mathewhe/aqua_rat huggingface dataset:
Question: Find the odd man out
253, 136, 352, 327, 631, 244
(A) 327
(B) 136
(C) 352
(D) 631
(E) 531
Rationale: The sum all three digits comes to 10 except 327
ANSWER:A
Answer: (A) 327
Question: The average weight of 10 men is increased by 2 ½ kg when one of the men who weighs 58 kg is replaced by a new man. What is the weight of the new man?
(A)  80 kg
(B)  83 kg
(C)  70 kg
(D)  75 kg
(E)  85 kg
Rationale: Since the average has increased by 2.5 kg, the weight of the man who stepped in must be equal to 58+10x2.5
58+25=83 Kg
Ans: 'B'
Answer: (B)  83 kg
Question: The speeds of 3 trains in the ratio 3:9:12. The ratio between time taken by them to travel the same distance is?
(A) 12:4:3
(B) 1:2:3
(C) 4:8:9
(D) 6:5:2
(E) 4:8:7
Rationale: Ratio of time taken is = 1/3 : 1/9 : 1/12 = 12:4:3
Answer is A
Answer: (A) 12:4:3
Question: Ram has passed his exam of 5 subject in 85% of marks. He has gotten 90, 75, 98 and 72 marks in four subjects. Therefore what is his marks in the fifth subject?
(A) 75
(B) 85
(C) 95
(D) 90
(E) 84
Rationale: EXPLANATION
Total marks of 4 subjects = (90 + 75 + 98 + 72 ) = 335
Marks of 5th subject = [ (85 x 5) – 335 ]
= (425 – 335)
= 90.
Answer D
Answer: (D) 90
Question: A grocer has a sale of Rs. 2500, Rs. 6500, Rs. 9855, Rs. 7230 and Rs. 7000 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 7500?
(A) s. 49180
(B) s. 49910
(C) s. 11915
(D) s 6997
(E) s. 5000
Rationale: Total sale for 5 months = Rs. (2500 + 6500 + 9855 + 7230 + 7000 ) = Rs. 33085.
Required sale = Rs. [ (7500 x 6) -33085]
= Rs. (45000 - 33085)
= Rs. 11915.
C
Answer: (C) s. 11915
Question: The cost price of 16 articles is equal to the selling price of 11 articles. Find the profit percent?
(A) 48 2/91%
(B) 45 5/11%
(C) 48 9/11%
(D) 48 2/91%
(E) 42 2/11%
Rationale: 16 CP = 11 SP
11 --- 2 CP
100 --- ? =>45 5/11%
Answer:B
Answer: (B) 45 5/11%
Question: Pat, Kate, and Mark charged a total of 144 hours to a certain project. If Pat charged twice as much time to the project as Kate and 1/3 as much time as Mark, how many more hours did Mark charge to the project than Kate?
(A) 18
(B) 80
(C) 72
(D) 90
(E) 108
Rationale: 80
all u do is do
2:1:6=>2x+x+6x=144=>x= 16
32:16:96
96-16=80
Answer B
Answer: (B) 80
Question: How many number of weights do u need to weigh 31 kg of rice if u have only one 1kg weights stone ?
(A) 30
(B) 31
(C) 5
(D) 4
(E) 3
Rationale: first measure 1kg rice by 1 kg weight
then use this 2kg (1kg rice+ 1 kg weight) to measure 2kg rice
now combine this to get 3kg rice + 1 kg weight to measure 4 kg rice
add this newly measure 4kg + 3kg + 1kg weight to measure 8 kg
add this 8kg+ 4kg + 3kg + 1kg weight to measure 16 kg rice
now combining all u get 31 kg rice + 1 kg weight
so the answer is 5
ANSWER:C
Answer: (C) 5
Question: If tuesday falls on 4th of month, then which day will fall three days after the 24th ?
(A) SUNDAY
(B) tuesday
(C) monday
(D) thursday
(E) friday
Rationale: Explanation:
The 4th day is tuesday, then 11, 18, 25th also tuesdays
Then 3 days after 24th is 27th, which is thursday
Answer: D) thursday
Answer: (D) thursday
Question: If the sum of two numbers is 42 and their product is 437, then find the
absolute difference between the numbers.
(A) 2
(B) 4
(C) 3
(D) 1
(E) 0
Rationale: Let the numbers be x and y. Then, x + y = 42 and xy = 437
x - y = sqrt[(x + y)2 - 4xy] = sqrt[(42)2 - 4 x 437 ] = sqrt[1764 – 1748] = sqrt[16] = 4.
Required difference = 4.
Answer is B.
Answer: (B) 4
Question: A student got 74% in math and 84% in history. To get an overall average of 75%, how much should the student get in the third subject?
(A) 61%
(B) 63%
(C) 65%
(D) 67%
(E) 69%
Rationale: 74 + 84 + x = 3*75
x = 67
The answer is D.
Answer: (D) 67%
Question: In one hour, a boat goes 11 km along the stream and 7 km against the stream. the sped of the boat in still water (in km/hr) is :
(A) 3
(B) 5
(C) 8
(D) 9
(E) 10
Rationale: Solution
Speed in still water= 1/2(11+7) km/hr= 9kmph. Answer D
Answer: (D) 9
Question: The current birth rate per ten thousand is 620, whereas corresponding death rate is 110 per ten thousand. The net growth rate in terms of population increase in percent is given by
(A) 6.5
(B) 4.5
(C) 5.5
(D) 5.2
(E) 5.1
Rationale: Sol.
Net growth on 1000 = (620 - 110) =510.
Net growth on 100 = (510/10000 Ã— 100)% = 5.1%.
Answer: E
Answer: (E) 5.1
Question: 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:
(A) 51:52
(B) 52:53
(C) 51:53
(D) 52:55
(E) 53:54
Rationale: Explanation:
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 IS B
Answer: (B) 52:53
Question: Find the odd man out. 1, 4, 9, 16, 25, 37, 49, 64, 81
(A) 16
(B) 25
(C) 37
(D) 49
(E) 81
Rationale: Explanation :
Each of the given numbers except 37 is a perfect square
Answer : Option C
Answer: (C) 37
Question: A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 38 years now, the son's age five years back was:
(A) 14 years
(B) 19 years
(C) 33years
(D) 38 years
(E) 3 years
Rationale: Let the son's present age be x years. Then, (38 - x) = x
2x = 38.
x = 19.
Son's age 5 years back (19 - 5) = 14 years.
ANSWER:A
Answer: (A) 14 years
Question: In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?
(A) 209
(B) 145
(C) 321
(D) 521
(E) 130
Rationale: We may have (1 boy and 3 girls) or (2 boys and 2 girls) or (3 boys and 1 girl) or (4 boys).
Required number
of ways	= (6C1 x 4C3) + (6C2 x 4C2) + (6C3 x 4C1) + (6C4)
= (6C1 x 4C1) + (6C2 x 4C2) + (6C3 x 4C1) + (6C2)
= (24 + 90 + 80 + 15)
= 209.
Ans: A
Answer: (A) 209
Question: What is the remainder when 6^381 is divided by 5 ?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: I also agree that the remainder is '1' (using the last digit of the powers of 7). Could we have the official answer please?B
Answer: (B) 1
Question: Which of the following is(are) true for a@b=b@a?
I. a@b=ab+ba
II. a@b=(a+b+1)(a-b)
III. a@b=(a/b)+(b/a)
(A) only Ⅰ
(B) only Ⅱ
(C) only Ⅲ
(D) only ⅠⅢ
(E) only ⅡⅢ
Rationale: -> If I. a@b=ab+ba, a@b=ab+ba=ba+ab=b@a (O).
If II. a@b=(a+b+1)(a-b), a@b=(a+b)(a-b)≠(b+a)/(b-a)=b@a (X).
If III.a@b=(a/b)+(b/a), a@b=(a/b)+(b/a)=(b/a)+(a/b)=b@a (O).
Thus, ⅠⅢ are the answers. Therefore, D is the answer.
Answer: (D) only ⅠⅢ
Question: How many integers from 1 to 100 exist such that each is divisible by 5 and also has 5 as a digit ?
(A) 10
(B) 12
(C) 11
(D) 20
(E) 25
Rationale: 5,15,25,35,40,50,55,65,75,85,95
So there are total 11 such type of numbers.
ANSWER :C
Answer: (C) 11
Question: The difference between a two-digit number obtained by interchanging the positions of its digits is 36. What is the difference between the two digits of that number?
(A) 4
(B) 9
(C) 3
(D) Cannot be determined
(E) None of theses
Rationale: Let the two-digit number be 10x + y.
Then, (10x + y) – (10y + x) = 36
or x – y = 4
Answer A
Answer: (A) 4
Question: train having a length of 240 metre passes a post in 24 seconds. How long will it take to pass a platform having a length of 650 metre?
(A) 89 sec
(B) 100 sec
(C) 90 sec
(D) 85 sec
(E) 99 sec
Rationale: speed = 240/24 = 10 m/s
req time = 240+650/10 = 89 sec
ANSWER A
Answer: (A) 89 sec
Question: A 2-year certificate of deposit is purchased for R dollars. If the certificate earns interest at a n annual rate of 6 percent compound quarterly, which of the following represents the value, in dollars, of the certificate at the end of 2 years?
(A) k(1.06)^2
(B) k(1.06)^8
(C) k(1.015)^2
(D) R(1.015)^8
(E) k(1.03)^4
Rationale: Annual Rate of interest= 6%
Quaterly rate of interest= 6/4% = 1.5%
Now, periods of compounding in 2 years= 8 (8 quarters)
Thus R(1.015)^8
Answer: D
Answer: (D) R(1.015)^8
Question: The price of a vehicle, passing through three hands, rises on the whole by 65%. If the first and the second sellers earned 20% and 25% profit respectively. Find the percentage profit earned by the third seller.
(A) 20%
(B) 5%
(C) 15%
(D) 10%
(E) None of these
Rationale: Explanation :
Solution: Let the original price of the vehicle be Rs. X and let the profit earned by the third seller be Y%.
Then, (100+Y)% of 125% of 120% of X = 165% of X.
[(100+Y)/100 * 125/100 * 120/100 * X] =165/100 * X.
100+Y = 165*100*100/(125*120) = 110 => Y= 10%
Answer : D
Answer: (D) 10%
Question: At 6'o clock clock ticks 6 times. The time between first and
last ticks was 30sec. How much time it takes at 12'o clock.
(A) 60sec
(B) 62sec
(C) 66sec
(D) 64sec
(E) 76sec
Rationale: At 6'0 clock, clock ticks 6 times.
So, there must be 5 intervals between clock ticks.
Time Between first and last ticks = 30sec
So, 1 interval = 30/5 = 6sec
So 6'o clock 5 *6=30sec
7'o clock 6 *6=36sec
.
.
.
10'o clock 9 *6=54sec
11'o clock 10*6=60sec
12'o clock 11*6=66sec
So, 66sec at 12'o clock.
ANSWER:C
Answer: (C) 66sec
Question: If A and B are two events such that P (A) = 3/4, P (B) = 1/2 and P (A n B) = 3/4,
find P (not A and not B).
(A) A)1
(B) B)1/2
(C) C)1/3
(D) D)1/4
(E) E)1/5
Rationale: P(not A and not B) = 1 - (P(A) + P(B) - P(AB))
which you might find somewhere in your text.
Substituting in our probabilities we get:
P(not A and not B) = 1 - (3/4 + 1/2 - 3/4)
P(not A and not B) = 1 - (1/2)
P(not A and not B) = 1/2.
B
Answer: (B) B)1/2
Question: What sum of money will produce Rs.70 as simple interest in 4 years at 3 1/2 percent?
(A) 263
(B) 500
(C) 367
(D) 368
(E) 339
Rationale: 70 = (P*4*7/2)/100
P = 500
Answer: B
Answer: (B) 500
Question: The sum of the present ages of two persons A and B is 60. If the age of A is twice that of B, find the sum of their ages 8 years hence?
(A) 22
(B) 76
(C) 70
(D) 98
(E) 71
Rationale: A + B = 60, A = 2B
2B + B = 60 => B = 20 then A = 40.
8 years, their ages will be 48 and 28.
Sum of their ages = 48 + 28 = 76.
Answer: B
Answer: (B) 76
Question: Find HCF of 4/5, 8/35, 2/15, 6/25 ?
(A) 2/125
(B) 6/360
(C) 2/525
(D) 2/720
(E) 3/680
Rationale: We know that the HCF for fraction can be calculated as:
HCF = (HCF of numerators) / (LCM of denominators)
= (HCF of 4, 8, 2, 6) / (LCM of 5, 35, 15, 25)
= 2 / (5 x 7 x 3 x 5)
= 2 /525
Ans - C
Answer: (C) 2/525
Question: Two persons start running simultaneously around a circular track of length 520 m from the same point at speeds of 18 kmph and 30 kmph. When will they meet for the first time any where on the track if they
are moving in the opposite direction ?
(A) 144
(B) 39
(C) 124
(D) 32
(E) 38
Rationale: Time taken to meet the first time = length of track/relative speed
= 520/ (18 +30) (5/18)
= 520/48 *(18/5) = 39 sec.
Answer : B
Answer: (B) 39
Question: 14.02 Ã— 0.001 = ?
(A) 0.1402
(B) 0.001402
(C) 1.4021
(D) 0.01402
(E) None of these
Rationale: 14.02 Ã— 0.001 = 0.01402
The answer is D.
Answer: (D) 0.01402
Question: If y is an integer, which of the following must also be an integer?
I. x/y
II. y/x
III. xy
(A) I alone
(B) II alone
(C) III alone
(D) I and III
(E) None of the above
Rationale: Lets take X = 5 and Y = 3
Then XY = 15 which is an integer.
But X/Y = 5/3 --> Not an integer.
Y/X = 3/5 --> Not an integer.
Hence C.
Answer: (C) III alone
Question: A, B, K start from the same place and travel in the same direction at speeds of 30 km/hr, 40 km/hr, 160 km/hr respectively. B starts two hours after A. If B and K overtake A at the same instant, how many hours after A did K start?
(A) 5.0
(B) 5.5
(C) 6.0
(D) 6.5
(E) 7.0
Rationale: In 2 hours, A travels 60 km.
B can catch A at a rate of 10 km/hr, so B catches A 6 hours after B starts.
So A and B both travel a distance of 240 km.
C needs 1.5 hours to travel 240 km, so C leaves 6.5 hours after A.
The answer is D.
Answer: (D) 6.5
Question: A dishonest dealer professes to sell goods at the cost price but uses a weight of 950 grams per kg, what is his percent?
(A) 5.3%
(B) 25%
(C) 65%
(D) 45%
(E) 35%
Rationale: Explanation:
950 --- 50
100 --- ? => 5.3%
Answer: A
Answer: (A) 5.3%
Question: Having received his weekly allowance, John spent 3/5 of his allowance at the arcade. The next day he spent one third of his remaining allowance at the toy store, and then spent his last $0.64 at the candy store. What is John’s weekly allowance?
(A) $2.40
(B) $3.00
(C) $3.20
(D) $3.60
(E) $4.80
Rationale: Total allowance=X
Amount spent at the arcade=3/5X
Amount Remaining=2/5X
Amount Spent at the toy store=2/5*1/3X=2/15X
Amount Remaining=2/5X-2/15X=4/15X
Now, 4/15X=$0.64
Therefore, X=$2.40. Answer A
Answer: (A) $2.40
Question: 3,7,12,18,26,__
(A) 36
(B) 38
(C) 39
(D) 40
(E) 41
Rationale: 7=3+4
12=7+5
18=12+6
26=18+8
36=26+10
ANSWER:A
Answer: (A) 36
Question: Mary decided to save a certain amount of her monthly salary each month and her salary was unchanged from month to month. If Mary's savings by the end of the year from these monthly savings were SEVEN times the amount she spent per month, what should be the fraction of her salary that she spent each month?
(A) 1/4
(B) 3/4
(C) 10/19
(D) 11/19
(E) 12/19
Rationale: Saving = S, Expenditure = E, Income = I
At the end of 12months; 12S=7E=7(I-S)
=> 19S = 7I => Savings = 7/19 I
Hence Expenditure = 1-(7/19) = 12/19
Answer (E)
Answer: (E) 12/19
Question: If Tim had lunch at $50.50 and he gave 40% tip, how much did he spend?
(A) A)$57.45
(B) B)$70.70
(C) C)$60.60
(D) D)$21.56
(E) E)$78.45
Rationale: The tip is 40% of what he paid for lunch.
tip = 40% of 50.50 = (40/100)*50.50 = $20.20
Total spent
50.50 + 20.20 = $70.70
correct answer is B)$70.70
Answer: (B) B)$70.70
Question: tipli and pikli are a married couple (dont ask me who he is and who she is)
They have two children, one of the child is a boy. Assume safely that the probability of each gender is 1/2.
What is the probability that the other child is also a boy?
Hint: It is not 1/2 as you would first think.
(A) 1/9
(B) 1/3
(C) 3/5
(D) 1/8
(E) 1/4
Rationale: B
1/3
This is a famous question in understanding conditional probability, which simply means that given some information you might be able to get a better estimate.
The following are possible combinations of two children that form a sample space in any earthly family:
Boy - Girl
Girl - Boy
Boy - Boy
Girl - Girl
Since we know one of the children is a boy, we will drop the girl-girl possibility from the sample space.
This leaves only three possibilities, one of which is two boys. Hence the probability is 1/3
Answer: (B) 1/3
Question: A train covers a distance of 12 km in 10 min. If it takes 15 sec to pass a telegraph post, then the length of the train is?
(A) 250 m
(B) 300 m
(C) 120 m
(D) 200 m
(E) 166 m
Rationale: Speed = (12/10 * 60) km/hr
= (72 * 5/18) m/sec
= 20 m/sec.
Length of the train
= 20 * 15
= 300 m.
Answer:B
Answer: (B) 300 m
Question: Each shelf of a bookcase contained 12 books. If the librarian took out 21 books and rearranged the remaining books so that all shelves but one contained 8 books and the last shelf contained 15 books, how many shelves does the bookcase have?
(A) 9
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Let x be the number of shelves.
No of books in the beginning =12*x
After taking out 21 books No of remaining books = 12x -21
when the remaining books are rearranged, each shelf except the last shelf has 8 books and the last shelf has 11 books. So No of remaining books is also equal to 8*(x-1)+11
12x-21=8(x-1)+15
4x=28
x=7. Answer E
Answer: (E) 7
Question: Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?
(A) 10800
(B) 648
(C) 1800
(D) 2700
(E) 180
Rationale: Let the required number of bottles be x.
More machines, More bottles (Direct Proportion)
More minutes, More bottles (Direct Proportion)
Machines	6: 10 :: 270 : x
Time (in minutes)	1	:	4
6 x 1 x x = 10 x 4 x 270
x =	(10 x 4 x 270)/(6)
x = 1800.
Answer is C.
Answer: (C) 1800
Question: What is the twenty-eighth decimal to the right in the fraction 32/33?
(A) 1
(B) 2
(C) 4
(D) 6
(E) 8
Rationale: 32/33 = 0.96969696969696
The even-numbered decimal places are 6.
The answer is D.
Answer: (D) 6
Question: Aamir saves 32% of his monthly salary. If he spends Rs. 27200, then find his savings?
(A) 15400
(B) 14300
(C) 13200
(D) 12800
(E) None of these
Rationale: Let the monthly salary of Aamir be Rs. x.
68% of x = 27200
=> x = (27200 * 100)/68 = 40000
His savings = 32/100 * 40000 = 12800.
ANSWER:D
Answer: (D) 12800
Question: The length of the bridge, which a train 130 m long and traveling at 45 km/hr can cross in 30 sec is?
(A) 247 m
(B) 275 m
(C) 245 m
(D) 285 m
(E) 345 m
Rationale: Speed = 45 * 5/18 = 25/2 m/sec.
Time = 30 sec
Let the length of bridge be x meters.
Then, (130 + x)/30 = 25/2
x = 245 m.
Answer: C
Answer: (C) 245 m
Question: what is rate of interest if principal.amount be 400,simple interest 180 and time 2year.
(A) 10
(B) 12.5
(C) 25
(D) 22.5
(E) 14.5
Rationale: s.i=(p*r*t)/100
180=800r/100
r=180/8=22.5%
answer D
Answer: (D) 22.5
Question: If a population of women in a town is 90% of men . What is the population of men as a % of population of women ?
(A) 108 %
(B) 105%
(C) 111%
(D) 112%
(E) 114%
Rationale: We're told that the number of Women in a town is equal to 90% of the number of Men in that town.
IF....
Men = 10
Women = 9
We're asked for the number of Men, as a percentage of the number of Women.
M/W = 10/9 = 1 1/9 = 1.111111 = 111%
ANSWER:C
Answer: (C) 111%
Question: A clock shows the time as 3:30 P.m. If the minute hand gains 2 minutes every hour, how many minutes will the clock gain by 3 a.m.?
(A) 23 Minutes
(B) 24 Minutes
(C) 25 Minutes
(D) 26 Minutes
(E) None of these
Rationale: if the minute hand gains 2 minutes in 1 hour the from 3:30 p.m-4:00 p.m it gains 1 min
then from 4:00p.m-3:00 a.m =11*2=22 total=23
ANSWER:A
Answer: (A) 23 Minutes
Question: $200 is divided amongst A,B and C so that A may get 2/3 as much as B and C together, B may get 6/9 as much as A and C together, then the share of A is
(A) $80
(B) $50
(C) $25
(D) $200
(E) $50
Rationale: A:(B+C) = 2:3
A's share = 200*2/5 = $80
Answer is A
Answer: (A) $80
Question: Find the C.I. on a sum of Rs.2000 for 6 months at 20% per annum, interest being compounded quarterly?
(A) 205
(B) 305
(C) 3025
(D) 5540
(E) 315
Rationale: C.I.= 2000(21/20)^2-1800
= 205
Answer: A
Answer: (A) 205
Question: If there are 2 wheelers and 4 wheelers parked in a school located at the heart of the city, find the number of 4 wheelers parked there if there were 58 wheels are parked there
(A) 10
(B) 33
(C) 22
(D) 21
(E) 20
Rationale: let 2x be the number of cycles(2 wheelers) and 4x be the number of 4 wheelers.
2x+4y=58
make use of options given. compute options with y value since we need to find out numb of 4 wheelers...if we give 10 to y then equation becomes 2x+40=58 n 9 two wheelers..other options exceeds the total value
ANSWER:A
Answer: (A) 10
Question: If on an item a company gives 25% discount, they earn 25% profit. If they now give 10% discount then what is the profit percentage.
(A) 40%
(B) 55%
(C) 35%
(D) 30%
(E) 50%
Rationale: If printed price is Rs 100,
sp after 25 % discount = Rs 75.
Then cp for 25 % profit = Rs 60.
If discount on Rs 100 is now 10%, then sp = Rs 90.
Profit on cp of Rs 60 = Rs 30
% age profit =50%
ANSWER:E
Answer: (E) 50%
Question: If X:Y = 8:9 and Y:Z = 5:2 then X:Y:Z is
(A) 40:45:18
(B) 40:45:19
(C) 40:42:18
(D) 41:45:18
(E) 40:55:18
Rationale: Solution:
X/Y = 8/9;
Y/Z = 5/2;
X:Y:Z = 8*5:9*5:9*2 = 40:45:18
Answer: Option A
Answer: (A) 40:45:18
Question: A shopkeeper loses 15%,if an article is sold for Rs. 170. What should be the selling price of the article to gain 20%?
(A) s.247
(B) s.248
(C) s.240
(D) s.229
(E) s.212
Rationale: Given that SP = Rs. 170 and loss = 15%
CP = [100(SP)]/(100 - l%) = (100 * 170)/85 = 20 * 6
= Rs. 200.
To get 20% profit, New SP = [(100 + p%)CP]/100
= (200 * 120)/100
= Rs.240
Answer:C
Answer: (C) s.240
Question: Machine A can do a certain job in 8 hours. Machine B can do the same job in 10 hours. Machine C can do the same job in 12 hours. All three machines start the job at 9:00 a.m. Machine A breaks down at 11:00 a.m., and the other two machines finish the job. Approximately what W time will the job be finished?
(A) Noon
(B) 12:30 p.m.
(C) 1:00 p.m.
(D) 1:30 p.m.
(E) 2:00 p.m.
Rationale: Ans: C (1:00pm)
From 9:00-11:00c(2 hrs)
A can do 1/8 Job/hr. so in 2 hours he can do 1/4 job.
B can do 1/10 job/hr so in 2 hrs. he can do 1/5 Job.
C can do 1/12 job/hr so in 2 hours he can do 1/6 job.
Total = 1/4+1/5+1/6 = 37/60 Job
Now balance work needs to be done by B and C.
Balance Work= 23/60 Job
Combined rate of B and C = 1/10+1/12 = 11/60 job/hr.
So they will do 22/60 work in 2 hrs (approx. to the balance work of 23/60)
Hence the Job will be completed 2hrs. after 11:00 i.e. @ 1:00pm=W
Ans: C (1:00pm)
Answer: (C) 1:00 p.m.
Question: To furnish a room in a model home an interior decorator is to select 2 chairs and 2 tables from the collection of chairs and tables in a warehouse that are all different from each other. If there are 5 chairs in the warehouse and if 150 different combinations are possible, how many tables t are there in the warehouse?
(A) 6
(B) 8
(C) 10
(D) 15
(E) 30
Rationale: Total number of ways to choose 2 chairs from 5 t= 5C2=10
Total number of combination=150
That means we need get 15 combinations from the selection of tables....
Screening through the answers.... 6C2=15..... 15*10=150
Answer is 6... A
Answer: (A) 6
Question: 0.012 x 0.5 = ?
(A) 0.0006
(B) 0.06
(C) 0.6
(D) 0.006
(E) 6.0
Rationale: 12 x 5 = 60.
Sum of decimal places = 4
0.012 x 0.5 = 0.006
Answer: Option D
Answer: (D) 0.006
Question: If y is the smallest positive integer such that 7350 multiplied by y is the square of an integer, then y must be
(A) 2
(B) 5
(C) 6
(D) 7
(E) 14
Rationale: i just tried plugging in the numbers and found out that
6*7350 = 44, 100, which is a square of 210
C
Answer: (C) 6
Question: There are 24 different four-digit integers than can be formed using the digits 2, 3, 4 and 5 exactly once in each integer. The addition problem above shows 4 such integers. What is the sum of all 24 such integers?
(A) 24,444
(B) 28,000
(C) 84,844
(D) 90,024
(E) 93,324
Rationale: Fast Solution:
First stage: we will look at the numbers that contain only 1 digit and the rest is zeros, e.g.: 5000,0200 (=200) ,0040 (=40)
- Let's look at the thousand digit:
* We have: 4 options 5000,4000,3000,2000 = (5+4+3+2)*1000= 14*1000
* We will use each option 3! times (because _X_,__,__,__ - you have 3! options to place the rest 3 numbers)
* that means that the total is :14*1000*3!
- We can do the same for the hundreds digit, tens digits and ones.
Second stage: We will sum every number
14*3!*1000 +
14*3!*100 +
14*3!*10 +
14*3!*1
-------------------
14*3!*1111 -> 14*6*1111=93,324
Backsolving and Picking Numbers aren’t feasible here, so we’ll have to use some (not-so) Straightforward Math. Consider the column on the right-hand side, representing the ones digit of each integer. There are 24 integers and 4 different digits, so each of the 4 digits must appear 6 times in the ones column. Thus, the sum of the ones place for the 24 integers is (6 × 2) + (6 × 3) + (6 × 4) + (6 × 5), or 6 × 14 = 84. Now we know that the correct choice must end with a 4, so eliminate choice (B).
The same pattern holds for the tens column EXCEPT that we have to add8to represent the amount carried over from the 84 in the ones column. So, the tens column must add up to 84 + 8 = 92. Now we see that we must have a 2 in the tens place, so eliminate choices (A) and (C).
For the hundreds place, the sum will be 84 + the 9 carried over from the 92 in the tens column; 84 + 9 = 93, so we must have a 3 in the hundreds place. Answer Choice (E) is the only possibility.
Alternatively, if the ones column adds up to 84, the tens column will be the same thing multiplied by 10, or 840. Similarly, the hundreds column will be 8,400 and the thousands column will be 84,000. Adding up these four numbers, we get 84 + 840 + 8,400 + 84,000 = 93,324.answer is E
Answer: (E) 93,324