MU-NLPC/Calc-aqua_rat huggingface dataset:
The price of a car depreciates in the first year by 25% in the second year by 20% in third year by 15% and so on. The final price of the car after 3 years, if the present cost of the car is Rs. 10,00,000 :
Choose the most appropriate option:  A) 7,80,000  B) 1,70,000  C) 6,90,000  D) 5,10,000  E) None of these

Solution: Solution: Price after third depreciation,   100 ==25%↓ ==> 75 == 20%↓==>60 == 15% ↓ ==> 51.   The price will be,   = Rs. 5, 10, 000.   Alternatively :   1000000*0.75*0.80*0.85 = Rs. 5, 10, 000.   Answer: Option 5,10,000
Answer: D
42.11 + 356.032 + 42.98 = ? Pick
A) 441.122 B) 422.243 C) 440.183 D) 622.443 E) None of these

Solution: Explanation :   42.11 + 356.032 + 42.98 = 441.122. 441.122nswer : Option 441.122
Answer: A
In objective test a correct ans score 4 marks and on a wrong ans 2 marks are ---. a student score 480 marks from 150 question. how many ans were correct?	Choose the most appropriate option:
A) 120
B) 130
C) 110
D) 150
E) 180

Solution: let x be the correct answer and y be the wrong answer   so the total number of questions is (x+y)=150   =>4x-2y=480   =>6x=780   hence x=130   ANSWER:130
Answer: B
When integer m is divided by 30, the remainder is 5. Which of the following has a remainder of 10 when divided by 15 ?
I. 3m
II. 7m
III. 4m + 10
IV. 6m
V .5m Choose the most appropriate option:  A) V Only  B) I Only  C) III Only  D) II Only  E) IV only

Solution: Take any value of n which leaves remainder 5 when divided by 15   i.e. Let, n=20 (i.e.15+5)   I. 3n = 3*20= 
3*20 = 60
60When divided by 30 remainder is NOT10   II. 5n= 5*20= 
5*20 = 100
100 When divided by 30 remainder is 10   III. 4n + 10= 4*20 + 10= 
4*20 + 10 = 90
90 When divided by 30 remainder is NOT10   V Only
Answer: A
A dishonest dealer professes to sell goods at the cost price but uses a weight of 600 grams per kg, what is his percent?  Choose the correct option: A) 15% B) 25% C) 65% D) 45% E) 66.7%

Solution: 66.7%xplanation:   600 --- 400   100 --- ? => 66.7%   Answer: 66.7%
Answer: E
A student scores 55% marks in 8 papers of 100 marks each. He scores 15% of his total marks in English. How much does he score in English? Select:
A) -2  B) 6  C) 7  D) 6  E) 18

Solution: Given student scores 55% marks in english in 8 papers of 100 marks each.   So,his total marks = 55/100 × 800 ⇒ 440   15% of his 440 marks is 440 × (15/100) ⇒ 66   So, he scored 66 marks in english.   Ans is option-2.   -2nswer:-2
Answer: A
In the first week of last month, Company X realized an average wholesale profit of $7140 per day from the sale of q units of Product Y. Which of the following CANNOT be the difference between Product Y’s sale price and cost per unit?
Choices: A) $3 B) $4 C) $7 D) $13 E) $51

Solution: The key operator that everyone seems to have missed is the average. The average profit of $7140 per day is equivalent to a total profit of $49980 for the whole week.   Therefore, the difference between sale price and cost per unit is equal to $49980, which is divisible by all of the answer choices, except for 13.   So, $13 is the answer.
Answer: D
Two trains start from same place at same time at right angles to each other. Their speeds are 36km/hr and 48km/hr respectively. After 30 seconds the distance between them will be ?	Choose the correct choice from the following answers.
A) 270 mts B) 190 mts C) 100 mts D) 500 mts E) 110 mts

Solution: Explanation:   Using pythagarous theorem,   distance travelled by first train = 36x5/18x30 = 300m   distance travelled by second train = 48x5/18x30 = 400m   so distance between them =âˆš( 90000 + 160000)= 
( 90000 + 160000) = 250_000
âˆš250000= 500mts.   Answer: 500 mts
Answer: D
261 ÷ ? × 15 + 270 = 405	Select
A) 24  B) 25  C) 36  D) 39  E) 43

Solution: Explanation:   261 ÷ ? × 15 = 405 - 270= 
405 - 270 = 135
135   (261 × 15)/?= 135   ? = (261 × 15)/135 = 39   Answer: Option 39
Answer: D
Paul sells encyclopedias door-to-door. He earns $150 on every paycheck, regardless of how many sets he sells. In addition, he earns commission as follows:
Commission Sales
10% $0.00 - $10,000.00
5% $10,000.01 --->
He does not earn double commission.That is, if his sales are $12,000, he earns 10% on the first $10,000 and 5% on the remaining $2,000.
His largest paycheck of the year was $1,320. What were his sales for that pay period? Choose the correct answer:
A) 13,400 B) 14,800 C) 16,400 D) 15,800 E) 19,600

Solution: His pay check was $1320.   Out of this, $150 was his fixed salary so the total commission he earned was $1320 - $150 = $1170   He earns 10% on the sales of first $10,000 which gives a commission of $1000.   He earns 5% on every subsequent dollar. Since he earns another $170, he must have had sales of another 170*(100/5)  1320 -  150= 
 1320 -  150 = 1_170
$1170   He earns 10% on the sales of first $10,000 which gives a commission of $1000.   He earns 5% on every subsequent dollar. Since he earns another $170, he must have had sales of another   170*(100/5)= 
  170*(100/5) = 3_400
3400   So his total sales must have been $10,000 + $3400= $13,400   13,400
Answer: A
The length of a rectangle is increased by 25% and its breadth is decreased by 20%. What is the effect on its area?  Choose the correct choice from the following answers:
A) 10000
B) 18999
C) 16990
D) 16007
E) 16991

Solution: 100 * 100= 
100 * 100 = 10_000
10000   125 * 80= 
125 * 80 = 10_000
10000   10000nswer:10000
Answer: A
A not-so-good clockmaker has four clocks on display in the window. Clock #1 loses 35 minutes every hour. Clock #2 gains 15 minutes every hour relative to Clock #1 (i.e., as Clock #1 moves from 12:00 to 1:00, Clock #2 moves from 12:00 to 1:15). Clock #3 loses 20 minutes every hour relative to Clock #2. Finally, Clock #4 gains 20 minutes every hour relative to Clock #3. If the clockmaker resets all four clocks to the correct time at 12 noon, what time will Clock #4 display after 6 actual hours (when it is actually 6:00 pm that same day)?  Choose one:
A) 5:00  B) 5:34  C) 5:42  D) 6:00  E) 6:24

Solution: C1 loses 15 minutes every hour. So after 60 minutes have passed, C1 displays that 60-15= 
60-15 = 45
45 minutes have passed.   C2 gains 15 minutes for every 60 minutes displayed on C1. Thus, the time displayed on C2 is 75/60= 5/4 the time displayed on C1. So after 60 minutes have passed, C2 displays the passing of (5/4 * 45) minutes.   C3 loses 20 minutes for every 60 minutes displayed on C2. Thus, the time displayed on C3 is 40/60 = 2/3 the time displayed on C2. So after 60 minutes have passed, C3 displays the passing of (2/3 * 5/4 * 45) minutes.   C4 gains 20 minutes for every 60 minutes displayed on C3. Thus, the time displayed on C4 is 80/60 = 4/3 the time displayed on clock 3. So after 60 minutes have passed, C4 displays the passing of  4/3 * 2/3 * 5/4 * 45= 
 4/3 * 2/3 * 5/4 * 45 = 50
50 minutes.   C4 loses 10 minutes every hour.   In 6 hours, C4 will lose   6*10= 
  6*10 = 60
60 minutes= 1 hour.   Since the correct time after 6 hours will be 6pm, C4 will show a time of 6-1 = 6:24pm.   The correct answer is 6:24.
Answer: E
How many two-digit numbers yield a remainder of 2 when divided by both 7 and 16?  Choices:
A) 0
B) 1
C) 2
D) 3
E) 4

Solution: Easier to start with numbers that are of the form 16p+2 ---> 18,34,50,66,82,98.   Out of these no number is also of the form 7q+2. Thus 0 is the answer. 0 is the correct answer.
Answer: A
A shopkeeper sold an article offering a discount of 5% and earned a profit of 18.75%. What would have been the percentage of profit earned if no discount was offered?  Choices
A) 60%
B) 23%
C) 25%
D) 56%
E) 73%

Solution: Let C.P. be Rs. 100.   Then, S.P. = Rs. 118.75   Let marked price be Rs. x. Then, 95/100 x = 118.75   x = 11875/95 = Rs. 125   Now, S.P. = Rs. 125, C.P. = Rs. 100   Profit % = 25%.   Answer: 25%
Answer: C
An article was sold after a discount of 20% and therewas a gain of 20%. If the profit madeon it was Rs.6 less thanthe discount offered on it, find its SP?  Choose the correct choice from the following:  A) Rs. 22  B) Rs. 65  C) Rs. 70  D) Rs. 72  E) Rs. 90

Solution: Let CP = Rs. 100x   SP = Rs. 120x   MP = 120x/80 * 100 = Rs. 150x   D = Rs. 150x - Rs. 120x = Rs. 30x   D - P = 30x - 20x = Rs. 6, 10x = Rs. 6   120x = 120/10 * 6 = Rs. 72   Rs. 70
Answer: C
A thief is noticed by a policeman from a distance of 150 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 11 km per hour respectively. What is the distance between them after 6 minutes ?
Choose the correct choice from the following choices:
A) 50 meter B) 100 meter C) 110 meter D) 120 meter E) 130 meter

Solution: Explanation:   Relative speed of the thief and policeman = (11 – 10) km/hr = 1 km/hr   Distance covered in 6 minutes =   1/60∗6=1/10=100meters   So distance between them after 6 minutes = 150 - 100= 
150 - 100 = 50
50 meters   Option 50 meter
Answer: A
Arun has certain number of books. It is not less than 15 and not more than 30. If he wants to give these books equally to 2 of his friends, then 1 book will remain. If he wants to give these books equally to 3 of his friends, then 2 books will remain. If he wants to give these books equally to 4 of his friends, then 3 books will remain. What is the number of books he had?	Answers
A) 18
B) 19
C) 17
D) 29
E) 23

Solution: If he wants to give these books equally to 2 of his friends, then 1 book will remain, it means possible number of books = 15,17,19,21,23,25,27,29   If he wants to give these books equally to 3 of his friends, then 2 books will remain, it means possible number of books = 17,20,23,26,29   If he wants to give these books equally to 4 of his friends, then 3 book will remain, it means possible number of books = 15,19,23,27   common number is only 23 so it will be answer   ANSW23R:23
Answer: E
What is the remainder when 4^381 is divided by 5 ?  Choose the most appropriate option:
A) 0  B) 1  C) 2  D) 3  E) 4

Solution: I also agree that the remainder is '4' (using the last digit of the powers of 7). Could we have the official answer please?4
Answer: E
The average of 11 numbers is 10.9. If the average of first six is 10.5 and that of the last six is 11.4 the sixth number is? Choose the correct choice:  A) 11.9  B) 11.0  C) 11.3  D) 11.5  E) 11.1

Solution: 1 to 11 = 11 * 10.9= 
11 * 10.9 = 119.9
119.9   1 to 6= 6 * 10.5= 
6 * 10.5 = 63
63   6 to 11= 6 * 11.4= 
6 * 11.4 = 68.4
68.4   63 + 68.4= 
63 + 68.4 = 131.4
131.4 – 119.9= 11.5   6th number = 11.5.Answer:11.5
Answer: D
A train running at the speed of 60 km/hr crosses a pole in 12 sec. What is the length of the train?	Options:
A) 120 m B) 200 m C) 115 m D) 110 m E) 150 m

Solution: Speed = 60 * 5/18 = 50/3 m/sec   Length of the train = speed * time = 50/3 * 12= 
50/3 * 12 = 200
200 m   Answer: 200 m
Answer: B
An investment gained an interest payment of $250 each month when the annual interest rate was 8%, how much more should we invest annually if we want to gain 12% more per month with a new annual interest rate of 7.5% ?	Choose the correct option:  A) $9,360  B) $9,100  C) $8,250  D) $7,300  E) $7,150

Solution: Answer is D : 7,300   Interest per annum with 8% interest rate is = 250* 12 = Principal * Interest Rate(8/100)   This gives Principal as 37,500$   For an revised interest of 12% more and new interest rate of 7.5% , ie. 250* 12 * 1.12 = Principal * Interest Rate (7.5/100)   This gives the new Principal as 44,800.   The question is how much more should we invest, so 44,800 - 37,500 = 7,300   ANSWER:$7,300
Answer: D
If the compound interest on a certain sum of money for 7 years at 10% per annum be Rs. 993, what would be the simple interest?
Choices.
A) Rs. 880
B) Rs. 890
C) Rs. 895
D) Rs. 2100
E) None

Solution: Let P = Principal   A - Amount   We have a = P(1 + R/100)3 and CI = A - P   ATQ 993 = P(1 + R/100)3 - P   ? P = 3000/-   Now SI @ 10% on 3000/- for 7 yrs = (3000 x 10 x 7)/100   = 2100/-   Answer: Rs. 2100.
Answer: D
What is the difference between the largest number and the least number written with the figures 3, 4, 7, 0, 3?
Choices
A) 98343 B) 34389 C) 43983 D) 43883 E) 43700

Solution: 74330 Largest   30347 Smallest   ------------   43983   ANSWER 43983
Answer: C
A certain restaurant offers 7 different salads, 5 different main courses, and 6 different desserts. If customers choose one salad, one main course, and two different desserts for their meal, how many different meals are possible? Choose the correct answer:
A) 125 B) 275 C) 525 D) 600 E) 1200

Solution: The number of possible choices for desserts is 65252 = 15   The number of possible meals is   7*5*15= 
  7*5*15 = 525
525   The answer is 525.
Answer: C
Because of the economic slowdown, a multinational company curtailed some of the allowances of its employees. John, the marketing manager of the company whose monthly salary has been reduced to Rs.42,000 is unable to cut more on his expenditure. He finds that there is a deficit of Rs.2,000 between his earning and expenses in the first month. This deficit, because of inflationary pressure, will keep on increasing by Rs.500 everymonth. John has a saving of Rs 60,000 which will be used to fill the deficit. After his savings get exhausted, John would start borrowing from his friends. How soon will he start borrowing?  Select the correct option
A) 9th months	B) 10th months	C) 11th months	D) 12th months	E) 13th months

Solution: Let the Rashid 's savings will last till 'nn' months.   ⇒n2[2×2000+(n−1)500]=60,000⇒n2[2×2000+(n−1)500]=60,000   [Expenditure every month increases by 500 rupees]   ⇒n2+7n−200=0⇒n2+7n−200=0   n=12.38n=12.38   ⇒ Rashid after Kartik's mother asked him to get the vegetables, milk and butter from the market and gave him the money in the denominator of 1 Rupee, 2 Rupee and 5 Rupee coins.   Kartik first goes to the grocery shop to buy vegetables. At the grocery shop he gives half of his 5 Rupee coins in return receives the same number of 1 Rupee coins.   Next he goes to the dairy shop to buy milk and butter and gives all 2 Rupee coins and in return get thirty 5 Rupee coins, which increase the number of five rupee coins by 75% more than the original number.   If the number of 1 rupee coins now is 50, the number of 1 rupee and 5 rupee coins originally were will start borrowing money from his friends.   13th months
Answer: E
The probability that a man will be alive for 10more yrs is 1/4 & the probability that his wife will alive for 10 more yrs is 1/3. The probability that none of them will be alive for 10 more yrs, is Select.
A) 1/2 B) 1 C) 2/3 D) 3/4 E) 2

Solution: Sol. Required probability = Pg.) x P(B) = (1— D x(1 —I) =: x 1=1/2   1/2ns.(1/2)
Answer: A
If w < y < -1, which of the following is true?
Choose the correct choice from the following answers:
A) w/y > wy
B) y/w > w+y
C) y/w > wy
D) y/w < w+y
E) y/w > w/y

Solution: Consider :   w= -3   y= -2   then put for every option. U'll get ans y/w > w+y.
Answer: B
A rope of which a calf is tied is increased from 16 m to 23 m, how much additional grassy ground shall it graze?  Choose the correct choice from the following answers.
A) 1217 B) 1219 C) 1210 D) 1212 E) 858

Solution: π (232 – 162) = 858   Answer:858
Answer: E
How many numbers from 19 to 79 are exactly divisible by 11? Choose the correct choice from the following answers
A) 5
B) 6
C) 9
D) 11
E) 12

Solution: 19/11 = 1 and 79/11 = 7 ==> 7 - 1= 
7 - 1 = 6
6 Numbers   Answer : 6
Answer: B
Miller Street begins at Baker Street and runs directly east for 4.5 kilometers until it ends when it meets Turner Street. Miller Street is intersected every 250 meters by a perpendicular street, and each of those streets other than Baker Street and Turner Street is given a number beginning at 1st Street (one block east of Baker Street) and continuing consecutively (2nd Street, 3rd Street, etc...) until the highest-numbered street one block west of Turner Street. What is the highest-numbered street that intersects Miller Street? Options:
A) 15th
B) 16th
C) 17th
D) 18th
E) 19th

Solution: 4.5 km / 250 m = 18.   However, the street at the 4.5-km mark is not 18th Street; it is Turner Street.   Therefore, the highest numbered street is 17th Street.   The answer is 17th.
Answer: C
Faiza has 9 purses, she gives 3 purse as gift. Now how many purse did she have?	Choose the correct choice:
A) 2	B) 6	C) 11	D) 9	E) 4

Solution: 9-3= 
9-3 = 6
6. Answer is 6
Answer: B
A lawyer's representation costs $150 for the first hour and $125 for each additional hour. What is the total cost, in dollars, of her representation for m hours, where m is an integer greater than 1?	Choose the correct answer:	A) 150 + 125 m	B) 150 + 125( m – 1)	C) 125 + 150 m	D) 125 + 150( m – 1)	E) 275( m – 1)

Solution: For the first hour the cost is 150.   As first hour is already calculated the remaining is m-1 and corresponding cost is 125.   Therefore answer is 150+125(m-1).   Answer 150 + 125( m – 1)
Answer: B
One year ago the ratio between Samir and Ashok’s age was 4:3. One year hence the ratio of their ages will be 5 :4. What is the sum of their present ages in years?
Choose the correct option
A) 12 years	B) 15 years	C) 16 years	D) Cannot be determined	E) none of these

Solution: Let their ages one year ago be 4x and 3x years.   (4x + 2)/(3x + 2) = 5/4   =>4(4x + 2) = 5(3x + 2)   => x = 2   Sum of their present ages   = (4x + 1 + 3x + 1)   =(7x + 2) = 16 years   ANSWER:16 years
Answer: C
A certain company has 18 equally qualified applicants for 4 open positions. How many different groups of 4 applicants can be chosen by the company to fill the positions if the order of selection does not matter? Choose the correct choice from the following
A) 18  B) 72  C) 180  D) 1,260  E) 3,060

Solution: This is a combination question since order is not important.   n!   k! (n-k!)   = 18!   4! 14!   = 18 * 17 * 16 * 15 * 14!   4 * 3 * 2 * 1 * 14!   = 3060 (Ans: 3,060)
Answer: E
What is the square root of 0.16	Answers
A) 0.4 B) 0.04 C) 0.004 D) 4 E) 1

Solution: Explanation:   as .4 * .4= 
.4 * .4 = 0.16
0.16   Option 0.4
Answer: A
What is the rate percent when the simple interest on Rs.4000 amount to Rs.320 in 2 Years?	Choose the correct option:
A) 4% B) 4.1% C) 4.2% D) 4.3% E) 4.5%

Solution: Interest for 1 year = 320/2= 
320/2 = 160
160   Interest on Rs 4000 p/a= 160   interest rate = 160/4000*100= 
160/4000*100 = 4
4%   4%nswer : 4%
Answer: A
When n is divided by 20, the remainder is 5. What is the remainder when n + 16 is divided by 5? Select the correct option.
A) 1 B) 3 C) 4 D) 5 E) 6

Solution: 1ssume n = 15   Remainder (n/20) = 5   n+16 = 31   Remainder (31/5) = 1   Option 1
Answer: A
The ratio of a compound, by weight, consisting only of substances x, y, and z is 4:6:10,
respectively. Due to a dramatic increase in the surrounding temperature, the composition of the
compound is changed such that the ratio of x to y is halved and the ratio of x to z is tripled. In the
changed compound, if the total weight is 174 lbs, how much does substance x weigh?	Pick:  A) 48  B) 36  C) 24  D) 12  E) 10

Solution: x:y=4:6   if the ratio is halevd then x:y=2:6   The old ratio of x to z was 4:10. If this ratio is tripled, then the new ratio of x to z is 12:10.   x:y=2:6=12:36 ( multiplied the ration with 6/6 to have a common co eff x in both the rations x:y and x:z)   so x:y:z= 12:36:10   and we know x + y + z = 174 lbs   from the ratio of x ,y and z we have x=12k y=36k z=10K   put it in the equation we have 12k+36k+10k=174   k=3   Hence x=12(3)=36   Ans 36
Answer: B
In how many years, Rs. 200 will produce the same interest at 6% as Rs. 800 produce in 2 years at 4½% ?  Choose the correct choice:
A) 4 years B) 6 years C) 8 years D) 9 years E) 12 years

Solution: Explanation :   Let Simple Interest for Rs.200 at 6% for n years = Simple Interest for Rs.800 at 4½ % for 2 years   200×6×n/100=800×9/2×2/100   200×6×n=800×9/2×2   200×6×n=800×9   n=6 years   Answer : Option 6 years
Answer: B
On one side of a coin there is the number 0 and on the other side the number 1. What is the probability that the sum of three coin tosses will be 0 ?  Choose the correct option:
A) 1/8
B) 1/2.
C) 1/5.
D) 3/8.
E) 1/3.

Solution: Assume the coin is unbiased.   Possible sums from 3 tosses = 0,1,2,3   O and 3 are possible in only 1 case each. (0,0,0 or 1,1,1)   1 is possible in 3C1 = 3 cases. (1,0,0; 0,1,0 or 0,0,1) or   similarly, 2 is possible in 3C2=3 cases (1,0,1; 1,1,0; 0,1,1)   So answer will be 1/8. Option 1/8.
Answer: A
At a party, there were five ten as many females as males and four times as many adults as children. Which of the following could be the number of people at the party?	Pick one.
A) 384  B) 258  C) 216  D) 120  E) 72

Solution: Five times as many females as males --> F = 10M.   Three times as many adults as children --> (F + M) = 4C.   The number of people at the party = F + M + C = 4C + C = 5C.   The number of people at the party must be a multiple of 5. The only answer choice which is a multiple of 5 is D.   Answer: 120.
Answer: D
Every disk in a bag is either blue, yellow or green. The ratio of blue disks to yellow disks to green disks in this bag is 3 : 7 : 8. If the total number of disks in the bag is 144, how many more green disks than blue disks are in the bag?
Choose the correct choice from the following
A) 25	B) 28	C) 30	D) 35	E) 40

Solution: Let B:Y:G = 3x:7x:8x.   3x + 7x + 8x = 18x 3  + 7  + 8= 
3  + 7  + 8 = 18
18x= 144 --> x= 8.   G - B = 8x - 3x = 5x 8  - 3= 
8  - 3 = 5
5x= 40.   The answer is 40.
Answer: E
In a graduating class of 233 students, 144 took geometry and 119 took biology. What is the difference between the greatest possible number and the smallest possible number of students that could have taken both geometry and biology? Choose the correct option: A) 114 B) 119 C) 113 D) 88 E) 31

Solution: Greatest Possible Number taken both should be 144 (As it is maximum for One)   Smallest Possible Number taken both should be given by   Total - Neither = A + B - Both   Both = A+B+Neither - Total (Neither must be 0 to minimize the both)   So 144 + 119 + 0 - 233= 
144 + 119 + 0 - 233 = 30
30   Greatest - Smallest is  144-30= 
 144-30 = 114
114   So answer must be A. 114
Answer: A
A pupil’s marks were wrongly entered as 83 instead of 63. Due to that the average marks for the class got increased by half. The number of pupils in the class is:  Choose the correct choice from the following options
A) 10	B) 20	C) 40	D) 73	E) 50

Solution: Let there be x pupils in the class.   Total increase in marks = (x × 1⁄2) = x⁄2.   ∴ x⁄2 = (83 - 63) ⇒ x⁄2 = 20 ⇒ x = 40.   Answer 40
Answer: C
A group of medical interns at Bohemus Medical School want to go on dates. There are 8 girls and 8 guys. Assuming girls go on dates with guys, how many possible ways can these 16 medical interns date each other? Choose the correct choice from the following choices
A) A)36320
B) B)37320
C) C)38320
D) D)39320
E) E)40320

Solution: 1st girl can go with 8 guys   2nd girl can go with remaining 7   3rd girl can go with remaining 6 and so on   so the total ways are 8!= 40320   40320 should be the answer
Answer: E
Find the invalid no.from the following series 2,3,12,37,86,166,288
Select the correct option.
A) 123  B) 145  C) 166  D) 173  E) 187

Solution: 3-2= 
3-2 = 1
1   12-3= 
12-3 = 9
9   37-12= 
37-12 = 25
25   86-37= 
86-37 = 49
49   166-86= 
166-86 = 80
80(this must be 81=167-86= 
167-86 = 81
81)   so wrong number in the sequence is 166   difference between two sucessive numbers sequence would be   1,9,25,49,81,121(square of 1,3,5,7,9,11)   166
Answer: C
In what ratio must water be added to 10 litres of milk at Rs.20 per litre so that cost of mixture is Rs.16 per litre?  Choose the correct answer
A) 3:2	B) 1:4	C) 2:3	D) 4:1	E) 4:3

Solution: C.P of 1 Lt of water =Rs.0   C.p Of 1 lt of Milk= Rs.20   So,   o(Cheaper) 20(Dearer)   16(Mixture)   4 : 16   (Dearer-Mixture) (Mixture-Cheaper)   so,   (Note: Just cross check)   4:16=1:4   ANSWER:1:4
Answer: B
If xy ≠ 0 and x^2y^2 − 2xy = 24, which of the following could be y in terms of x?
I. 6/x
II. -4/x
III. 1/x  Choose the most appropriate option:  A) I only  B) II only  C) I and II only  D) I and III  E) II and III

Solution: (x^2)(y^2) –2xy - 24 = 0   (xy – 6)(xy + 4) = 0   xy – 6 = 0 or xy + 4 = 0   xy = 6 or xy = -4   Since we need y in terms of x, we can isolate y in both of our equations.   y = 6/x or y = -4/x   Answer: I and II only
Answer: C