MU-NLPC/Calc-aqua_rat huggingface dataset:
4000 was divided into two parts such a way that when first part was invested at 3% and the second at 5%, the whole annual interest from both the investments is Rs.144, how much was put at 3%?
Pick
A) Rs.2500  B) Rs.2700  C) Rs.2800  D) Rs.5000  E) Rs.6000

Solution: Explanation:   (x*3*1)/100 + [(4000 - x)*5*1]/100 = 144   3x/100 + 200 â€“ 5x/100 = 144   2x/100 = 56 Ã¨ x = 2800   ANSWER IS Rs.2800
Answer: C
A starts walking at 4 kmph and 4 hours after his start B starts cycling at 10 kmph. After how much distance will B catch up with A
Pick one
A) 26.2 km B) 25.7 km C) 23.2 km D) 26.67 km E) None of these

Solution: Explanation:   Distance travelled by each of them is to be made equal.   => Distance travelled walking = Distance covered cycling.   Let after 4 hours of walking, A walk for x hours more before B catches up with him.   => Distance = Speed * Time   (4+x)4 = 10x   x = 8/3   Therefore, It takes B 8/3 hours to catch up with A. 26.67 kmistance: 8/3 x 10 = 80/3 km = 26.67   ANSWER: 26.67 km
Answer: D
The positive value of x that satisfies the equation (1 + 2x)^5 = (1 + 2x)^4 is between
Bunuel, can you please explain this one?  Pick one:
A) 0 and 0.5
B) 0.5 and 1
C) 1 and 1.5
D) 1.5 and 2
E) 2 and 2.5

Solution: Trial and error would probably be the easiest way to solve this problem. When x is large enough positive number, then because of the exponents (5>4), LHS will be more than RHS (as you increase the positive value of x the distance between the values of LHS and RHS will increase).   Try x=1 --> LHS=3^5=81*3= 
81*3 = 243
243 and RHS=4^4=64*4= 
64*4 = 256
256, so (1 + 2x)^5 < (1 + 3x)^4. As you can see LHS is still slightly less than than RHS. So, the value of x for which (1 + 2x)^5= (1 + 3x)^4 is slightly more than 1.   Answer: 0.5 and 1.
Answer: B
The cash difference between the selling prices of an article at a profit of 4% and 6% is Rs. 3. The ratio of the two selling prices is? Answers.
A) 52:56 B) 52:53 C) 52:50 D) 22:56 E) 52:51

Solution: Let C.P. of the article be Rs. x.   Then, required ratio = 104% of x / 106% of x   = 104/106 = 52/53 = 52:53   Answer: 52:53
Answer: B
The ratio of investments of two partners P and Q is 7:5 and the ratio of their profits is 7:10. If P invested the money for 5 months, find for how much time did Q invest the money?	Choose the most appropriate option: A) 17 B) 10 C) 178 D) 162 E) 72

Solution: 7*5: 5*x = 7:10   x = 10   Answer:10
Answer: B
What is the greatest number of 4 digits that when divided by any of the numbers 6, 9, 12, 17 leaves a remainder of 2?	Pick one:
A) 9792
B) 9982
C) 9794
D) 9906
E) None of these

Solution: Apply hit and trial method at each option   9792/9= 0 remainder (failed)   9982/9= 1 remainder (failed)   9794/6= 2   9794/9= 2   9794/12=2   9793/17= 2   ANSWER:9794
Answer: C
A 4-letter code word consists of letters A, B, and C. If the code includes all the three letters, how many such codes are possible?
Select the correct option
A) 72
B) 48
C) 36
D) 24
E) 18

Solution: 3 letters A, B and C can be arranged in 3! ways = 6 ways   4th letter can be chosen in 3 ways   Total number of ways = 6*3= 
6*3 = 18
18   ANS 18: 18
Answer: E
A man swims downstream 72 km and upstream 45 km taking 9 hours each time; what is the speed of the current?  Options.
A) 1.9  B) 1.5  C) 1.4  D) 1.1  E) 1.2

Solution: 72 --- 9 DS = 8   ? ---- 1   45 ---- 9 US = 5   ? ---- 1 S = ?   S = (8 - 5)/2= 
(8 - 5)/2 = 3/2 = around 1.5
1.5   Answer: 1.5
Answer: B
Two unemployed young men decided to start a business together. They pooled in their savings, which came to Rs. 2,000. They were both lucky, their business prospered and they were able to increase their capital by 50 per cent every three years. How much did they have in all at the end of eighteen years?	Choose the correct choice:
A) Rs. 22,781.25	B) Rs. 24,150.25	C) Rs. 28,140.50	D) Rs. 18,000	E) Rs. 19,000

Solution: P = 2000, r = 50/100= 
50/100 = 1/2 = around 0.5
0.5, t=18/3= 
18/3 = 6
6 (number of years)   C= P ( 1 + r )^(t)   C = 2000 ( 1 + 0.5)^(6)   C = 22781.25rs.   Rs. 22,781.25NSWER:Rs. 22,781.25
Answer: A
In a circle with a radius of 6, what is the area of the biggest rectangle that can be cut out of this circle ? Choose the correct choice from the following answers.
A) 12  B) 96  C) 50  D) 72  E) 144

Solution: The biggest rectangle would be a square, whose diagonal is 12 (6+6)   if side of square is a, 144=a^2+a^2=2a^2   so area of square=a^2=144/2= 
144/2 = 72
72   ANSWER: 72
Answer: D
A person travelled from his house to office at 30km/hr and office to house at 15km/hr. Then find the average speed? Choose the correct choice:  A) 15km/hr  B) 20km/hr  C) 32km/hr  D) 24km/hr  E) 25km/hr

Solution: Average speed = (2*30*15)/(30+15)= 
(2*30*15)/(30+15) = 20
20km/hr   Answer is 20km/hr
Answer: B
A man can row 30 km downstream and 20 km upstream in 4 hours. He can row 45 km downstream and 40 km upstream in 7 hours. Find the speed of man in still water?  Pick one
A) 12.8  B) 12.5  C) 12.9  D) 12.1  E) 12.2

Solution: Let the speed of the man in still water be a kmph and let the speed of the stream be b kmph.   Now 30/(a + b) + 20/(a - b) = 4 and 45/(a + b) + 40/(a - b) = 7   Solving the equation, the speed of man in still water is 12.5 kmph.   Answer: 12.5
Answer: B
How many multiples of 5 are less than 5000, and also multiples of 50? Pick one.
A) 100 B) 208 C) 625 D) 832 E) 833

Solution: The LCM of 5 and 50 is 50. Divide   5000/50= 
  5000/50 = 100
100.xxx. So 100 is your answer.
Answer: A
If two numbers are in the ratio 6:7. If 10 is added to both of the numbers then the ratio becomes 7:8 then find the smallest number? Choose the correct choice from the following answers:  A) 10  B) 60  C) 30  D) 40  E) 50

Solution: Explanation:   6:7   6x + 10 : 7x + 10 = 7 : 8   8[6x + 10] = 7[7x + 10]   48x + 80 = 49x + 70   49x - 48x = 80 - 70= 
80 - 70 = 10
10   Then smallest number is= 6   6x = 60   Answer: Option 60
Answer: B
A fruit-salad mixture consists of apples, peaches, and grapes in the ratio 12:8:7, respectively, by weight. If 54 pounds of the mixture is prepared, the mixture includes how many more pounds of apples than grapes?  Choose the correct choice from the following options
A) 15	B) 10	C) 9	D) 6	E) 4

Solution: We can first set up our ratio using variable multipliers. We are given that a fruit-salad mixture consists of apples, peaches, and grapes, in the ratio of 6:5:2, respectively, by weight. Thus, we can say:   apples : peaches : grapes = 12x : 8x : 7x   We are given that 54 pounds of the mixture is prepared so we can set up the following question and determine a value for x:   12x + 8x + 7x = 54   27x = 54   x = 2   Now we can determine the number of pounds of apples and of grapes.   pounds of grapes = (7)(2) = 14   pounds of apples = (12)(2) = 24   Thus we know that there are  24-14= 
 24-14 = 10
10 more pounds of apples than grapes.   Answer is 10.
Answer: B
In what time will a railway train 30 m long moving at the rate of 36 kmph pass a telegraph post on its way?  Choose one:
A) 5 sec B) 4 sec C) 3 sec D) 6 sec E) 1 sec

Solution: T = 30/36 * 18/5= 
30/36 * 18/5 = 3
3 sec   Answer: 3 sec
Answer: C
Angelina walked 600 meters from her home to the grocery at a constant speed. She then walked 480 meters to the gym at double the speed. She spent 40 seconds less on her way from the grocery to the gym than on her way from home to the grocery. What was Angelina's speed, in meters per second, from the grocery to the gym?
Select the correct option:
A) 2
B) 3
C) 4
D) 9
E) 12

Solution: let the speed be X...   so time taken from home to grocery= 600/x..   the speed to gym = 2x..   so time taken = 480/2= 
480/2 = 240
240/x..   its given 600/x-240/x=40..   360/x=40..   x=9m/secs..   so grocery to gym=2*9= 
2*9 = 18
18m/s...   9
Answer: D
An alchemist discovered that the formula expressing the correct proportions needed to turn ordinary metal into gold is G = 3/2M + 15, where G is the number of gold bars and M is the number of metal bars. If a metal bar weighs twice as much as a gold bar, how many metal bars will yield an equal weight of gold?	Pick one
A) 10
B) 15
C) 22.5
D) 30
E) 67.5

Solution: Plug in the answer choices!   A --- 30/2 + 15 = 30 --- wrong   B --- 45/2 + 15 = not an integer --- wrong   C --- 22.5(3/2) + 15 = not an integer --- wrong   30 --- 90/2+15 = 60 --- CORRECT   ANSWER:30
Answer: D
It is being given that (232 + 1) is completely divisible by a whole number. Which of the following numbers is completely divisible by this number? Choices: A) (296 + 1) B) (216 + 1) C) (216 - 1) D) (217 - 1) E) None

Solution: Let 232 = x. Then, (232 + 1) = (x + 1).   Let (x + 1) be completely divisible by the natural number N. Then,   (296 + 1) = [(232)3 + 1] = (x3 + 1) = (x + 1)(x2 - x + 1), which is completely divisible by N, since (x + 1) is divisible by N.   Option (296 + 1)
Answer: A
If ‘DELHI’ is coded as ‘FGNJK’, then ‘PUNE’ is coded as
Choose the correct choice from the following answers.
A) RWPG  B) TGFR  C) UHTG  D) WEDS  E) OKJY

Solution: D= 4 = 4+2= 
4+2 = 6
6= F   E = 5 = 5+2= 
5+2 = 7
7= G   SIMILRWPGRLY,   P = 16 = 16+2= 
16+2 = 18
18=R   U = 21 = 21+2= 
21+2 = 23
23=W   N = 14 = 14+2= 
14+2 = 16
16= P   E = 5 = 5+2= 
5+2 = 7
7= G   SO RWPGNS IS   RWPG
Answer: A
David and Lewis leave Chennai for Hyderabad simultaneously at 8 P.M in the night driving in two cars at speeds of 50 mph and 70 mph respectively. As soon as Lewis reaches Hyderabad he returns back to Chennai along the same route and meets David on the way back. If the distance between the two cities is 350 miles, how far from Chennai did David and Lewis meet?	Select the correct option:	A) 250 miles	B) 240 miles	C) 230 miles	D) 235 miles	E) 75 miles

Solution: Time taken by Lewis to reach Hyderabad = 350/70= 
350/70 = 5
5 hours   In 5 hours, David travels 50*5= 
50*5 = 250
250 miles   So distance at which they meet should be greater than 250 miles.   Only A satisfies.   250 milesnswer is 250 miles.
Answer: A
How many Q ways can you group 3 people from 4 sets of twins if no two people from the same set of twins can be chosen? Choose the correct choice.
A) 3	B) 16	C) 28	D) 32	E) 56

Solution: Ways to select 3 people from 8 people (4 twins x 2) = 8C3 = 56   Ways to select 1 twin + 1 people = 4C1*6C1 = 24   Ways to select a group 3 people from 4 sets of twins if no two people from the same set of twins can be chosen Q= 56 - 24= 
56 - 24 = 32
32   Ans: 32
Answer: D
In how many different number of ways 5 men and 3 women can sit on a shopa which can accommodate persons?  Choose the correct option:  A) 25  B) 30  C) 75  D) 40  E) 56

Solution: 8p2 = 8 x 7 = 56   56)
Answer: E
A salesman sold twice as much pears in the afternoon than in the morning. If he sold $450 kilograms of pears that day, how many kilograms did he sell in the afternoon?
Answers.
A) 120 B) 180 C) 300 D) 280 E) 320

Solution: 3x=450   x=150   Therefore, the salesman sold 150kg in the morning and 2⋅150=300 kg in the afternoon. So answer is 300.
Answer: C
A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that exactly three bulbs are good.
A. 20/31  Choose the correct answer:
A) 80/63	B) 20/63	C) 20/93	D) 20/03	E) 20/53

Solution: Explanation:   Required probability = (⁵C₃ . ⁴C₁)/⁹C₄ = (10 * 4)/126 = 20/63   Answer: Option 20/63
Answer: B
In a certain supermarket, a triangular display of cans is arranged in 9 rows, numbered 1 through 9 from top to bottom. Each successively numbered row contains 3 more cans than the row immediately above it. If there are fewer than 120 cans in the entire display, how many cans are in the seventh row?  Choose the correct choice from the following options
A) 13	B) 15	C) 17	D) 19	E) 21

Solution: Let x be the number of cans in row 1.   The total number of cans is x + (x+3) + ... + (x+24) =   9x + 3(1+2+...+8) =   9x + 3(8)(9)/2 =   9x + 108   Since the total is less than 120, x must equal 1.   The number of cans in the 7th row is 1 + 3(6) = 19   The answer is 19.
Answer: D
By travelling at 40 kmph, a person reaches his destination on time. He covered two-third the total distance in one-third of the total time. What speed should he maintain for the remaining distance to reach his destination on time?	Choose the correct choice from the following answers
A) 20 kmph
B) 17 kmph
C) 15 kmph
D) 14 kmph
E) 13 kmph

Solution: Let the time taken to reach the destination be 3x hours. Total distance   = 40 * 3= 
40 * 3 = 120
120x km   He covered 2/3 * 120= 
2/3 * 120 = 80
80x km in 1/3 * 3x= x hours So, the remaining 40x km, he has to cover in 2x hours. Required speed   = 40x/2x = 20 kmph.   20 kmphnswer:20 kmph40 /2= 
40 /2 = 20
20 kmph.   20 kmphnswer:20 kmph
Answer: A
If a and b are the two values of t that satisfy
the equation t^2 â€“ 12t + 20 = 0, with a > b, what is the value of a â€“ b?
Choose the most appropriate option:
A) 2 B) 4 C) 6 D) 8 E) 10

Solution: Factor the left side of the equation:   t^2 â€“ 12t + 20 = 0   (t â€“ 2)(t â€“ 10) = 0   t = 2, t = 10   Thus, a = 10 and b = 2. So a â€“ b = 10 â€“ 2 = 8.   The answer is 8.
Answer: D
Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1120?
Choose the correct choice
A) 1000  B) 2877  C) 2769  D) 2776  E) 9871

Solution: 1120 = P [1 + (5*12/5)/100]   P= 1000   1000nswer:1000
Answer: A
If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 3 years the amount to be paid is?  Choose the correct choice
A) 3377	B) 2688	C) 2688	D) 8436	E) 1268

Solution: A = 7500(26/25)^3 = 8436   Answer: 8436
Answer: D
Which is the odd number out?
9421, 7532, 9854, 8612, 6531, 8541  Answers:
A) 8612	B) 8626	C) 2579	D) 6642	E) 7493

Solution: C   8612.   8612ll the other numbers have their digits in descending order.
Answer: A
Which of the following can be a perimeter q of a triangle inscribed in a circle of radius 1?
I. 0.001
II. 0.010
III. 0.100  Choose the correct choice from the following choices.
A) I only  B) III only  C) II and III only  D) I, II, and III  E) Not I, II, or III

Solution: Yes,the length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.   But how do you use the above property to solve the question?   The lower limit of the perimeter of an inscribed triangle in a circle of ANY radius is 0: q>0.   Answer is I, II, and III.
Answer: D
A car is purchased on hire-purchase. The cash price is $23 000 and the terms are a deposit of 10% of the price, then the balance to be paid off over 60 equal monthly instalments. Interest is charged at 12% p.a. What is the monthly instalment?  Answers
A) $503  B) $504  C) $515  D) $543  E) $552

Solution: $552xplanation:   Cash price = $23 000   Deposit = 10% Ã— $23 000 = $2300   Loan amount = $23000 âˆ’ $2300   Number of payments = 60   = $20700   I=p*r*t/100   I=12420   Total amount = 20700 + 12420= 
20700 + 12420 = 33_120
$33120   Regular payment= total amount /number of payments =552   Answer: $552
Answer: E
A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is?	Answers.
A) 22 B) 50 C) 888 D) 277 E) 21

Solution: Speed of the train relative to man = 125/10 = 25/2 m/sec.   = 25/2 * 18/5= 
25/2 * 18/5 = 45
45 km/hr   Let the speed of the train be x km/hr. Then, relative speed= (x - 5) km/hr.   x - 5 = 45 => x = 50 km/hr.   Answer: 50
Answer: B
The total age of A and B is 13 years more than the total age of B and C. C is how many year younger than A
Select the correct option: A) A)11 B) B)12 C) C)13 D) D)14 E) E)15

Solution: Explanation:   Given that A+B = 13 + B + 13= 
+ 13 = 13
> A – 13= 13 + B – B = 13   => 13 is younger than A by 13 years   Answer: Option 13
Answer: C
Niki covers a distance in 45 min , if she drives at a speed of 60 km/h on an average. Find the speed at which she must drive at to reduce the time of the journey by 50%.	Choose the correct option
A) 101.02 kmph  B) 121.62 kmph  C) 100.62 kmph  D) 111.00 kmph  E) 121.00 kmph

Solution: Given Speed = 60 Kmph.   It means Niki covered 60 km in 60 min (1 hour). So, in 45 min he will cover 45 km.   50% time reduced = 45 - 50% of 45 = 22.5 min.   Thus, Niki needs to cover 45 km in 22.5 min (0.37hour).   Speed * Time = Distance.   Speed * 0.37 = 45   Speed = 121.62 kmph.   ANSWER : OPTION 121.62 kmph
Answer: B
Anup was asked to find the value of 7/12 of a sum of money T. Instead of multiplying the same by 7/12,he divided it by 7/12 and his answer exceeded the correct answer by 95. The correct answer is:  Choose the most appropriate option.
A) 48
B) 89
C) 84
D) 69
E) 49

Solution: T=12/7*x-7/12*x=95 --> x=84 --> 7/12*x=49.   So if bythe correct answerquestion means 7/12 of the amount then the answer should be 49.
Answer: E
What is the difference between the place values of two fives in the numeral 7589452
Choose the correct choice from the following answers.
A) 499950 B) 411150 C) 500050 D) 500000 E) 50

Solution: Required difference = 500000-50= 
500000-50 = 499_950
499950   499950nswer is 499950
Answer: A
At the wholesale store you can buy an 8-pack of hot dogs for $1.75, a 20-pack for $3.05, and a 250-pack for $22.95. What is the greatest number of hot dogs you can buy at this store with $250?	Pick one.
A) 1,108 B) 2,100 C) 2,108 D) 2,628 E) 2,256

Solution: To maximize number of hot dogs with 250$   Total number of hot dogs bought in 250-pack = 22.95*10= 
22.95*10 = 229.5
229.5$   Amount remaining= 250 - 229.5= 
250 - 229.5 = 20.5
20.5$   Total number of hot dogs bought in 20-pack= 3.05*6= 
3.05*6 = 18.3
18.3$   Amount remaining= 20.5 - 18.3= 
20.5 - 18.3 = 2.2
2.2$   Total number of hot dogs bought in 8-pack= 1.55*1= 
1.55*1 = 1.55
1.55$   Amount remaining= 2.2 - 1.75= 
2.2 - 1.75 = 0.45
0.45$   This amount is too less to buy any 8- pack .   Greatest number of hot dogs one can buy with 250 $= 250*10+20*6+8*1= 
250*10+20*6+8*1 = 2_628
2628   Answer 2,628
Answer: D
An accurate clock shows 8 o'clock in the morning. Through how many degrees will the hour hand rotate when the clock shows 2 o'clock in the afternoon?	Choose the most appropriate option
A) 144
B) 150
C) 168
D) 180
E) None

Solution: Explanation :   Angle traced by hour hand in   5 hrs 10 min. = (360/12 x 6)   = 180.   Answer : 180
Answer: D
For the infinite sequence of numbers a1, a2, a3, ..., an, ..., for all n > 1, an = an−1an−1 + 4 if n is odd and an = an−1 if n is even. What is the value of a1a1 if a34 = 68?  Choose one:  A) 10  B) 11  C) 12  D) 13  E) 21

Solution: a34= 68 = a33 - 1= 
33 - 1 = 32
a32 - 1 +4 ... and so on   So observing the trend,   a34= a1 +(32/2) * 4 - (34/2) * (-1)   [32/2 to get all the even n (from 32 to 2) and 34/2 to get all the odd n (from 33 to 1) including 33 and 1]   a1 = 68-64+17= 
68-64+17 = 21
21   Hence, answer will be 21.
Answer: E
A and B can do a piece of work in 12 days and 16 days respectively. Both work for 3 days and then A goes away. Find how long will B take to complete the remaining work?
Answers: A) 6 days B) 7 days C) 4 days D) 9 days E) 2 days

Solution: 3/12 + (3 + x)/16 = 1   x = 9 days   Answer: 9 days
Answer: D
Patanjali walked for 3 days. She walked 18 miles on the first day, walking 3 miles per hour. On the second day she walked for one less hour but she walked one mile per hour, faster than on the first day. On the third day she walked the same number of hours as on the first day, but at the same speed as on the second day. How many miles in total did she walk?
Choose the most appropriate option:
A) 24
B) 44
C) 58
D) 60
E) 62

Solution: Patanjali walked 18 miles on the first day, walking 3 miles per hour i.e. total time of walk on Day-1 = 18/3= 
18/3 = 6
6 Hours   Second day time of walk= 6-1= 
6-1 = 5
5 hours and Speed= 3+1= 
3+1 = 4
4 miles per hour i.e. Distance walked on second day= 5*4= 
5*4 = 20
20 miles   Third day time of walk= 6 hours and Speed = 4 miles per hour i.e. Distance walked on second day = 6*4= 
6*4 = 24
24 miles   Total Distance travelled on three days= 18+20+24= 
18+20+24 = 62
62   Answer: Option 62
Answer: E
It takes Jack 2 more hours than Tom to type 20 pages. If working together, Jack and Tom can type 25 pages in 3 hours, how long will it take Jack to type 40 pages?	Choose one:  A) 5  B) 6  C) 8  D) 10  E) 12

Solution: let's take answer choice D -10 h   if it took 10 h for 40 pages, then it took 5 hours for 20 pages   since it takes Jack 2 more hours than Tom to type 20 pages, Tom's time is 5-2= 
5-2 = 3
3 h   their combo time 5*3 /(5+3)=15/8   if it takes 3 h for 25 pages, then it will take 12/5 h ( =20*3/25) for 20 pages   as u see 15/8 <12/5 . so D is out, and we should check 12, whose number is more than D's   answer choice 12 = 12 for 40 pages or 6 for 20 pages   then Tom's time =6-2= 
6-2 = 4
4 h   combo time=6*4/(6+4)=12/5   if it takes 3 h for 25 pages, then it will take 12/5 h ( =20*3/25) for 20 pages   12/5=12/5   answer choice 12
Answer: E
If cement, gravel and sand are to be mixed in 7:10:13 and 5 tons of cement is available how many tons of mixture can be produced assuming that sufficient gravel and sand is readily available. Choose the correct choice from the following choices:  A) 35 7/8  B) 36  C) 34 2/7  D) 21 3/7  E) 34 6/7

Solution: Cement:Gravel:Sand = 7:10:13 --> total of   7+10+13= 
  7+10+13 = 30
30 parts.   If we use 8 tons of cement, then we'll get 5/7*30=21 3/7 tons of mixture.   Answer: 21 3/7.
Answer: D
The avg weight of A,B & C is 84 kg. If D joins the group, the avg weight of the group becomes 80 kg.If another man E who weights is 6 kg more than D Replaces A, Then the avgof B,C,D&E becomes 79 kg. What is the weight of A? Choose the correct choice from the following answers:
A) 45
B) 65
C) 75
D) 78
E) 90

Solution: A + B + C = 3 *84= 
3 *84 = 252
252   A + B + C + D= 4 * 80= 
4 * 80 = 320
320 ---- (i)   So, D= 68& E = 68 + 6= 
68 + 6 = 74
74   B + C + D +E= 79 * 4= 
79 * 4 = 316
316 --- (ii)   From Eq. (i) & (ii)   A-E= 320 – 316 = 4   A = E +4 = 74 + 4= 
74 + 4 = 78
78   78
Answer: D
A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?  Pick one.
A) 1/5	B) 2/5	C) 3/5	D) 4/5	E) None of them

Solution: Suppose the vessel initially contains 8 litres of liquid.   Let x litres of this liquid be replaced with water.   Quantity of water in new mixture = (3 -(3x/8)+ x)litres   Quantity of syrup in new mixture = (5 - 5x/8) litres   Therefore, (3 - (3x/8)	+ x)	= 5 -	5x/8)   = 5x + 24 = 40 - 5x   = 10x = 16   = x = 8/5   So, part of the mixture replaced = (8/5 x 1/8)= 1/5   1/5nswer is 1/5.
Answer: A
The average of thirteen numbers is 9. The average of first six numbers is 5 and the average of last six numbers is 7. What is the middle number?  Pick one:
A) 47
B) 45
C) 25
D) 37
E) 44

Solution: The total of thirteen numbers = 13X9 = 117   The total of first 6 and last 6 numbers is = 6 X 5+6 X 7 = 72   So, the middle number is  (117 - 72 )= 
 (117 - 72 ) = 45
45   45
Answer: B
A man spent 1/5 of his loan amount on house construction and 1/4 of the remaining on his office renovation. How much fraction of the loan amount is he left with after spending on house and office renovation?	Choose the correct choice from the following answers:	A) 3/5	B) 2/6	C) 5/4	D) 1/5	E) 4/3

Solution: The man spent 1/5 his loan amount on house construction, remaining amount is 4/5   He spent 1/4 of the remaining amount for office renovation, 1/4*4/5=4/20   Total loan amount spent on house and office renovation =1/5+4/20   To get a common denominator we use 20, so 1/5 is 4/20   4/20+4/20=8/20 is the total amount spent on house construction and office renovation.   remaining 12/20 is left with the man, 3/5   3/5nswer is 3/5
Answer: A
If a and b are different values and a – b = 6(√a - √b), then in terms of b, a equals:	Choices:
A) √b B) b C) b - 12√b + 36 D) b + 2√b + 1 E) b^2 – 2b√b + b

Solution: (√a)^2 - (√b)^2 = 6(√a - √b) -----> ( √a + √b) ( √a - √b) = 6(√a - √b) -------> √a + √b = 6, so   √a = 6 - √b, square both sides and solve. Answer is b - 12√b + 36.
Answer: C