mathewhe/aqua_rat huggingface dataset:
Question: If both 112 and 33 are factors of the number a * 43 * 62 * 1311, then what is the smallest possible value of a?
(A) 121
(B) 3267
(C) 363
(D) 33
(E) None of the above
Rationale: Explanatory Answer
Step 1: Prime factorize the given expression
a * 43 * 62 * 1311 can be expressed in terms of its prime factors as a * 28 * 32 * 1311
Step 2: Find factors missing after excluding 'a' to make the number divisible by both 112 and 33
112 is a factor of the given number.
If we do not include 'a', 11 is not a prime factor of the given number.
If 112 is a factor of the number, 112 should have been in 'a'
33 is a factor of the given number.
If we do not include 'a', the number has only 32 in it.
Therefore, if 33 has to be a factor of the given number 'a' has to contain 31 in it.
Therefore, 'a' should be at least 112 * 3 = 363 if the given number has 112 and 33 as its factors.
The smallest value that "a" can take is 363.
Choice C is the correct answer.
Answer: (C) 363
Question: Of the students at a certain high school, 90 percent took a course in algebra or geometry and 10 percent took courses in both. If the percent of students who took a course in algebra was 3 times the percent of students who took a course in geometry, what percent of the students took a course in algebra but not geometry?
(A) 35%
(B) 45%
(C) 55%
(D) 65%
(E) 70%
Rationale: You can also just use the formula
n(A or B) = n(A) + n(B) - n(A and B)
90 = 3X + X - 10
X = 25
3X = 75
This is the number of people who took algebra including those who took both. To get the number of people who took only algebra, 75 - 10 = 65%
Answer (D)
Answer: (D) 65%
Question: If a certain sample of data has a mean of 25.0 and a standard deviation of 3.0, which of the following values is more than 2.5 standard deviations from the mean?
(A) 12.0
(B) 13.5
(C) 17.5
(D) 23.5
(E) 26.5
Rationale: The standard deviation is 3. 2.5 standard deviations, which is just 2.5 x 3.0 is 7.5. The only answer more than 7.5 away from the mean is C.
Answer: (C) 17.5
Question: At the time of marriage, a man was 7 years elder to his wife. 10 years after their marriage, his age is 4/3 times the age of his wife. What was wife's age at the time of marriage ? Choose one answer.
(A) 36 years
(B) 30 years
(C) 26 years
(D) 24 years
(E) 11 years
Rationale: let wifes age= x
husband age = x+7
now after 10 years of mrg x+10 wifes age
x+7+10 husbands age
4/3(x+10)=x+7+10
after solving x=11
ANSWER:E
Answer: (E) 11 years
Question: 45 x ? = 60% of 900
(A) 16.2
(B) 12
(C) 5
(D) 500
(E) None
Rationale: Answer
Let 45 x A = (60 x 900)/100
∴ A = (60 x 9)/45 = 12
Correct Option: B
Answer: (B) 12
Question: A 500 meter long train crosses a signal post in 40 seconds. How long will it take to cross a 3 kilometer long bridge, at the same speed?
(A) 2 min 48 sec
(B) 4 min 48 sec
(C) 4 min 38 sec
(D) 4 min 18 sec
(E) 4 min 8 sec
Rationale: S = 500/40 = 12.5 mps
S = 3600/12.5 = 288 sec = 4 min 48 sec
ANSWER:B
Answer: (B) 4 min 48 sec
Question: If an amount of Rs 42,460 is distributed equally
amongst 22 persons, how much amount would each
person get?
(A) Rs 1905
(B) Rs 2000
(C) Rs 1930
(D) Rs 765
(E) None
Rationale: Required amount =42460/22 = Rs 1930
Answer C
Answer: (C) Rs 1930
Question: What is the average of four tenths and two thousandths
(A) 0.2022
(B) 0.3325
(C) 0.201
(D) 0.2012
(E) 0.2114
Rationale: Explanation:
Four tenths = 0.4
two thousandths = 0.002
The average is (0.4 + 0.002)/2 = 0.201
Answer: C
Answer: (C) 0.201
Question: If x^2 - 1 = 0 and x < 0, which of the following must be equal to 0 ?
(A)  x^2 - 9x
(B)  x^2 - 9x + 20
(C)  x^2 - 2x + 3
(D)  x^2 + 2x + 1
(E)  x^2 + 5x + 6
Rationale: x^2-1 = 0
x= +1 or x = -1
if we substitute x= -1 in the equation x^2 +2x+1 = 1-2+1 = 0
D is also the answer
Answer: (D)  x^2 + 2x + 1
Question: A factory has 500 workers, 18 percent of whom are women. If 50 additional workers are to be hired and all of the present workers remain, how many of the additional workers must be women in order to raise the percent of women employees to 20 percent?
(A)  3
(B)  10
(C)  20
(D)  30
(E)  35
Rationale: Currently the factory has 0.18*500=90 women.
After 50 additional workers are hired, there will be total of 550 workers and we need 0.2*550=110 of them to be women, so we need 110-90=20 more women.
Answer: C.
Answer: (C)  20
Question: An airplane flies along the four sides of a square field at the speeds of 200, 400, 600 and 800 km/h. The average speed of the plane around the field in km/h is
(A) 384
(B) 400
(C) 500
(D) 284
(E) None of these
Rationale: Explanation :
Let each side of the square field be x km.
So, average speed of the plane
= 4x/((x/800)+(x/600)+(x/400)+(x/200))
= (4*2400)/(3+4+6+12) = 9600/25
= 384
Answer : A
Answer: (A) 384
Question: If N = 2^0.1 and N^b = 16, b must equal
(A) 3/80
(B) 3/5
(C) 40
(D) 5/3
(E) 80/3
Rationale: 10/100 = 1/10
N = 2 ^ 1/10
N^b = 2^4
(2^1/10)^b = 2^4
b = 40
Answer: C
Answer: (C) 40
Question: A can run 4 times as fast as B and gives B a start of 63 m. How long should the race course be so that A and B might reach in the same time?
(A) 70 m
(B) 60 m
(C) 80 m
(D) 65 m
(E) 84 m
Rationale: Speed of A:Speed of B=4:1
means in a race of 4m A gains 3m.
then in a race of 63m he gains 63*(4/3)
I.e 84m
ANSWER:E
Answer: (E) 84 m
Question: Find the amount on Rs.5000 in 2 years, the rate of interest being 4% per first year and 5% for the second year?
(A) 3377
(B) 2678
(C) 5460
(D) 1976
(E) 1671
Rationale: 5000 * 104/100 * 105/100 => 5460
Answer: C
Answer: (C) 5460
Question: A straight fence is to be constructed from posts 6 inches wide and separated by lengths of chain 9 feet long. If a certain fence begins and ends with a post, which of the following could not be the length of the fence in feet? (12 inches = 1 foot)
(A) 29
(B) 48
(C) 55
(D) 67
(E) 86
Rationale: There is one post for each length of chain, plus one final post at the end.
The length of the fence in feet is 9.5x + 0.5, where each is the number of chain lengths.
The length of the fence is an integer when x = 1,3,5,7,...
The length of the fence could be 10, 29, 48, 67, 86,...
The answer is C.
Answer: (C) 55
Question: In how many ways can the letters of the word ED456 be rearranged such that the numbers always appear together?
(A) 25
(B) 16
(C) 36
(D) 9
(E) 29
Rationale: ED456
456 will come together as a group which can be arranged in 3!=6ways.
456,E,D can be arranged in 3!=6 ways.
total possible arrangements = 6*6=36 ways
ANSWER:C
Answer: (C) 36
Question: A, B, C, D and E play a game of cards. A says to B, "If you give me 3 cards, you will have as many as I have at this moment while if D takes 5 cards from you, he will have as many as E has." A and C together have twice as many cards as E has. B and D together also have the same number of cards as A and C taken together. If together they have 150 cards, how many cards has C got ?
(A) 28
(B) 29
(C) 31
(D) 35
(E) 37
Rationale: Explanation:
Clearly, we have :
A = B - 3 ...(i)
D + 5 = E ...(ii)
A+C = 2E ...(iii)
B + D = A+C = 2E ...(iv)
A+B + C + D + E=150 ...(v)
From (iii), (iv) and (v), we get: 5E = 150 or E = 30.
Putting E = 30 in (ii), we get: D = 25.
Putting E = 30 and D = 25 in (iv), we get: B = 35.
Putting B = 35 in (i), we get: A = 32.
Putting A = 32 and E = 30 in (iii), we get: C = 28.
Answer: A
Answer: (A) 28
Question: Two employees X and Y are paid a total of Rs. 330 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?
(A) s.150
(B) s.200
(C) s.250
(D) s.350
(E) s.400
Rationale: Let the amount paid to X per week = x
and the amount paid to Y per week = y
Then x + y = 330
But x = 120% of y = 120y/100 = 12y/10
âˆ´12y/10 + y = 330
â‡’ y[12/10 + 1] = 330
â‡’ 22y/10 = 330
â‡’ 22y = 3300
â‡’ y = 3300/22 = 300/2 = Rs.150
A)
Answer: (A) s.150
Question: A certain car increased its average speed by 4 miles per hour in each successive 5-minute interval after the first interval. If in the first 5-minute interval its average speed was 20 miles per hour, how many miles did the car travel in the third 5-minute interval?
(A) 1.0
(B) 1.5
(C) 2.0
(D) 2.5
(E) 3.0
Rationale: In the third time interval the average speed of the car was 20+4+5=29 miles per hour;
In 5 minutes (1/12 hour) at that speed car would travel 29*1/12=2.5 miles.
Answer: D.
Answer: (D) 2.5
Question: Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 24 kmph and 48 kmph. After how much time will the trains meet?
(A) 20/8 sec
(B) 20/4 sec
(C) 20/7 sec
(D) 22/7 sec
(E) 5 sec
Rationale: They are moving in opposite directions, relative speed is equal to the sum of their speeds.
Relative speed = (24 + 48)*5/18 = 4*5 = 20 mps.
The time required = d/s = 100/20 = 5 sec.Answer:E
Answer: (E) 5 sec
Question: A man sells a horse for Rs.800 and loses something, if he had sold it for Rs.980, his gain would have been double the former loss. Find the cost price of the horse?
(A) 868
(B) 869
(C) 865
(D) 860
(E) 861
Rationale: CP = SP + 1CP = SP - g
800 + x = 980 - 2x
3x = 180 => x = 60
CP = 800 + 60 = 860
Answer: D
Answer: (D) 860
Question: Find the lowest common multiple of 24, 36 and 40.
(A) 360
(B) 420
(C) 510
(D) 320
(E) 280
Rationale: LCM=2*2*2*3*3*5=360.
Answer is A
Answer: (A) 360
Question: The measurement of a rectangular box with lid is 25cmx4cmx18cm. Find the volume of the largest sphere that can be inscribed in the box (in terms of πcm3). (Hint: The lowest measure of rectangular box represents the diameter of the largest sphere)
(A) 11.12
(B) 10.11
(C) 72
(D) 10.66
(E) 9.2
Rationale: d=4, r=2;
Volume of the largest sphere= 4/3πr3
= 4/3 *π*2*2*2= 10.66πcm3 ANSWER:D
Answer: (D) 10.66
Question: Length of a rectangular plot is 10 mtr more than its breadth. If the cost of fencing the plot at 26.50 per meter is Rs. 5300, what is the length of the plot in mtr?
(A) 55 m
(B) 60 m
(C) 80 m
(D) 82 m
(E) 84 m
Rationale: Let breadth = x metres.
Then, length = (x + 10) metres.
Perimeter = 5300 m = 200 m.
26.50
2[(x + 10) + x] = 200
2x + 10 = 100
2x = 90
x = 45.
Hence, length = x + 10= 55 m
A
Answer: (A) 55 m
Question: The concentration of spirit in three different vessels A, B and C are 30%, 50% and 25% respectively. If 4 litres from vessel A, 5 litres from vessel B and 6 litres from vessel C are mixed, find the concentration of spirit in the resultant solution.
(A) 32.54%
(B) 33%
(C) 34.67%
(D) 35%
(E) 36.62%
Rationale: Quantity of spirit in new solution=(4*30/100)+(5*50/100)+(6*25/100)=1.2+2.5+1.5=5.2 liters
So % concentration of spirit=100*5.2/(4+5+6)=34.67%
ANSWER:C
Answer: (C) 34.67%
Question: The side of a rhombus is 24 m and length of one of its diagonals is 18 m. The area of the rhombus is?
(A) 410.47
(B) 403.47
(C) 420.47
(D) 400.47
(E) 300.47
Rationale: area of the rhombus = 1/2 * p * √4(a)2 - (p)2
a= 24 ; p = 18
A=1/2 * 18 *√4(24)2 - (18)2
=1/2 * 18 *√2304 - 324
=1/2 * 18 *√1980
A =400.47
Answer : D
Answer: (D) 400.47
Question: If the C.I. on a sum for 2 years at 12 1/2 % per annum is Rs. 510, the S.I. on the same sum at the same rate for the same period of time is?
(A) 298
(B) 278
(C) 299
(D) 480
(E) 276
Rationale: Let the sum be Rs. P. Then,
[P(1 + 25/(2 * 100))2 - P] = 510
P[(9/8)2 - 1] = 510.
Sum = Rs. 1920
So, S.I. = (1920 * 25 * 2) / (2 * 100) = Rs. 480
Answer: D
Answer: (D) 480
Question: If the number a60,858,61b is evenly divisible by 88, what are the values of a and b?
(A) b = 6, a = 6
(B) b = 2, a = 3
(C) b = 2, a = 1
(D) b = 4, a = 6
(E) b = 4, a = 3
Rationale: a60,858,61b, divisible by 88.
Factors of 88 = (8)(11)
Divisible by 8: if the last 3 digits of the number are divisible by 8.
61b/8 => 616/8 = 77 => b = 6
Divisibe by 11: subtract the last digit from the number, over and over again, as necessary. If the remaining number is divisible by 11, the original number is divisible by 11.
a6085861-6 => a608585-5 => a60858-0 => a6085-8 => a607-7 => a60-0 => a6-0 => a6 => 66/11 = 6.
So a = 6.
Answer: A
Answer: (A) b = 6, a = 6
Question: From a pack of cards, two cards are drawn one after the other, with replacement. What is the probability that the first card is a club and the second card is a king or queen?
(A) 2/13
(B) 3/13
(C) 1/26
(D) 1/52
(E) 3/52
Rationale: P(club) = 1/4
P(king or queen) = 2/13
P(club then a king/queen) = 1/4 * 2/13 = 1/26
The answer is C.
Answer: (C) 1/26
Question: Select the non termination decimal among the following.
(A) 22/3
(B) 3/4
(C) 4/5
(D) 7/8
(E) 9/10
Rationale: A. Non terminating decimal means that 22/3 = 7.33333 and so on.
Answer: (A) 22/3
Question: Two pipes A and B can fill a cistern in 9 and 18 minutes respectively, and a third pipe C can empty it in 24 minutes. How long will it take to fill the cistern if all the three are opened at the same time?
(A) 6 min
(B) 7 min
(C) 8 min
(D) 10 min
(E) 17 min
Rationale: 1/9 + 1/18 - 1/24
= 1/8
8/1= 8
Answer:C
Answer: (C) 8 min
Question: How many liters of water must be evaporated from 50 liters of a 8-percent sugar solution to get a 10-percent solution?
(A) 8
(B) 10
(C) 12
(D) 14
(E) 16
Rationale: 8% of a 50 liter solution is 4L which is 10% of the solution at the end.
The solution at the end must be 40 L.
We need to evaporate 10 liters.
The answer is B.
Answer: (B) 10
Question: The salary of a worker is first increased by 20% and afterwards reduced by 20%. What is the net change in the worker's salary?
(A) 4% decrease
(B) 8% decrease
(C) 4% increase
(D) 8% increase
(E) no change
Rationale: Let x be the original salary.
The final salary is 0.8(1.2x) = 0.96x
The answer is A.
Answer: (A) 4% decrease
Question: A family consists of grandparents, parents and three grand children. The average age of the grandparents is 67 years, that of the parents is 36 years and that of the grandchildren is 6 years. What is the average age of the family?
(A) 28 4â„7 years
(B) 31 5â„7 years
(C) 32 years
(D) 27 1â„2 years
(E) None of these
Rationale: Required average = (67Ã—2+36Ã—2+6Ã—3/2+2+3)
=224/7
= 32 years
Answer C
Answer: (C) 32 years
Question: How many digits to the right of the decimal point are there in the product of .32655 * 65.01?
(A) 8
(B) 5
(C) 4
(D) 6
(E) 7
Rationale: Product of is .32655 * 65.01 is 21.2290155.
Therefore number of digits to right of decimal point is 7
Answer is E.
Answer: (E) 7
Question: Laura has a deck of standard playing cards with 18 of the 54 cards designated as aheart.If Laura shuffles the deck thoroughly and then deals 10 cards off the top of the deck, what is the probability that the 10th card dealt is a heart?
(A) 1/4
(B) 1/3
(C) 5/26
(D) 12/42
(E) 13/42
Rationale: No replacement there, 10 cards are dealt and we are asked to find the probability that 10th card is a heart.
If there is no replacement then how is the (P) that the 10th card is 18/54 ??
there are many cases here to be considered here if there is no replacement such as:
H- Denotes heart X-may be any diamond, spade or club.
1. HXXXXXXXXH
2. HHXXXXXXXH
3. HHHXXXXXXH
.
.
.
.
.
9. HHHHHHHHHH
10. XXXXXXXXXH
All cases from 1 to 10 will have different probabilities for heart to be at the 10th place and it will take hell lot of time to calculate all of them.
For according to me the above solution by Ian is only valid if cards are replaced (Every card has a 18/54 = 1/3 chance of being a heart; it doesn't matter if it's the top card in the deck or the tenth card in the deck.)If that's the case that brings back me to my original question ----how do we determine that the cards are replaced or not?? based on the question given ....
B
Answer: (B) 1/3
Question: A man who goes to work long before sunrise every morning gets dressed in the dark. In his sock drawer he has 6 black and 8 blue socks. What is the probability that his first pick was a black sock, but his second pick was a blue sock?
(A) 24/91
(B) 24/90
(C) 24/97
(D) 24/95
(E) 24/93
Rationale: This is a case of without replacement. We have to multiply two probabilities. 1. Probability of picking up a black sock, and probability of picking a blue sock, given that first sock is black.
6C114C1×8C113C1=24/91
Answer:a
Answer: (A) 24/91
Question: If y exceeds x by 20%, then x is less than y by?
(A) 16 2/8%
(B) 16 8/3%
(C) 16 2/3%
(D) 76 2/3%
(E) 17 2/3%
Rationale: X=100	y=120
120------20
100-------? => 16 2/3%
Answer:C
Answer: (C) 16 2/3%
Question: 1600 men have provisions for 28 days in the temple. If after 4 days, 400 men leave the temple, how long will the food last now?
(A) 82 days
(B) 26 days
(C) 32 days
(D) 34 days
(E) 25 days
Rationale: 1600 ---- 28 days
1600 ---- 24
1200 ---- ?
1600*24 = 1200*x
x = 32 days
Answer:C
Answer: (C) 32 days
Question: A positive integer is divisible by 3 if and only if the sum of its digits is divisible by 3. If the six-digit integer is divisible by 3, and n is of the form 4k2,k21, where k represents a digit that occurs twice, how many values could n have?
(A) 2
(B) 3
(C) 6
(D) 5
(E) 4
Rationale: 4k2k21
Taking sum of the numericals = 4 + 2 + 2 + 1 = 9
We require the values of K such that they are also divisible by 3
402021
432321
462621
492921
Answer = 4 = E
Answer: (E) 4
Question: One root of the quadratic equation x2 - 12x + a = 0, is thrice the other. Find the value of a?
(A) 29
(B) -27
(C) 28
(D) 7
(E) None of these
Rationale: Let the roots of the quadratic equation be x and 3x.
Sum of roots = -(-12) = 12
a + 3a = 4a = 12 => a = 3
Product of the roots = 3a2 = 3(3)2 = 27.
ANSWER:E
Answer: (E) None of these
Question: Find the angle between the hour hand and the minute hand of a clock when 3.25.
(A) 47 1/2°
(B) 45 1/2°
(C) 48 1/2°
(D) 46 1/2°
(E) 42 1/2°
Rationale: angle traced by the hour hand in 12 hours = 360°
Angle traced by it in three hours 25 min (ie) 41/12 hrs=(360*41/12*12)° =102 1/2°
angle traced by minute hand in 60 min. = 360°.
Angle traced by it in 25 min. = (360 X 25 )/60= 150°
Required angle = 1500 – 102 1/2°= 47 1/2°
Answer is A.
Answer: (A) 47 1/2°
Question: A rectangular rug with side lengths of 2 feet and 6 feet is placed on a square floor that has an area of 65 square feet. If the surface of the rug does not extend beyond the area of the floor, what fraction of the area of the floor is not covered by the rug?
(A) A.3/16
(B) 1/4
(C) C.1/2
(D) 53/65
(E) 7/8
Rationale: Area of the rectangular rug = 2*6 = 12
Fraction not covered by the rug = (Total Area - Rug area) / Total Area
= (65 - 12)/65
= 53/65=D
Answer: (D) 53/65
Question: The cross-section of a cannel is a trapezium in shape. If the cannel is 10 m wide at the top and 6 m wide at the bottom and the area of cross-section is 640 sq m, the depth of cannel is?
(A) 34
(B) 97
(C) 37
(D) 80
(E) 22
Rationale: 1/2 * d (10 + 6) = 640
d = 80
Answer: D
Answer: (D) 80
Question: 2 hours after train A leaves Lucknow a train B leaves the same stationtraveling in the same direction at an average speed of 16 km/hr. After traveling 6 hrsthe train B overtakes the train A. What is the average speed of the train A?
(A) 12 km/hr
(B) 16.5 km/hr
(C) 17 km/hr
(D) 18 km/hr
(E) None of these
Rationale: Explanation :
Total distance covered by B=16*6=96kmTotal time taken by A to cover same distance=2+6=8 hrsaverage speed of A=96/8=12 km/hr
Answer : A
Answer: (A) 12 km/hr
Question: A trader sells 85 meters of cloth for Rs. 8500 at the profit of Rs. 15 per metre of cloth. What is the cost price of one metre of cloth?
(A) Rs. 80
(B) Rs. 85
(C) Rs. 90
(D) Rs. 95
(E) None of these
Rationale: SP of 1m of cloth = 8500/85 = Rs. 105
CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth
= Rs. 100 - Rs. 15 = Rs. 85.
ANSWER:B
Answer: (B) Rs. 85
Question: How much more would Rs.15000 fetch, after two years, if it is put at 20% p.a. compound interest payable half yearly than if is put at 20% p.a. compound interest payable yearly?
(A) A)Rs.3,961.50
(B) B)Rs.3,962.50
(C) C)Rs.3,963.50
(D) D)Rs.3,964.50
(E) E)Rs.3,965.50
Rationale: 15000(11/10)4 - 15000(6/5)2 = 3,961.50
ANSWER:A
Answer: (A) A)Rs.3,961.50
Question: Tough and Tricky questions: Word Problems.
A salesman's income consists of commission and base salary. His weekly income totals over the past 7 weeks have been $406, $413, $420, $436, $395, $410, $360. What must his average (arithmetic mean) income over the next two weeks be to increase his average weekly income to $500 over the 9-week period?
(A) $570
(B) $790
(C) $630
(D) $830
(E) $715
Rationale: OFFICIAL SOLUTION:
(D) First, we need to add up the wages over the past 7 weeks: $406 + $413 + $420 + $436 + $395 + $410 + $360 = $2840.
To average $500 over 9 weeks, the salesman would need to earn: $500 × 9 = $4500.
Subtract $2840 from $4500 to determine how much he would need to earn, in total, over the next 2 weeks to average $500 for the 9 weeks: $4500 – $2840 = $1660.
Dividing $1660 by 2 will give us the amount he needs to earn on average over the next 2 weeks: $1660/2 = $830.
The correct answer is choice (D).
Answer: (D) $830
Question: A student was asked to find the arithmetic mean of the numbers 13,31,78,92,115,103,68,10,57,21,34 and a. He found the mean to be 60. What should be the remainder in the place of a?
(A) 98
(B) 105
(C) 120
(D) 165
(E) 132
Rationale: We have (13+31+78+92+115+103+68+10+57+21+34+a) / 12 = 60
622+a= 720
a = 98
Answer is A
Answer: (A) 98
Question: How many 5 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 vowel, and each letter can be used only once?
(A) 21
(B) 42
(C) 120
(D) 600
(E) 720
Rationale: Vowel: E O
Consonants: V R M N T
First letter can be filled in 2 Ways ( As the question states that first letter has to be a vowel)
Fifth letter can be filled in 1 Ways ( As the question states that the last letter has to be a vowel)
Now since each letter can be used only once, and 2 letters out of 7 letters are already used in First and Fifth letter
Second letter can be filled in 5 Ways
Third letter can be filled in 4 Ways
Fourth letter can be filled in 3 Ways
So, Total number of ways = 2 Ways x 5 Ways x 4 ways x 3 ways x 1 ways = 120
Answer C
Answer: (C) 120
Question: Average of 80 numbers are 42. When 5 more numbers are included, the average of 85 numbers become 45. Find the average of 5 numbers.
(A) 82
(B) 89
(C) 93
(D) 98
(E) 69
Rationale: Solution: Total of 80 numbers = 80*42 = 3360;
Now, total of 85 numbers = 85*45 = 3825;
Hence, sum of 5 numbers = 3825-3360 = 465;
Average of five numbers = 465/5 = 93.
Solve while reading Method:
Average of 80 number was 42, when 5 more numbers are added average become 45, that means 3 is given to each number to make their average 45 and 5 numbers also keep 45 as to maintain the entire average.
So, the sum of five numbers = 240+225 = 465,
Hence, average of five numbers = 93.
Answer: Option C
Answer: (C) 93
Question: A man sells an article at a profit of 25%. If he had bought it at 20% less and sold it for Rs.10.50 less, he would have gained 30%. Find the cost of the article.
(A) 30
(B) 40
(C) 50
(D) 60
(E) 70
Rationale: Let C.P=100
Gain=25%
S.P=125
Supposed C.P=80
Gain=30%
S.P=(130*80)/100=104
Diff=(125-104)=21
Diff 21 when C.P=100
then Diff 10.50 when C.P=(100*10.50)/21=50
ANSWER:C
Answer: (C) 50
Question: if abcd is four digit highest number that is divisible by 10.9.22 give remainder 4,9,10. find bc
(A) 75
(B) 89
(C) 95
(D) 98
(E) 97
Rationale: 9954.............>95
ANSWER:C
Answer: (C) 95
Question: Which of the following numbers completes
the sequence 3, 8, 14, 21, 29, 38, 48, 59, 71, 84, ___?
(A) 35
(B) 36
(C) 37
(D) 98
(E) 109
Rationale: The numbers increase at a somewhat steady rate, so you have to figure out how much
you have to add to each number to produce the next in the sequence: 3 + 5 = 8; 8 + 6 = 14;
14 + 7 = 21; 21 + 8 = 29, and so on. The rule for the sequence is to add successively larger
numbers to each number; therefore, the next number is 84 + 14 = 98.
correct answer D)98
Answer: (D) 98