MU-NLPC/Calc-aqua_rat huggingface dataset:
7.51 8.22 7.86 8.36
8.09 7.83 8.30 8.01
7.73 8.25 7.96 8.53
A vending machine is designed to dispense 8 ounces of coffee into a cup. After a test that recorded the number of ounces of coffee in each of 1000 cups dispensed by the vending machine, the 12 listed amounts, in ounces, were selected from the data above. If the 1000 recorded amounts have a mean of 8.1 ounces and a standard deviation of 0.2 ounces, how many of the 12 listed amounts are within 1.5 standard deviation of the mean?	Choose the correct choice from the following.
A) Four	B) Six	C) Nine	D) Ten	E) Eleven

Solution: Mean = 8.1   Standard Deviation = 0.2   within 1.5 standard deviation of the mean   i.e. 1.5 standard deviation ABOVE the mean = 8.1+1.5*0.2= 
8.1+1.5*0.2 = 8.4
8.4   and 1.5 standard deviation BELOW the mean= 8.1-1.5*0.2= 
8.1-1.5*0.2 = 7.8
7.8   hence, 9 values fall within 1.5 SD from Mean   Answer: Option Nine
Answer: C
The speeds of 3 cars in the ratio 2:3:4. The ratio between time taken by them to travel the same distance is?  Pick
A) 2:3:4 B) 6:4:3 C) 8:7:5 D) 11:12:15 E) 9:2:5

Solution: Ratio of time taken is = 1/2 : 1/3 : 1/4 = 6:4:3   Answer is 6:4:3
Answer: B
What will come in place of the x in the following Number series? 65536, 32768, 16384, 8192, x
Choose the correct choice:
A) 4090	B) 4098	C) 4094	D) 4092	E) 4096

Solution: Go on dividing by 2 to the next number   Answer : 4096
Answer: E
A train 100 meters long completely crosses a 350-meter long bridge in 40 seconds. What is the speed of the train in km/h?	Choices:
A) 37.5 km/h
B) 40.5 km/h
C) 43.5 km/h
D) 46.5 km/h
E) 49.5 km/h

Solution: speed = distance / time = (100 + 350)/40 = 450/40 (m/s) * 3600/1000 = 40.5 km/h   The answer is 40.5 km/h.
Answer: B
The average age of 3 boys is 15 years and their ages are in the proportion 1:2:3. The age of the youngest boy is?
Pick one:
A) 10 years
B) 12 years
C) 15 years
D) 18 years
E) 7.5 years

Solution: Total age of 3 boys = 15*3= 
15*3 = 45
45   ratio of their ages= 1:2:3   Age of the youngest = 45*1/6= 
45*1/6 = 15/2 = around 7.5
7.5 years   Answer is 7.5 years
Answer: E
Rohan ranked eleventh from the top and twenty-seventh from the bottom among the students who passed the annual examination in a class. If the number of students who failed in the examination was 12, how many students appeared for the examination?	Select:
A) 48 B) 49 C) 50 D) Cannot be determined E) None of these

Solution: here .. from top its 11th and from bottom its 27th that means at top 10 members are there and bottom 26 members are there so  26+10+1= 
 26+10+1 = 37
37. 37 memebers are passed, in above question 12 members are failed in examination so therefore 37+12= 
37+12 = 49
49.   ANSWER:49
Answer: B
In a weight-lifting competition, the total weight of Joe's two lifts was 600 pounds. If twice the weight of his first lift was 300 pounds more than the weight of his second lift, what was the weight, in pounds, of his first lift?  Choose the correct answer
A) 225
B) 275
C) 300
D) 350
E) 400

Solution: This problem is a general word translation. We first define variables and then set up equations.   We can define the following variables:   F = the weight of the first lift   S = the weight of the second lift   We are given that the total weight of Joe's two lifts was 600 pounds. We sum the two variables to obtain:   F + S = 600   We are also given that twice the weight of his first lift was 300 pounds more than the weight of his second lift. We express this as:   2F = 300 + S   2F – 300 = S   We can now plug in (2F – 300) for S into the first equation, so we have:   F + 2F – 300 = 600   3F = 900   F = 300   Answer is 300
Answer: C
According to the directions on a packet of smoothie mix, 1 3-ounce packet of smoothie mix is to be combined with 12 ounces of water to make a smoothie. How many 2-ounce packets of smoothie mix are required to prepare 150 12-ounce smoothies?  Choose the most appropriate option.
A) 120	B) 150	C) 180	D) 240	E) 600

Solution: This question wasn't particularly grueling, but I think it's the first where I had the opportunity to solve it via theory andinspectionthat many on this board suggest as strategy on the GMAT. It actually came to me by accident. Basically, if we thought that the 3 packets of powder were included in the 12 ounces of water, that would mean we would need 150 packets of smoothie mix (along with 12(150) ounces of water for a total of 150 packets. However, we know, after a more careful reading of the stimulus, that the 3 ounces are NOT included in the 12 ounces. As such, the answer has to be LESS than 150 packets, since 150 would be too much powder considering you already have 150(12) ounces of water and need less packets than water to make a smoothie. As such, the only answer less than 150 is 120, A. Does this make sense? Or am I way off base?   180
Answer: C
Mohan paid a sum of money for purchasing 30 pens, which he recovered in full when he sold 15 of them. What was his percentage of profit or loss per pen?  Select.
A) 60% B) 70% C) 80% D) 90% E) 100%

Solution: E   33.33%   If the sum he paid whilst purchasing 30 pens = A,   Then the Cost Price of each pen = A/30.   Since the amount he got whilst selling 15 pens is also = A   Then the Selling Price of each pen = A/15.   Since Selling Price > Cost Price, he made a profit.   Profit per pen = Selling Price - Cost Price = A/15 - A/30 = A/30.   Profit percentage per pen = Profit per pen / Cost per pen x 100 = (A/30) / (A/30) x 100 = 100% Answer :100%
Answer: E
In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?  Choose the correct choice.
A) 620  B) 640  C) 690  D) 710  E) 720

Solution: The word 'OPTICAL' has 7 letters. It has the vowels 'O','I','A' in it and these 3 vowels should always come together. Hence these three vowels can be grouped and considered as a single letter. That is, PTCL(OIA).   Hence we can assume total letters as 5 and all these letters are different.   Number of ways to arrange these letters   =   5   !   =   5   ×   4   ×   3   ×   2   ×   1   =   120   =5!=5×4×3×2×1=120   All the 3 vowels (OIA) are different   Number of ways to arrange these vowels among themselves   =   3   !   =   3   ×   2   ×   1   =   6   =3!=3×2×1=6   Hence, required number of ways   =   120   ×   6   =   720   720)
Answer: E
Pipe A can fill a tank in 7 hours, pipe B in 14 hours and pipe C in 42 hours. If all the pipes are open,in how many hours will the tank be filled ?
Pick.
A) 4	B) 4.2	C) 4.5	D) 4.3	E) 4.1

Solution: 1/7+1/14+1/42=10/42=1/4.2. so 4.2 hrs   ANSWER:4.2
Answer: B
A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 700 m long?  Choose the correct choice from the following choices.
A) 288 B) 190 C) 188 D) 188 E) 12

Solution: L = S*T   S= 1200/120= 
1200/120 = 10
10 m/Sec.   Total length (D)= 1900 m   T = D/S   T = 1900/10= 
1900/10 = 190
190 Sec   Answer:190
Answer: B
An integer n between 1 and 99, inclusive, is to be chosen at random. What is the probability that n(n+1) will be divisible by 3 ?	Choose the correct option:	A) 1/9	B) 1/3	C) 1/2	D) 2/3	E) 5/6

Solution: n(n+1) to be divisible by 3 either n or n+1 must be a multiples of 3.   In each following group of numbers: {1, 2, 3}, {4, 5, 6}, {7, 8, 9}, ..., {97, 98, 99} there are EXACTLY 2 numbers out of 3 satisfying the above condition. For example in {1, 2, 3} n can be: 2, or 3. Thus, the overall probability is 2/3.   Answer: 2/3.
Answer: D
The wheels revolve round a common horizontal axis. They make 15, 20 and 48 revolutions in a minute respectively. Starting with a certain point on the circumference down wards. After what interval of time will they come together in the same position?	Choose the correct choice from the following answers:
A) 1 min
B) 2 min
C) 3 min
D) 4 min
E) None

Solution: Time for one revolution = 60/15= 
60/15 = 4
4   60/ 20= 
60/ 20 = 3
3   60/48= 5/4   LCM of 4, 3, 5/4   LCM of Numerators/HCF of Denominators = 60/1= 
60/1 = 60
60   1 minNSWER:1 min
Answer: A
The HCF and LCM of two numbers m and n are respectively 6 and 210. If m + n = 60, then 1/m + 1/n is equal to Choose the most appropriate option: A) 1/35 B) 3/35 C) 1/21 D) 2/35 E) None

Solution: Answer   We have, m x n = 6 x 210 = 1260   âˆ´ 1/m + 1/n = (m + n)/mn = 60/1260 = 1/21   1/21orrect Option: 1/21
Answer: C
On what dates of April, 2001 did Wednesday fall?	Choose one.
A) 2nd, 9th, 16th, 23rd	B) 4th, 11th, 18th, 25th	C) 3rd, 10th, 17th, 24th	D) 1st, 8th, 15th, 22nd, 29th	E) None of these

Solution: Explanation :   We need to find out the day of 01-Apr-2001   01-Apr-2001 = (2000 years + period from 1-Jan-2001 to 01-Apr-2001)   We know that number of odd days in 400 years = 0   Hence the number of odd days in 2000 years = 0 (Since 2000 is a perfect multiple of 400)   Days from 1-Jan-2001 to 01-Apr-2001 = 31 (Jan) + 28 (Feb) + 31 (Mar) + 1(Apr) = 91   91 days = 13 weeks = 0 odd day   Total number of odd days = (0 + 0)= 
(0 + 0) = 0
0 odd days   0 odd day= Sunday. Hence 01-Apr-2001 is Sunday.   Hence first Wednesday of Apr 2011 comes in 04th and successive Wednesdays   come in 11th, 18th and 25th   Answer : Option 4th, 11th, 18th, 25th
Answer: B
The sticks of same length are used to form a triangle as shown below.If 87 such sticks are used then how many triangles can be formed?  Select the correct option.
A) 43	B) 44	C) 45	D) 465	E) 47

Solution: First triangle is formed by using 3 sticks, but any subsequent triangle may be formed by using 2 sticks. Therefore, If 1st triangles uses 3 sticks, Remaining sticks = 87 - 3= 
87 - 3 = 84
84. With these 84, we can form 42 triangles. So total= 42 + 1= 
42 + 1 = 43
43   43nswer:43
Answer: A
A coin has two sides. One side has the number 1 on it and the other side has the number 2 on it. If the coin is flipped three times what is the probability that the sum of the numbers on the landing side of the coin will be greater than 5?  Choose the correct option
A) 3/8 B) 1/16 C) 1/8 D) 1/2 E) 1/4

Solution: One approach to solve the problem is to list the different possibilities for a toss of coin three times. Because there are two outcomes and the coin is tossed three times, the table will have 2*2*2 or 8 rows.   Next add the resulting rows together to find the sum (the fourth column in the table below).   Toss 1 | Toss 2 | Toss 3 | Sum   1 ---------- 1 -------- 1 ------ 3   1 ---------- 1 -------- 2 ------ 4   1 ---------- 2 -------- 1 ------ 4   1 ---------- 2 -------- 2 ------ 5   2 ---------- 1 -------- 1 ------ 4   2 ---------- 1 -------- 2 ------ 5   2 ---------- 2 -------- 1 ------ 5   2 ---------- 2 -------- 2 ------ 6   From the table we see that there are 1 situations where the sum of the tosses will be greater than 5. And there are 8 possible combinations resulting in a probability of   1/8 or a probability of 1/8.   SO the correct answer is 1/8.
Answer: C
Adam has s pairs of shoes, which is 1/2 as many as Katherine and twice as many as Julie. In terms of s, how many pairs of shoes do the three of them have combined? Pick: A) 7/2*s B) 11s C) 2s D) 5/2*s E) 13/4*

Solution: == s +2s + s/2 ==> 3s + 1/2 s = 7/2*s   7/2*sns .7/2*s
Answer: A
A table is bought for Rs.800/- and sold at Rs.600/- find gain or loss percentage
Choose the correct answer:
A) 25% gain
B) 20% loss
C) 20% gain
D) 25% loss
E) None

Solution: Formula = (Selling price ~ Cost price)/Cost price * 100   = (600 - 800)/800 = 25% loss   25% loss
Answer: D
Two numbers are less than third number by 34% and 37% respectively. How much percent is the second number less than by the first  Choose the correct option: A) 8% B) 10% C) 9% D) 11% E) 22%

Solution: Let the third number is x.   then first number = (100-34)= 
(100-34) = 66
66% of x= 66x/100   Second number is (63x/100)   Difference = 66x/100 - 63x/100 = 3x/100   So required percentage is, difference is what percent of first number   (3x/100 * 100/63x * 100 )% = 22% ANSW22%R :22%
Answer: E
The average of first 10 prime numbers is?  Pick one.
A) 12.9 B) 12.6 C) 12.3 D) 512.4 E) 12.1

Solution: Sum of 10 prime no. = 129   12.9verage = 129/10= 
129/10 = 129/10 = around 12.9
12.9   12.9nswer: 12.9
Answer: A
The speed of a boat in still water is 12 kmph. What is the speed of the stream if the boat can cover 32 km downstream or 16 km upstream in the same time?	Choose the correct answer.
A) 5 kmph B) 6 kmph C) 7 kmph D) 4 kmph E) 10 kmph

Solution: X = the speed of the stream   (12 + X) / (12 - X) = 2/1   12+ X = 24 - 2X   3X = 12   X = 4 km/hour   If the speed of the stream is 4km/hour, then the 'downstream' speed of the boat is   12+4= 
  12+4 = 16
16km/hour and the 'upstream' speed of the boat is 12-4= 
12-4 = 8
8km/hour. In that way, if the boat traveled for 2 hours, it would travel 2x8= 16km downstream and 2x16 = 32km/hour upstream.   Answer : 4 kmph
Answer: D
The value of a machine depreciates at the rate of 10% every year. It was purchased 3 years ago. If its present value is Rs. 8748, its purchase price was :
Select:
A) 12000  B) 10000  C) 15000  D) 20000  E) 25000

Solution: Purchase = 8748/(1-10/100^3) = 12000   12000NSWER 12000
Answer: A
A man is 20 mins late to the office if he walks at 20 kmph, and 15 mins earlier if he walks at 30 kmph. How much time will he be early/late if he walks at 25 kmph?	Pick.
A) early 1 min  B) early 2 min  C) late 1 min  D) late 2 min  E) none

Solution: let distance be x,then   time1= x/20*60,   t2=x/30*60   difference b/w both time is 35min then   x/20-x/30=35 so x=35   now for 25kmph    35/25*60= 
 35/25*60 = 84
84 min   for 20kmph time=105 min   for 30kmph time= 70min   in 30 kmph he is early by 15 min then actual time is 85 min   so the anser is he is early by 1 min   ans=early 1 min   t=35/25*60   early 1 minNSWER:early 1 min
Answer: A
Calculate the value of 8.14 x 10^3 ?	Choose the correct answer
A) 81400000  B) 8140000  C) 814000  D) 8140  E) 814

Solution: 8.14 x 10^6 = 8.14 x 1000 = 8140.   Answer = 8140
Answer: D
The ratio of two numbers is 4 : 5 and their H.C.F. is 4. Their L.C.M. is  Select.
A) 48	B) 22	C) 80	D) 27	E) 35

Solution: Explanation:   Let the numbers be 4x and 5x. Then, their H.C.F. = x. So, x = 4.   So, the numbers 16 and 20.   L.C.M. of 16 and 20 = 80.   Answer: Option 80
Answer: C
A certain debt will be paid in 52 installments from January 1 to December 31 of a certain year. Each of the first 12 payments is to be $410; each of the remaining payments is to be $65 more than each of the first 12 payments. What is the average (arithmetic mean) payment that will be made on the debt for the year?  Pick one:  A) 443  B) 450  C) 460  D) 468  E) 475

Solution: Total number of installments = 52   Payment per installment for the first 12 installments = 410   Payment per installment for the remaining 32 installments = 410+65= 
410+65 = 475
475   Average= (12*410 + 40*475)/52= 
(12*410 + 40*475)/52 = 460
460   Answer 460
Answer: C
One out of every 5000 computer chips is defective. If 2 out of every 30 defective chips have defective processors and there are 30 defective processors in the first batch, how many computer chips are there in the first batch?
Choices:
A) 450
B) 900
C) 90,000
D) 2250,000
E) 900,000

Solution: (D) Read the whole question to get the feel of what they are asking you to find. Then start with the smallest amount and work your way outwards. We are told that two out of every 30 defective chips have a defective processor. Let x be the total number of defective processors in the batch. Because we know 2 out of every 30 defective chips will have defective processors, and the total number of defective processors in the batch is 30, we can write out an equation: (2/30)x = 30. This can be simplified to (1/15)x = 30. Multiplying each side by 15, we arrive at x = 450. This tells us that there are 450 defective chips in the whole batch. Because we know that 1 out of every 1000 chips is defective, we can set up a proportion. If 1 out of every 5000 chips is defective, then 450 out of y chips would be defective, where y is the total number of chips in the batch. This can be set up as an equation as follows: 1/5000 = 450/y. Solve for y and you will get the total number of chips in the batch: 2250,000.   The answer is (2250,000).
Answer: D
If Solomon distributes his toys in the ratio of 1/4 : 1/6 : 1/10 : 1/9 between his four friends A, B, C and D, then find the total number of toys Solomon should have?  Options:
A) 111.7  B) 118.7  C) 113.7  D) 218.7  E) 418.7

Solution: Here, A : B : C : D = 1/4 : 1/6 : 1/10 : 1/9   1) L.C.M of 4 : 6 : 10 : 9 is 180   2) Find the number of pens each friend received --------- (To find no. of pens each friend has, multiply the ratio with the L.C.M. calculated)   A = (1/4) x 180 = 45   B = (1/6) x 180 = 30   C = (1/10) x 180 = 18   D = (1/7) x 180 = 25.7   3) Total number of toys = (45 x + 30 x + 18 x + 25.7 x) = 118.7 x   Minimum number of pens (x) = 1   Therefore, total number of pens = 118.7 pens.   Correct option :118.7
Answer: B
Anil spends 40% of his income on rent, 30% of the remaining on medicines and 20% of the remaining on education. If he saves Rs. 840 every month, then find his monthly salary?	Choose the correct choice from the following.
A) RS.3500
B) Rs.1500
C) Rs.4500
D) Rs.2500
E) Nill

Solution: Answer: Option D   Let's anil's salary be Rs. 100.   Money spent on Rent = 40% of 100 = Rs. 40.   Money spent on medical grounds = 30% of (100 - 40) = 3/10 * 60 = Rs. 18.   Money spent on education = 20% of (60 - 18) = 1/5 * 42 = Rs. 8.40   anil saves 100 - (40 + 18 + 8.40) i.e., Rs. 33.60   for 33.6 ---> 100 ; 840 ---> ?   Required salary = 840/33.6 * 100 = Rs. 2500
Answer: D
When a certain tree was first planted, it was 4 feet tall, and the height of the tree increased by a constant amount each year for the next 6 years. At the end of the 6th year, the tree was 1/4 taller than it was at the end of the 4th year. By how many feet did the height of the tree increase each year?  Choices.
A) 1	B) 2/5	C) 1/2	D) 2/3	E) 6/5

Solution: Say, the tree grows by x feet every year.   Then, 4 + 6x = (1+1/4)(4+4x)   or, x = 1   1nswer 1
Answer: A
Ravi purchased a refrigerator and a mobile phone for Rs. 15000 and Rs. 8000 respectively. He sold the refrigerator at a loss of 4 percent and the mobile phone at a profit of 10 percent. Overall he make a.
Choose the correct choice from the following options
A) 223  B) 277  C) 288  D) 200  E) 812

Solution: Let the SP of the refrigerator and the mobile phone be Rs. r and Rs. m respectively.   r = 15000(1 - 4/100) = 15000 - 600   m = 8000(1 + 10/100) = 8000 + 800   Total SP - Total CP = r + m - (15000 + 8000) = -600 + 800 = Rs. 200   As this is positive, an overall profit of Rs. 200 was made.   Answer: 200
Answer: D
If y > 0, (1y)/20 + (3y)/10 is what percent of y? Options.
A) 35%  B) 50%  C) 60%  D) 70%  E) 80%

Solution: can be reduced to y/20+3y/10 =7y/20=35%   35%
Answer: A
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Matt and Peter can do together a piece of work in 20 days. After they have worked together for 12 days Matt stops and Peter completes the remaining work in 14 days. In how many days Peter complete the work separately.	Choose the correct choice from the following choices:
A) 26 days
B) 27 days
C) 23 days
D) 35 days
E) 24 days

Solution: Together they complete the job in 20 days means they complete 12/20 of the job after 12 days.   Peter completes the remaining (8/20) of the job in 14 days which means that the whole job(1) can be completed in X days.   <=> 8/20->14 <=> X=14/(8/20)= 
14/(8/20) = 35
35Thus the answer is 35 days.
Answer: D
The average weight of 6 person's increases by 4.5 kg when a new person comes in place of one of them weighing 75 kg. What might be the weight of the new person?	Choose the correct choice from the following options
A) 160 kg B) 175 kg C) 180 kg D) 102 kg E) 190 kg

Solution: Total weight increased = (6 x 4.5) kg = 27 kg.   Weight of new person = (75 + 27)= 
(75 + 27) = 102
102 kg   Option 102 kg
Answer: D
If Aug 15th,2012 falls on Thursday then June 11th,2013 falls on which day ?
Answers:  A) monday  B) saturday  C) friday  D) wednesday  E) sunday

Solution: First,we count the number of odd days for the left over days in the given period.   Here,given period is 15.8.2012 to 11.6.2013   Aug Sept Oct Nov Dec Jan Feb Mar Apr May Jun   16 30 31 30 31 31 28 31 30 31 11(left days)   2 + 2 + 3 + 2 + 3 + 3 + 0 + 3 + 2 + 3 + 4 (odd days) = 6 odd days   So,given day Thursday + 6 = Wednesday is the required result.   Answer: wednesday) Wednesday
Answer: D
-88 × 39 + 312 = ?  Answers:
A) -3200
B) 3120
C) -3120
D) 3200
E) 3208

Solution: -88 × 39 + 312 = -88 × (40-1) + 312   = -88 × 40 + 88 + 312   = -3520 + 88 + 312   = -3120   Answer is -3120
Answer: C
Rob traveled a distance of 30 km, covering the first 10 km in x minutes, the next 10 km in y minutes and the last 10 km in z minutes. If he totally took 3y minutes to cover the whole distance, then which of the following cannot be true? Assume x , y and z are different. Answers:
A) z=3x	B) x=3z	C) y=2x	D) x=2y	E) y=3x

Solution: Rob Travelled for x,y and for z min.   Total Time : x + y + z   Which is equal to : 3y   Equating both sides we get   x+y+z = 3y   => x+z =2y ........ Eqn 1   Looking out at options   D Says x =2y   Using it in Eqn 1   2y + z = 2y   => Z = 0 mins, Which I guess is not possible.   The Ans isx=2y
Answer: D
A certain cube floating in a bucket of water has between 75 and 85 percent of its volume below the surface of the water. If between 9 and 16 cubic centimeters of the cube's volume is above the surface of the water, then the length of a side of the cube is approximately
Choose one:	A) 4	B) 5	C) 7	D) 8	E) 9

Solution: If sides are 7, vol=7^3=343   75%= 257.25, 85%=291.55   so vol above water, between 85.75 and 51.45 -->too big   If side are 4, vol = 64   75%=48, 85%=54.4   vol above water between 16 and 9.6   So 4 should be the answer.   Check option C,   If sides are 5, vol = 125   75%= 93.75, .85%=106.25   vol above water between 18.75-31.25   (Sides are 4 cubic centimeters)   4
Answer: A
An inspector rejects 0.08% of the meters as defective. How many will be examine to project ? Select the correct option:
A) 5500 B) 7500 C) 3500 D) 2500 E) 4500

Solution: Let the number of meters to be examined be x.   Then, 0.08% of x =2   [(8/100)*(1/100)*x] = 2   x = [(2*100*100)/8= 
(2*100*100)/8 = 2_500
2500.   Answer is 2500.
Answer: D
In how many ways can the letters of the word, ‘LANGUAGE’ be arranged in such a way that the vowels always come together?
Pick:
A) 600 B) 700 C) 720 D) 750 E) 780

Solution: In the word ‘LANGUAGE’ we treat the vowels AUAE as one letter. Thus, we have LNGG (AUAE).   This we have 5 letters of which G occurs 2 times and the rest are different.   Number of ways arranging these letters= 5!/2! =5*4*3= 
5*4*3 = 60
60   Now, 4 letters of which A occurs 2 times and the rest are different, can be arranged in 4!/2!= 4*3= 
4*3 = 12
12.   Therefore, Required number of ways= 60*12= 
60*12 = 720
720   ANSWER: 720
Answer: C
Out of 15 consecutive numbers, 2 are chosen at random. The probability that they are both odds or both primes is? Choose the correct option
A) 1/1 B) 1/7 C) 1/8 D) 1/3 E) 1/2

Solution: A leap year has 52 weeks and two days   Total number of cases = 7   Number of favourable cases = 1   i.e., {Saturday, Sunday}   Required Probability = 1/7   Answer:1/7
Answer: B
What is the difference between the compound interest on Rs.12000 at 20% p.a. for one year when compounded yearly and half yearly? Choose one:
A) 337
B) 120
C) 266
D) 287
E) 612

Solution: When compounded annually, interest   = 12000[1 + 20/100]1 - 12000 = Rs.2400   When compounded semi-annually, interest   = 12000[1 + 10/100]2 - 12000 = Rs.2520   Required difference = 2520 - 2400 = Rs.120   Answer:120
Answer: B
Compound interest earned on a sum for the second and the third years are Rs.2500 and Rs.2625 respectively. Find the rate of interest?
Select the correct option
A) 10% p.a. B) 5% p.a. C) 15% p.a. D) 12.5% p.a. E) None of these.

Solution: Rs.2625 - 2500 = Rs.125 is the interest on Rs.2500 for one year.   Rate of interest = (125/2500) * 100= 
(125/2500) * 100 = 5
5% p.a   ANSWER:5% p.a.
Answer: B