
If the equation x^2−x=k has at least one solution, which of the following must be true?  Choose the correct choice from the following options:
A) k ≥-1/4
B) k < −9
C) k = 9
D) k ≤ 9
E) k ≥ −9

Solution: x^2−x=k   => x^2−x - k = 0   For a quadratic equation to have at least one solution, its discriminant (b^2-4ac) should be non-negative.   b^2-4ac ≥0   => 1- 4*1*(-k) ≥0   =>1 + 4k ≥0   => k ≥ -14   k ≥-1/4nswer k ≥-1/4
Answer: A
The product of all the prime numbers less than 14 is closest to which of the following powers of 10 ?
Choose the correct choice
A) 10^5 B) 10^8 C) 10^7 D) 10^6 E) 10^9

Solution: Product of Prime numbers less than 14 is 2*3*5*7*11*13   2*5= 
2*5 = 10
10 .   10*11*3*7*13= 10*10*3*10*10 (approximately) ~ Product will be >10^4 <10^6 i.e. 10^5   10^5 is the answer
Answer: A
In a box of 9 pencils, a total of 2 are defective. If a customer buys 3 pencils selected at random from the box, what is the probability that neither pencils will be defective?  Select the correct option: A) 5/12 B) 1/15 C) 2/13 D) 2/15 E) 1/17

Solution: First, there are 7C3 ways you can select 3 good pencils from 4 good ones.   Second, there are 9C3 ways you select 3 pencils from 6 ones in the box.   Then, the probability that neither pen will be defective is: 7C3/9C3=35/84 = 5/12   5/12nswer is 5/12
Answer: A
The fourth proportional to 5, 8, 15 is:	Options:
A) 18
B) 24
C) 19
D) 20
E) 22

Solution: Let the fourth proportional to 5, 8, 15 be x.   Then, 5 : 8 : 15 : x   5x = (8 x 15)   x =	(8 x 15)/5   x=120/5= 
120/5 = 24
24   Answer: Option 24
Answer: B
Given the equation a^2 +a^(-3)=4.125, which of the following options is the correct value of a? Choose the correct choice.
A) 2
B) 1
C) 0
D) 3
E) 5

Solution: Plugging in the various option into the equation to find out which is correct:   a^2 +a^(-3)= 4.125   2^2 +2^(-3) = 4.125 Ans. 2
Answer: A
A train 500 m long can cross an electric pole in 20 sec and then find the speed of the train? Select:
A) 90
B) 67
C) 28
D) 26
E) 27

Solution: Length = Speed * time   Speed = L/T   S = 500/20= 
500/20 = 25
25 M/Sec   Speed= 25*18/5 (To convert M/Sec in to Kmph multiply by 18/5)   Speed = 90 Kmph   90nswer:90
Answer: A
#88
A necklace is made by stringing Q no individual beads together in the repeating pattern red bead, green bead, white bead, blue bead, and yellow bead. If the necklace design begins with a red bead and ends with a white bead, then Q could equal
Pick one.
A) 16	B) 28	C) 41	D) 54	E) 65

Solution: You can just write out the pattern and count: RGWBYRGWBYRGWBY... But to save time a good test taker will just look for a pattern. Min # is 3, because W is the third one. Then every 5 beads another white comes, so it must be 3+5= 
3+5 = 8
8   3+5+5= 
3+5+5 = 13
13   3+5+5+5= 
3+5+5+5 = 18
18   3+5+5+5+5= 
3+5+5+5+5 = 23
23   So you see it ends in either 8 or 3. Pick an answer that ends in either 8 or 3. Only one answer does, b.
Answer: B