MU-NLPC/Calc-aqua_rat huggingface dataset:
The sequence a1, a2, a3, a4. a5 is such that an = a n-1 +5 for 2≤ n ≤ 5. If a5 = 39 what is the value of a1 ?
Choose the correct choice from the following answers:  A) 1  B) 6  C) 19  D) 16  E) 21

Solution: Here, each value of an is the previous value plus 5   Since the numbers are less, the fastest way to solve this problem is to successively subtract 5 from a5 till you reach a1   a5 = 39   a4 = 34   a3 = 29   a2 = 24   a1 = 19 <<<< Ans 19
Answer: C
What is the probability that Company Q's advertisement will be one of the first two be shown during the first commercial break?  Pick one:
A) 1/ 225	B) 1 / 30	C) 1 /15	D) 2 / 15	E) 4 /15

Solution: Q 1/15 + (14/15) * 1/14 = 2/15 2 / 15
Answer: D
In a jar there are balls in different colors: blue, red, green and yellow.
The probability of drawing a blue ball is 1/8.
The probability of drawing a red ball is 2/5.
The probability of drawing a green ball is 7/10.
If a jar cannot contain more than 50 balls, how many yellow balls are in the Jar?  Pick:
A) 12	B) 15	C) 23	D) 7	E) 5

Solution: answer of 1st   just add the given probabilities p(blue)+p(red)+p(green) i.e   1/8+2/5+ 3/10=5+16+12/40   now we know p(blue)+p(red)+p(green)+p(yellow)=1   33/40+p(yellow)=1   p(yellow)=33/40   i.e why yellow balls are 7.   7
Answer: D
In a box, there are 10 blue, 12 white and 10 yellow bulbs. One bulb is picked up randomly. What is the probability that it is neither white nor blue?	Choose the correct answer.
A) 3/16
B) 5/16
C) 8/32
D) 2/32
E) 9/32

Solution: Total number of bulbs = (10 + 12 + 10)= 
(10 + 12 + 10) = 32
32.   Let E= event that the bulb drawn is neither white nor blue = event that the bulb drawn is yellow.   Therefore, P(E)=10/32= 5/32   ANSWER:5/16
Answer: B
A car takes 6 hours to cover a distance of 540 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?
Choose the most appropriate option:
A) 35 Kmph
B) 48 Kmph
C) 52 Kmph
D) 54 Kmph
E) 60 Kmph

Solution: Time = 6   Distance = 540   3/2 of 6 hours = 6 * 3/2= 
6 * 3/2 = 9
9 Hours   Required speed= 540/9= 
540/9 = 60
60 Kmph   60 Kmph)
Answer: E
Edward traveled the entire 60 miles trip. If he did the first 3 miles of at a constant rate 24 miles per hour and the remaining trip of at a constant rate 48 miles per hour, what is the his average speed, in miles per hour? Answers:
A) 20mph	B) 24mph	C) 30mph	D) 32mph	E) 53mph

Solution: Average speed=sum of distance/sum of time. If he travelled the first 3 miles at 24 miles/hr, it would take 0.125 hr. For the remaining trip, if he went at 48 miles/1hr, it would take 1 hour. Then, the average speed is 60miles/(0.125+1)hrs=53miles/1hr.   Therefore, the answer is 53mph.
Answer: E
How many different 6-letter sequences are there that consist of 2A, 7B's and 3C's ?	Select the correct option: A) 6 B) 60 C) 120 D) 360 E) 720

Solution: How many different 6-letter sequences are there that consist of 2 A, 7B's, and 3 120's?   (A) 6   (B) 60   (120) 120   (D) 360   (E) 720 (ANS 120)
Answer: C
100 liters of a mixture contains milk and water in the ratio 7:3. If 10 liters of this mixture be replaced by 10 liters of milk, the ratio of milk to water in the new mixture would be? Choose the correct option
A) 7:8
B) 8:3
C) 3:8
D) 8:7
E) 7:1

Solution: Quantity of milk in 100 liters if mix = 100*7/10= 
100*7/10 = 70
70 liters   Quantity of milk in 110 liters of new mix= 80+10 = 80liters   Quantity of water in it = 110-80= 
110-80 = 30
30 liters   Ratio of milk and water in new mix= 80:30 = 8:3   Answer is 8:3
Answer: B
What is the sum of all digits for the number 10^29 - 41?	Choices
A) 257
B) 242
C) 231
D) 202
E) 187

Solution: 10^29 is a 30-digit number: 1 followed by 29 zeros.   10^29 - 41 is a 29-digit number: 27 9's and 59 at the end.   The sum of the digits is  27*9+5+9= 
 27*9+5+9 = 257
257.   The answer is 257.
Answer: A
The ratio of Red Balls to Blue Balls is 3:7. 70% of the Red balls and 30% of the Blue balls are tennis balls. How many of the balls are tennis balls?  Choose the correct answer:
A) 44%
B) 40%
C) 45%
D) 42%
E) 48%

Solution: let total no of Balls 100, Red Ball 30 and Blue Ball 70, so tennis ball for Red and Blue Ball respectively 30* 70/100= 
30* 70/100 = 21
21 and   70* 30/100= 
  70* 30/100 = 21
21   so total 42 tennis balls out of 100 balls..so required % is 42%   ANSWER:42%
Answer: D
20% loss on the selling price is what percent loss on the cost price? Choose the correct choice from the following options.
A) 27/7%
B) 47/11%
C) 50/3%
D) 63/8%
E) 101/110%

Solution: Let S.P. = $100   Then, loss = $20   C.P. = 100+20= 
100+20 = 120
$120   Loss%= 20/120 * 100 = 50/3%   Answer is 50/3%
Answer: C
When the number 9y30012 is exactly divisible by 11, what is the smallest whole number that can replace y?  Pick one:  A) 1  B) 2  C) 5  D) 6  E) 8

Solution: The given number =9y30012   Sum of the odd places =2+0+3+9= 
2+0+3+9 = 14
14   Sum of the even places= 1+0+y   (Sum of the odd places)- (Sum of even places) = Number (exactly divisible by 11)   14-(1+y) = divisible by 11   13 � y = divisible by 11.   Y must be 2, to make given number divisible by 11.   2
Answer: B
If 6 persons can do 6 times of a particular work in 6 days, then, 7 persons can do 7 times of that work in
?
Choose the correct choice from the following choices:
A) 3 days  B) 7 days  C) 6 days  D) 11 days  E) 15 days

Solution: That is, 1 person can do one time of the work in 6 days.   Therefore, 7 persons can do 7 times work in the same 6 days itself.   Option '6 days'
Answer: C
A boat goes 100 km downstream in 10 hours, and 75 m upstream in 15 hours. The speed of the stream is?	Options.
A) 22 1/2 B) 22 18/2 C) 28 1/2 D) 22 1/5 E) 22 1/4

Solution: 100 --- 10 DS = 10   ? ---- 1   75 ---- 15 US = 5   ? ----- 1 S = (10 - 5)/2   = 22 1/2 kmph.22 1/2nswer: 22 1/2
Answer: A
Of the three- digit integers greater than 700, how many have two digits W that are equal to each other and the remaining digit different from the other two?  Choose the most appropriate option.
A) 90 B) 82 C) 80 D) 45 E) 36

Solution: three-digit integers greater than 700: 701 to 999, inclusive.   possible values for hundreds-digit--> 7,8,9   possible values for tens-digit and ones-digit --> 0, 1,2,3,4,5,6,7,8,9   when hundreds-digit and tens-digit are the same: (3x1x10)-3=27 ---> we minus three to exclude 777, 888 and 999   when hundreds-digit and ones-digit are the same: (3x10x1)-3=27 ---> we minus three to exclude 777, 888 and 999   when tens-digit and hundreds-digit are the same:[(3x10x1)-3]-1=26 ---> we minus three to exclude 777, 888 and 999; we minus one to exclude 700   W=27+27+26= 
27+27+26 = 80
80   Answer: 80
Answer: C
A cheese factory sells its cheese in rectangular blocks. A normal block has a volume of three cubic feet. If a large block has twice the width, twice the depth, and three times the length of a normal block, what is the volume of cheese in a large block in cubic feet? Choose the correct choice
A) 18 B) 6 C) 27 D) 48 E) 36

Solution: Volume of cube=lbh=3   New cube l ,b, h are increases of 3l,2b,2h   New volume of cube =3l*2b*2h=12lbh   3 *2 *2= 
3 *2 *2 = 12
12lbh=12*3= 
12*3 = 36
36   Answer: 36
Answer: E
A can do a piece of work in 12 days. When he had worked for 2 days B joins him. If the complete work was finished in 8 days. In how many days B alone can finish the work?
Choose the correct choice
A) 2 days
B) 25days
C) 9 days
D) 18 days
E) 3 days

Solution: Explanation:   8/12 + 6/x = 1   X = 18 days   Answer: 18 days
Answer: D
The length of the longest tape in cm which can be used to measure exactly, the length 10m; 3m 85cm; and 11m 50cm is:  Pick
A) 5 B) 35 C) 34 D) 36 E) 38

Solution: The three lengths in cm are 1000, 385 & 1150.   HCF of 700, 385 & 1295 is 5.   Hence, the answer is 5 cm.   5NSWER:5
Answer: A
If y exceeds x by 35%, then x is less than y by? Choose the correct choice from the following
A) 16 2/9%
B) 25 5/27%
C) 16 2/3%
D) 12 2/3%
E) 16 1/3%

Solution: X=100	y=135   135------35   100-------? => 25 5/27%   Answer:25 5/27%
Answer: B
The value of a 10.5% stock, in which an income of Rs.756 is derived by investing Rs.9000, brokerage being% is : Choose the correct choice from the following choices:
A) Rs. 113.5
B) Rs. 120
C) Rs. 124.75
D) Rs. 137.5
E) Rs. 145.8

Solution: For an income of Rs.756, investment = Rs.9000   For an income of Rs., investment = = Rs.125   For a Rs.100 stock, investment = Rs.125.   Market value of Rs. 100 stock = = Rs. 124.75   Rs. 124.75
Answer: C
There are 2 sections A and B in a class, consisting of 16 and 14 students respectively. If the average weight of section A is 20kg and that of section B is 25kg, Find the average of the whole class? Choose the correct choice from the following answers:
A) 33.5kg
B) 37.25kg
C) 42.45kg
D) 55.12kg
E) 29.78kg

Solution: Total weight of 36+44 students = 16*20 + 14*25= 
16*20 + 14*25 = 670
670   33.5kgverage weight of the class is= 670/20= 
670/20 = 67/2 = around 33.5
33.5 kg   33.5kgnswer is 33.5kg
Answer: A
A jar full of whiskey contains 40% alcohol. A part of this whisky is replaced by another containing 19%
alcohols and now the percentage of alcohol was found to be 26%. The quantity of whisky replaced is  Choose the correct option:
A) 43
B) 34
C) 32
D) 23
E) 38

Solution: Explanation :   Concentration of alcohol in 1st Jar = 40%   Concentration of alcohol in 2nd Jar = 19%   After the mixing, Concentration of alcohol in the mixture = 26%   By the rule of alligation,   Concentration of alcohol in 1st Jar Concentration of alcohol in 2nd Jar   40% 19%   Mean   26%   7 :14   Hence ratio of 1st and 2nd quantities = 7 : 14 = 1 : 2   Answer : Option 23
Answer: D
Two trains of length 300 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 90 kmph. In how much time will the trains cross each other?  Select:
A) 87/7 sec B) 80/7 sec C) 80/9 sec D) 80/5 sec E) 15 sec

Solution: Relative speed = (54 + 90)* 5/18 = 8 * 5= 
8 * 5 = 40
40 mps.   The time required= d/s = (100 + 300 + 200)/40   = 600/40= 
600/40 = 15
15 sec.   Answer: 15 sec
Answer: E
A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. How far is the place?	Options:
A) 2.89	B) 2.88	C) 2.85	D) 2.84	E) 2.82

Solution: M = 6   S = 1.2   DS = 6 + 1.2= 
6 + 1.2 = 7.2
7.2   US= 6 - 1.2= 
6 - 1.2 = 4.8
4.8   x/7.2 + x/4.8= 1   x = 2.88   Answer:2.88
Answer: B
By selling an umbrella for Rs. 300, a shop keeper gains 20%. During a clearance sale, the shopkeeper allows a discount of 10% on the marked price. His gain percent during the sale is?	Choose the correct choice from the following answers
A) 5% B) 2% C) 8% D) 3% E) 4%

Solution: Marked price = Rs. 300   C.P. = 100/120 * 300 = Rs. 250   Sale price = 90% of Rs. 300 = Rs. 270   Required gain % = 20/250 * 100= 
20/250 * 100 = 8
8%.   Answer: 8%
Answer: C
A company has issued 500 preferred shares and 400 common shares both of par value Rs. 100 each. The dividend on a preferred share and a common share is 8% and 12%, respectively. The company had a total profit of 150000 rupees out of which some amount was kept in reverse fund and the remaining disturbed as dividend. Find the amount kept in reserve fund.
Choose the correct choice from the following answers:
A) 141000 B) 141500 C) 141300 D) 141250 E) 141200

Solution: Face value of each preferred share = 100   Dividend per preferred share = 100×8/100   Total dividend in all preferred shares = (500×100×8)/100=Rs.4000   Face value of each common share = 100   Dividend per common share = 100×12/100   Total dividend in all common shares = 400×100×12/100 = Rs.4800   Total dividend = Rs.4000 + Rs.4800 = Rs.8800   amount kept in reserve fund = Rs.150000 - Rs.8800 = Rs.141200   Answer is 141200.
Answer: E
A waitress's income consists of her salary and tips.During one week ,her tips were 11/4 of her salary.What fraction of her income for the week came from tips?	Select the correct option
A) 1/9 B) 1/6 C) 1/3 D) 4/9 E) 11/15

Solution: Her tips were 11/4 of her salary.   Let's say her salary =$4   This mean her tips = (11/4)($4) =$11   So, her TOTAL INCOM11/15 =$4+$11=$15   What fraction of her income for the week came from tips   $11/$15 4+ 11= 
4+ 11 = 15
$15   What fraction of her income for the week came from tips   $11/$15=11/15   = 11/15
Answer: E
If the sum of one-third and one-half of a number exceeds two-third of a number by 5, the number is Choose the correct answer
A) 30
B) 32
C) 36
D) 40
E) 50

Solution: Explanation:   Let the number be x. Then,   x/3 + x/2 = 2x/3 + 5   = 5x/6 - 2x/3 = 5   = x/6 = 5   = x = 30   30nswer: Option 30
Answer: A
What least number mustbe subtracted from 427398 so that remaining no.is divisible by 15  Choose the correct answer
A) 3
B) 4
C) 6
D) 7
E) 8

Solution: Explanation:   On dividing 427398 by 15 we get the remainder 3, so 3 should be subtracted   3nswer: Option 3
Answer: A
The distance between two cities A and B is 330 Km. A train starts from A at 8 a.m. and travel towards B at 60 km/hr. Another train starts from B at 9 a.m and travels towards A at 75 Km/hr. At what time do they meet? Answers:  A) 10 a.m  B) 10.30 a.m  C) 11 a.m  D) 11.30 a.m  E) None of these

Solution: Explanation:   Suppose they meet x hrs after 8 a.m   then,   [Distance moved by first in x hrs] + [Distance moved by second in (x - 1) hrs] = 330.   Therefore, 60x + 75(x - 1) = 330.   => x = 3.   So,they meet at (8 + 3) i.e, 11a.m.   Answer: 11 a.m
Answer: C
A man gets a simple interest of Rs.800 on a certain principal at the rate of 5% p.a in two years. Find the compound interest the man will get on twice the principal in two years at the same rate. Choose one
A) Rs.500  B) Rs.250  C) Rs.5012.50  D) Rs.5062.50  E) 410

Solution: Let the principal be Rs.P   S.I at 5% p.a in 8 years on Rs.P = Rs.800   (P)(8)(5)/100 = 800   P = 2000   C.I on Rs.2P i.e., Rs.4000 at 5% p.a in two years   =4000{ [1 + 5/100]2 - 1} = 4000{ 212 - 202 /202}   = Rs.410   ANSW410R:410
Answer: E
How should we mix two rice packets to get one 1kg packet priced at Rs 8 when the prices of 1 kg packets of the two types are Rs 7.1 and Rs 9.2. Options.
A) 4:3
B) 4:7
C) 4:9
D) 4:2
E) 4:1

Solution: Explanation:   No explanation is available for this question!   4:3NSWER: 4:3
Answer: A
If DON is coded as 18 and MASS is coded as 29 Then KING is coded as
Choose the correct choice:	A) 21	B) 20	C) 19	D) 17	E) None

Solution: KING = 11+9+14+7= 
11+9+14+7 = 41
41 i.e (4*4)+(1*1)=17   MASS = 13+1+19+19= 
13+1+19+19 = 52
52 i.e (5*5)+(2*2)=29   17ON = 4+14+15= 
4+14+15 = 33
33 i.e(3*3)+(3*3)=18   ANSWER:17
Answer: D
A reduction of 30% in the price of oil enables a house wife to obtain 9kgs more for Rs.900, what is the reduced price for kg? Choose the correct option:	A) 72	B) 27	C) 40	D) 30	E) 20

Solution: 900*(30/100)= 
900*(30/100) = 270
270 ---- 9   ? ---- 1=> Rs.30   Answer:30
Answer: D
A company bought for its 7 offices 2 computers of brand N and 4 computers of brand M. In how many ways could computers be distributed among the offices if each office can have only 1 computer.  Options:
A) 196  B) 105  C) 256  D) 292  E) 312

Solution: This problem has to do withcombinations. Here's the general idea: if you have a set of n elements, and you are going to choose r of them (r < n), then the number of combinations of size r one could choose from this total set of n is:   # of combinations = nCr = (n!)/[(r!)((n-r)!)]   where n! is the factorial symbol, which means the product of every integer from n down to 1. BTW, nCr is readn choose r.   In this problem, let's consider first the three computers of brand M. How many ways can three computer be distributed to seven offices?   # of combinations = 7C4 = 35   There are 35 different ways to distribute three computers to 7 offices. (The massive amount of cancelling that occurred there is very much typical of what happens in the nCr formula.)   One we have distributed those three M computers, we have to distribute 2 N computers to the remaining four offices. How many ways can two computer be distributed to four offices?   # of combinations = 3C2 = 3   For each of the 35 configurations of distributing the M computers, we have 3 ways of distributing the N computers to the remaining offices. Thus, the total number of configurations is 35*3= 
35*3 = 105
105. Answer choice=105
Answer: B
How many 4 letter combinations can be made from the letters of the word VERMONT if the first letter has to be a vowel and the last letter has to be a consonant, and each letter can be used only once?  Choose the correct answer:
A) 21  B) 42  C) 120  D) 600  E) 200

Solution: Vowel: 200 O   Consonants: V R M N T   First letter can be filled in 2 Ways ( As the question states thatfirst letter has to be a vowel)   Fourth letter can be filled in 5 Ways ( As the question states thatthe last letter has to be a consonant)   Now since each letter can be used only once, and 2 letters out of 7 letters are already used in First and fourth letter   Second letter can be filled in 5 Ways   Third letter can be filled in 4 Ways   So, Total number of ways = 2 Ways x 5 Ways x 4 ways x 5 ways = 200   Answer 200
Answer: E
At a party, there were five times as many girls as boys and three times as many adults as children. Which of the following could NOT be the number of people at the party?	Choose the most appropriate option.
A) 258
B) 259
C) 216
D) 120
E) 72

Solution: Five times as many girls as boys --> F = 5M.   Three times as many adults as children --> (F + M) = 3C.   The number of people at the party = F + M + C = 3C + C = 4C.   The number of people at the party must be a multiple of 4. The only answer choice which is NOT a multiple of 4 is A.   258nswer: 258.
Answer: A
The price of rice falls by 20%. How much rice can be bought now with the money that was sufficient to buy 10 kg of rice previously?
Choose the correct choice from the following:
A) 5 kg
B) 12,5 kg
C) 25 kg
D) 30 kg
E) None

Solution: Solution: Let Rs. 100 be spend on rice initially for 10 kg.   As the price falls by 20%, new price for 10 kg rice,   = (100 -20% of 100) = 80   New price of rice = 80/10 = Rs. 8 per kg.   Rice can bought now at = 100/8 = 12,5 kg.   Answer: Option 12,5 kg
Answer: B
If a population of women in a town is 80% of men . What is the population of men as a % of population of women ? Choose the correct choice from the following choices.
A) A)200% B) B)100% C) C)50% D) D)65% E) E)125%

Solution: We're told that the number of Women in a town is equal to 50% of the number of Men in that town.   IF....   Men = 10   Women = 8   We're asked for the number of Men, as a percentage of the number of Women.   M/W = 10/8 = 5/4 = 125%   Answer is 125%
Answer: E
What proximate value should come in place of the question mark (?) in the following question?
8.595 Ã— 1084 + 2568.34 â€“ 1708.34 = ?  Select the correct option.
A) 6,000 B) 12,000 C) 10,000 D) 10148 E) 12312

Solution: ? â‰ˆ 8.6 Ã— 1080 + 2560 â€“ 1700 â‰ˆ 9288 + 860 â‰ˆ 10148   Answer 10148
Answer: D
A financier claims to be lending money at simple interest, But he includes the interest every six months for calculating the principal. If he is charging an interest of 10%, the effective rate of interest becomes. Choose the correct choice from the following options.
A) 9.25% B) 10% C) 10.25% D) 9% E) None of these

Solution: Explanation :   Let the sum is 100.   As financier includes interest every six months , then we will calculate SI for 6 months, then again for six months as below:   SI for first Six Months = (100*10*1)/(100*2) = Rs. 5   Important: now sum will become  100+5= 
 100+5 = 105
105   SI for last Six Months= (105*10*1)/(100*2) = Rs. 5.25   So amount at the end of year will be  (100+5+5.25)= 
 (100+5+5.25) = 110.25
110.25   Effective rate= 110.25 - 100= 
110.25 - 100 = 10.25
10.25   Answer : 10.25%
Answer: C
What percent of 120 are 90? Pick.
A) 33  B) 66  C) 75  D) 44  E) 31

Solution: (?% /100) * 120 = 90   ? = 75%   Answer: 75
Answer: C
for doing any work A take 50% more time than B.if both together finish the work in 18 days,then B alone in how much days finish the work? Choose the correct choice from the following choices.
A) 35 days
B) 30 days
C) 40 days
D) 45 days
E) 50 days

Solution: let 30 days take x days in finishing work   then,A take=150x/100 days=3x/2 days   so,1/x+2/3x=1/18,5/3x=1/18,3x=90,x=30   hence,whole work 30 days finish in 30 days   answer 30 days
Answer: B
A shopkeeper has 100 kg of apples. He sells 50% of these at 25% profit and remaining 50% at 30% profit. Find his % profit on total.
Choose the correct choice from the following:
A) 27.5%	B) 25.6%	C) 31.5%	D) 35.9%	E) 29.5%

Solution: Total number of apples = 100   Let the cost price be x   Selling price at 25% profit = 1.25x   Selling price at 30% profit = 1.3x   Profit % = ((SP - CP)/CP)*100   Profit % = ((1/2)*100*1.25x + (1/2)*100*1.3x - 100x)/100x * 100 = (255-200)/2= 
(255-200)/2 = 55/2 = around 27.5
27.5%   27.5%nswer is 27.5%
Answer: A
Tough and Tricky questions: Word Problems.
It takes Sarah 14 minutes to do one oil change, and it takes Alice 10 minutes. If Sarah and Alice both begin doing oil changes at exactly 9:00 a.m. without pausing, when is the first time at which they will finish changing the oil of a car simultaneously?  Pick
A) 10:00 a.m.  B) 10:42 a.m.  C) 12:00 a.m.  D) 1:00 p.m.  E) 2:00 p.m.

Solution: LCM of 1014   10 = 2 * 5   14 = 2 * 7   LCM = 2 * 5 * 7= 
2 * 5 * 7 = 70
70= 1 hour 10 minutes   1010AM   10:42 a.m.
Answer: B
John’s salary is reduced by 40% and then reduced salary is increased by 40%. Find ,how many percentage his present salary is less as compared to his previous salary?
Choose the correct answer:
A) 12%
B) 14%
C) 16%
D) 18%
E) 20%

Solution: 40*40   -------- = 16%   100   Answer: 16%
Answer: C
What is the ratio between perimeters of two squares one having 3 times the diagonal then the other?	Choose the correct choice from the following
A) 3: 2	B) 3: 0	C) 4: 1	D) 3: 1	E) 2: 2

Solution: d = 3d d = d   a√2 = 3d a√2 = d   a = 3d/√2 a = d/√2 => 3: 1   Answer: 3: 1
Answer: D
Distance between two stations A and B is 778 km. A train covers the journey from A to B at 84 km per hour and returns back to A with a uniform speed of 56km per hour. Find the average speed of the train during the whole journey? Choose the correct choice from the following answers
A) 67.0 km /hr	B) 67.2 km /hr	C) 69.0 km /hr	D) 69.2 km /hr	E) 69.8 km /hr

Solution: let us assume A =x,67.2 km /hr=y   distance between two stations a and b=2*x*y= 2xy   but,train cover a journey of   A=56 km/hr 67.2 km /hr=84 km/hr   Average speed =[2xy/x+y]km/hr   = 2*84*56/(84+56) km/hr   =[2*84*56/140] km/hr   = 67.2 km/hr   ANSWER:67.2 km /hr
Answer: B
What is the least possible product of 4 different integers, each of which has a value between –1 and 10, inclusive?	Choose the most appropriate option.
A) –5040  B) –3600  C) –720  D) –600  E) –120

Solution: Maximize the total product with a -ve sign   so -1 * 10 * 9 * 8 = 720 * -1 = -720   Answer is –720.
Answer: C
The average weight of 16 kids in a class is 50.25 kg and that of the remaining 8 kids is 45.15 kg. Find the average weights of all the kids in the class. Pick:
A) A)48.55  B) B)49  C) C)51  D) D)61  E) E)62

Solution: Required average   = (50.25 x 16 + 45.15 x 8)/(16 + 8)   = (804 + 361.20)/24   = 1165.20/24= 
1165.20/24 = 48.55
48.55kg   48.55nswer is 48.55
Answer: A
At what time between 5.30 and 6 will the hands of a clock be at right angles?
Select the correct option:  A) 43	7/12	min. past 5.  B) 43	7/13	min. past 5.  C) 42	7/11	min. past 5.  D) 42	7/18	min. past 5.  E) 43	7/11	min. past 5.

Solution: At 5 o'clock, the hands are 25 min. spaces apart.   To be at right angles and that too between 5.30 and 6, the minute hand has to gain   (25 + 15)= 
  (25 + 15) = 40
40 min. spaces.   55 min. spaces are gained in 60 min.   40 min. spaces are gained in 60/55 x 40 min= 43 7/11 min.   Required time = 43	7/11	min. past 5.   Answer: 43	7/11	min. past 5.
Answer: E
A tradesman by means of his false balance defrauds to the extent of 10%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?  Choose the correct option: A) 29% B) 17% C) 44% D) 46% E) 21%

Solution: g% = 10 + 10 + (10*10)/100= 
10 + 10 + (10*10)/100 = 21
21%   Answer: 21%
Answer: E