mathewhe/aqua_rat huggingface dataset:
Question: The cost to rent a small bus for a trip is x dollars, which is to be shared equally among the people taking the trip. If 10 people take the trip rather than 20, how many more dollars, in terms of x, will it cost per person?
(A)  x/6
(B)  x/16
(C)  x/20
(D)  3x/40
(E)  3x/80
Rationale: Just plugging in values
X= 200
Cost per person if we consider 10 = 20
Cost per person if we consider 20 = 10
Difference between costs is 10 dollars.
Plugging in the value of x into the answer choices, let's see which one yields a result of 10. And that is C.
Answer: (C)  x/20
Question: A certain club has 10 members, including Harry. One of the 10 members is to be chosen at random to be the president, one of the remaining 9 members is to be chosen at random to be the secretary, and one of the remaining 8 members is to be chosen at random to be the treasurer. What is the probability that Harry will be either the member chosen to be the president or the member chosen to be the treasurer?
(A)  1/720
(B)  1/80
(C)  2/10
(D)  1/9
(E)  1/6
Rationale: This question is much easier than it appears.
Each member out of 10, including Harry, has equal chances to be selected for any of the positions (the sequence of the selection is given just to confuse us). The probability that Harry will be selected to be the president is 1/10 and the probability that Harry will be selected to be the treasurer is also 1/10. So, the probability that Harry will be selected to be either the president or the the treasurer is 1/10+1/10=2/10.
Answer: C
Answer: (C)  2/10
Question: A parking garage rents parking spaces for $12 per week or $30 per month. How much does a person save in a year by renting by the month rather than by the week?
(A)  $140
(B)  $160
(C)  $220
(D)  $240
(E)  $264
Rationale: 12$ per week!
An year has 52 weeks.
Annual charges per year = 52* 12 = 624$
30$ per month!
An year has 12 months.
Annual charges per year = 12 * 30 = 360$
624 - 360 = 264
Ans E
Answer: (E)  $264
Question: A straight line in the xy- plane has a slope of 4 and a y-intercept of 4. On this line, what is the x-coordinate of the point whose y-coordinate is 800 ?
(A) 233
(B) 299
(C) 333
(D) 199
(E) 339
Rationale: Eq of line = Y = MX +C
M = 4,
C= 4
Y=4X + 4,
Substitute Y by 800 as given in question.
800=4X+4 , X = 199.
correct option is D
Answer: (D) 199
Question: Simplify: 5005-5000+10
(A) 4505
(B) 4509
(C) 4501
(D) 4500
(E) None of them
Rationale: 5005-5000+10=5005-(5000/10)=5005-500=4505
Answer is A
Answer: (A) 4505
Question: Amy’s retirement portfolio contains only stocks and bonds. At the beginning of 2016, her portfolio had an allocation of 60% stocks and 40% bonds. Over the course of 2016, the total value of her portfolio increased by 8%, with the value of her stock holdings increasing by 10%. By what percent did the value of her bond holdings increase?
(A) 4%
(B) 5%
(C) 6%
(D) 7%
(E) 7.5%
Rationale: Thus total value of Bond at the end of 2016 is 420 ( ie, 1080 - 660 )
So, Per unit value of Bond at the end of 2016 is 420/40=10.50
Hence, percentage increase is 0.50/10∗100=5%, answer will be (B)
Answer: (B) 5%
Question: Two trains of length 170 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. In how much time will the trains cross each other?
(A) 100/7 sec
(B) 80/7 sec
(C) 57/7 sec
(D) 120/7 sec
(E) 114/7 sec
Rationale: Relative speed = (54 + 72)* 5/18 = 7 * 5 = 35 mps.
The time required = d/s = (170 + 100 + 300)/35
= 570/35 = 114/7 sec.
ANSWER:E
Answer: (E) 114/7 sec
Question: Each night before he goes to bed, Jordan likes to pick out an outfit to wear the next day. He has 13 different shirts, 10 different pairs of jeans, and 8 pairs of sneakers. If an outfit consists of 1 shirt, 1 pair of jeans, and 1 pair of sneakers, how many different outfits does Jordan have?
(A) 30
(B) 90
(C) 240
(D) 1040
(E) 960
Rationale: Total # of outfits = 13 * 10 * 8 = 1040
Answer - D
Answer: (D) 1040
Question: A train 390 metres long is moving at a speed of 25 kmph. It will cross a man coming from the opposite direction at a speed of 2 km per hour in :
(A) 30 sec
(B) 32 sec
(C) 36 sec
(D) 38 sec
(E) 52 sec
Rationale: Relative speed = (25+2) km/hr = 27 km/hr
= (27×5/18) m/sec = 15/2 m/sec.
Time taken by the train to pass the man =(390×2/15) sec=52 sec
ANSWER :E
Answer: (E) 52 sec
Question: How many bricks, each measuring 25cm*11.25cm*6cm, will be needed to build a wall 8m*6m*22.5m
(A) 6100
(B) 6200
(C) 6300
(D) 6400
(E) None of these
Rationale: Explanation:
To solve this type of question, simply divide the volume of wall with the volume of brick to get the numbers of required bricks
So lets solve this
Number of bricks =
Volume of wall /Volume of 1 brick=800∗600∗22.5 /25∗11.25∗6=6400
Option D
Answer: (D) 6400
Question: In what time will a railway train 80 m long moving at the rate of 36 kmph pass a telegraph post on its way?
(A) 8 sec
(B) 1 sec
(C) 9 sec
(D) 6 sec
(E) 2 sec
Rationale: T = 80/36 * 18/5
= 8 sec
Answer:A
Answer: (A) 8 sec
Question: In an electric circuit, two resistors with resistances x and y are connected in parallel. If R is the combined resistance of these two resistors, then the reciprocal of R is equal to the sum of the reciprocals of x and y. What is R if x is 4 Ohms and y is 5 Ohms?
(A) 7/9
(B) 20/9
(C) 7/20
(D) 9/20
(E) 11/20
Rationale: 1/R = 1/x + 1/y
1/R = 1/4+1/5 = 9/20
R = 20/9
The answer is B.
Answer: (B) 20/9
Question: Which of the following number is divisible by 24 ?
(A) 3125736
(B) 35718
(C) 63810
(D) 537804
(E) None of these
Rationale: 24 = 3 x8, where 3 and 8 co-prime.
Clearly, 35718 is not divisible by 8, as 718 is not divisible by 8.
Similarly, 63810 is not divisible by 8 and 537804 is not divisible by 8.
Consider option (D),
Sum of digits = (3 + 1 + 2 + 5 + 7 + 3 + 6) = 27, which is divisible by 3.
Also, 736 is divisible by 8.
3125736 is divisible by (3 x 8), i.e., 24.
A)
Answer: (A) 3125736
Question: In the arithmetic sequence t1, t2, t3, ..., tn, t1=23 and tn= tn-1 - 3 for each n > 1. What is the value of n when tn = 8?
(A) -1
(B) 6
(C) 10
(D) 14
(E) 20
Rationale: We know that t1 = 23
So, using the given formula we have:
t1=(t1-1) -3 =23
t0 - 3 = 23
t0= 26
The same way we find that t2= 20
It seems that the sequence goes like this:
t0 = 26
t1 = 23
t2 = 20
t3 = 17
t4 = 14
t5 = 11
t6 = 8
So, ourANS is B.
Answer: (B) 6
Question: If equal numbers of people are born on each day, find the approximate percentage of the people whose birthday will fall on 29thFebruary.(if we are to consider people born in 20thcentury and assuming no deaths).
(A) 0.374
(B) 0.5732
(C) 0.0684
(D) None of these
(E) Cannot be determined
Rationale: Explanation :
Let the number of people born on each day = n.
Total years in the 20th century = 100.
Total number of leap years (years in which 29th February appear) = 25.
Sample Space (days) = 365*75 + 366*25 = 36525 days.
So, Sample Space (population) = 36525*n
Favourable Set (population) = 25*n
Hence, the required probability = 25 * n /36525*n = 0.000684.
= 0.0684%.
Answer : C
Answer: (C) 0.0684
Question: I know a number which when multiplied by multiple of 9 i.e 9 18 27 36 45 ... the output consist of number containing only one digit.
Can you identify the number ?
(A) 12345678
(B) 12345674
(C) 12745679
(D) 12345679
(E) 12645679
Rationale: D
12345679
12345679 × 9 = 111111111 (only 1s)
12345679 × 18 = 222222222 (only 2s)
12345679 × 27 = 333333333 (only 3s)
12345679 × 36 = 444444444 (only 4s)
12345679 × 45 = 555555555 (only 5s)
Answer: (D) 12345679
Question: What is the maximum value of vx - yz. If the value of v,x,y,z have to be chosen from the set A where A(-3,-2,-1,0,1,2,3)
(A) 15
(B) 66
(C) 25
(D) 88
(E) 17
Rationale: Explanation:
To maximize the value of vx - yz, we make yz negative and vx as maximum as possible using given value.
vx−yz=(−3)2−(−3×2)vx−yz=(−3)2−(−3×2) = 15
Answer:A
Answer: (A) 15
Question: In terms of percentage profit, which among following the best transaction
(A) C.P. 36, Profit 17
(B) C.P. 50, Profit 24
(C) C.P. 40, Profit 19
(D) C.P. 60, Profit 29
(E) None of these
Rationale: Explanation:
Hint: Calculate profit percent as
Profit% = (profit/cost) * 100
Option D
Answer: (D) C.P. 60, Profit 29
Question: Excluding stoppages, the speed of a train is 35 kmph and including stoppages it is 22 kmph. Of how many minutes does the train stop per hour?
(A) 82
(B) 17
(C) 22
(D) 82
(E) 18
Rationale: Explanation:
T = 13/35 * 60 = 22
Answer: Option C
Answer: (C) 22
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) 31:32
(B) 39:42
(C) 48:46
(D) 52:63
(E) 52:53
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: Option E
Answer: (E) 52:53
Question: What will be the difference between simple interest and compound interest @10% per annum on a sum of Rs. 1000 after 4 years?
(A) Rs. 31
(B) Rs. 32.10
(C) Rs. 40.40
(D) Rs. 64.10
(E) None
Rationale: Solution
S.I.	=Rs(1000x10x4 / 100)
= Rs.400.
C.I.	=Rs.[1000x(1x10/100)4-1000]
= Rs. 464.10
∴ Difference = Rs.(464.10 - 400)
= Rs. 64.10
Answer D
Answer: (D) Rs. 64.10
Question: A man can row his boat with the stream at 19 km/h and against the stream in 11 km/h. The man's rate is?
(A) 4 kmph
(B) 2 kmph
(C) 7 kmph
(D) 8 kmph
(E) 3 kmph
Rationale: DS = 19
US = 11
S = ?
S = (19 - 11)/2 = 4 kmph
Answer:A
Answer: (A) 4 kmph
Question: Set A consists of 19 elements. The average of set A is L. If a new element is added to the set and the average grows by K, what is the value of the new element?
(A) a) L(1 + K / 5)
(B) b) L * (K/100) - 20L
(C) c) 20L(1+K/100)
(D) d) 20(1+K/100)-19L
(E) e) L*(K/5)-19
Rationale: Let's assume the value of new element to bea. So converting the word problem into equation,
(19*L + a) / (19 + 1) = L + k ==> after solving the equation we will get a (value of newly added element) = L + 20K
But according to the answer options, problem writer wanted to conveyk% percent rise in average value.
If we consider this case than resulting equation will be,
(19*L + a) / ( 19+1 ) = L + (K/100)*L ==> 19L + a = 20 [ L + KL/100]
==> a= 20L + KL/5 -19L
==> a= L + KL/5 , which is equivalent to option [A]
Answer: (A) a) L(1 + K / 5)
Question: Money invested at x%, compounded annually, triples in value in approximately every 112/x years. If $1800 is invested at a rate of 8%, compounded annually, what will be its approximate worth in 28 years?
(A) $16,200
(B) $5,600
(C) $8,100
(D) $15,000
(E) $22,500
Rationale: x=8%
112/x years=112/8=14 years
Now, money triples every 14 years
Therefore, in 14 yrs , if $1800 triples to $5400, in 28 years, it will again triple to $5400*3=$16,200
Answer A
Answer: (A) $16,200
Question: If 3 pounds of dried apricots that cost x dollars per pound are mixed with 3 pounds of prunes that cost y dollars per pound, what is the cost, in dollars, per pound of the mixture?
(A) (3x + 3y)/5
(B) (3x + 3y)/(x + y)
(C) (3x + 3y)/(xy)
(D) 5(3x + 3y)
(E) 3x + 3y
Rationale: Total Cost = Weight(in pounds) * Price/pound;
To find Total cost/pound, Divide by total pounds.
Cost of Dried apricots = 3x;
Cost of prunes = 3y;
Cost per pound = (3x + 3y)/5;
Ans is (A).
Answer: (A) (3x + 3y)/5
Question: The weight of every type A widget is the same, the weight of every type B widget is the same, and the weight of every type C widget is the same. If the weight of 7 type A widgets is equal to the weight of 2 type B widgets, and the weight of 4 type B widgets is equal to the weight of 7 type C widgets. What is the ratio of the total weight of 1 type A widget and 1 type B widget, to the total weight of 1 type B widget and 1 type C widget?
(A) 3:5
(B) 5:7
(C) 7:9
(D) 9:11
(E) 11:13
Rationale: 4B = 7C and so B = 7C/4
7A = 2B and so A = 2B/7 = C/2
A+B = C/2 + 7C/4 = 9C/4
B+C = 7C/4 + C = 11C/4
The ratio of A+B:B+C = 9:11
The answer is D.
Answer: (D) 9:11
Question: The product of two positive integers is 675 and their difference is 2. What is the bigger number?
(A) 21
(B) 23
(C) 25
(D) 27
(E) 29
Rationale: Let's use trial and error to find the two numbers.
25*23 = 575 (too low)
27*25 = 675
The answer is D.
Answer: (D) 27
Question: What is the area of square field whose side of length 15 m?
(A) 225 sq m
(B) 220 sq m
(C) 100 sq m
(D) 30 sq m
(E) 35 sq m
Rationale: Explanation:
15 * 15 = 225 sq m
ANSWER IS A
Answer: (A) 225 sq m
Question: A and B are two partially filled buckets of water. If 5 liters are transferred from A to B, then A would contain one-third of the amount of water in B. Alternatively, if 4 liters are transferred from B to A, B would contain one-half of the amount of water in A. Bucket A contains how many liters of water?
(A) 11
(B) 52/5
(C) 17
(D) 21
(E) 23
Rationale: Let A contains A, B contains B liters
so, (A-5)/(B+5)= 1/3.......(1)
again, (B-4)/(A+4)= 1/2..........(2)
from (1)(2) we find A= 52/5
ans: (B)
Answer: (B) 52/5
Question: Average of 10 matches is 32, How many runs one should should score to increase his average by 5 runs.
(A) A)70
(B) B)76
(C) C)78
(D) D)80
(E) E)87
Rationale: Explanation:
Average after 11 innings should be 37
So, Required score = (11 * 37) - (10 * 32)
= 407 - 320 = 87
Answer: Option E
Answer: (E) E)87
Question: Three boys, two girls, and two women are to be seated on a bench. If one specific boy must be seated on one of the end seats, and one specific girl must me seated exactly in the middle, find the number of possible arrangements.
(A) 48
(B) 144
(C) 240
(D) 288
(E) 120
Rationale: "One specific boy is seated to either of end seat", lets call him b1
"One specific girl is seated in the middle", lets call her g1
Note the question says *specific girl* and *specific boy*, so we do not consider for example the other girl , g2, being seated on seat #4. Same goes with the specific boy, b1.
b1 can be seated 2 different seats : 2!
g1 is seated on the seat #4, fixed (no other alternative) : 1
the remaining 5 seats can be filled with the remaining people b2,b3,g2,w1,w2: 5!
2! x 1 x 5! = 240
Answer C
Answer: (C) 240
Question: In a race of 200 m, A can beat B by 21 m and C by 15 m. In a race of 425 m, C will beat B by ?
(A) 30 m
(B) 75 m
(C) 85 m
(D) 25 m
(E) 15 m
Rationale: Explanation:
A:B = 100 : 79
A:C = 100 : 85
=> B:C = 79:85
When C covers 85 m , B Covers 79 m
When C covers 425 m , B Covers
=> 395 m
So C beats B by (425 - 395) = 30 m.
Answer: A
Answer: (A) 30 m
Question: Positive Integer A gives the remainder of 12 when divided by another positive Integer B. If A/B = 47.24, what is the value of B?
(A) 96
(B) 75
(C) 48
(D) 25
(E) 50
Rationale: .24 of B = Remainder
.24 of B = 12
B = (12 *100) / 24 = 50.
E
Answer: (E) 50
Question: How many positive integers less than 1000 are multiples of 5 but NOT of 4 or 7?
(A) 114
(B) 121
(C) 122
(D) 129
(E) 136
Rationale: There are 1000/5=200 multiples of 5 . now we have to find the number of multiples of 5 and 4 that is 20 between 0 to 1000 and 5 and 7 that is 35 between 0 to 1000.
multiples of 20=1000/20=50 multiples. and multiples of 35= 1000/35 =28.5 so 28 multiples of 35.
So multiples of 5 between o to 1000 not including multiples of 20 and 35 are equal to 200-78 = 122 multiples.
So the answer is C.
Answer: (C) 122
Question: If k^3 is divisible by 168, what is the least possible value of integer k?
(A) 36
(B) 42
(C) 48
(D) 54
(E) 60
Rationale: k^3 = 168*x = 2^3*3*7*x
The factors of k must at minimum include 2*3*7 = 42.
The answer is B.
Answer: (B) 42
Question: At a certain supplier, a machine of type A costs $22,000 and a machine of type B costs $50,000. Each machine can be purchased by making a 20 percent down payment and repaying the remainder of the cost and the finance charges over a period of time. If the finance charges are equal to 40 percent of the remainder of the cost, how much less would 2 machines of type A cost than 1 machine of type B under this arrangement?
(A) $7,920
(B) $11,200
(C) $12,000
(D) $12,800
(E) $13,200
Rationale: Total Cost of 2 Machines of Type A
= 20% of (Cost of 2 machine A) + remainder + 40 % remainder
= 20% of 44000 + (44000 - 20% of 44000) + 40% of (44000 - 20% of 44000)
= 58080
Total Cost of 1 Machine of Type B
= 20% of (Cost of 1 machine B) + remainder + 40 % remainder
= 20% of 50000 + (50000 - 20% of 50000) + 40% of (50000 - 20% of 50000)
= 66000
Diff = 66000 - 58080 = 7900
Hence, A.
Answer: (A) $7,920
Question: The average age of father and his two sons is 24 Years. Five years ago, the average age of the two sons was 15 Years. If the difference between the ages of the two sons is four years, what is the present age of the father?
(A) 45
(B) 32
(C) 47
(D) 48
(E) 49
Rationale: The total present age of father and two sons is 3x24 = 72 yrs
The total present age of sons is (15+5) X 2 = 40Years
so, present age of father is 72 â€“ 40 = 32 yrs
Answer B
Answer: (B) 32
Question: What is the cost of leveling the field in the form of parallelogram at the rate of Rs.30/10 sq.metre, whose base & perpendicular distance from the other side being 64m & 74m respectively?
(A) s. 6000
(B) s. 6300
(C) s.4736
(D) s. 6480
(E) s. 7000
Rationale: Area of the parallelogram = Length of the base * Perpendicular height
= 64 * 74 = 4736 m.
Total cost of levelling = Rs. 4736
C
Answer: (C) s.4736
Question: Due to construction, the speed limit along an 9-mile section of highway is reduced from 55 miles per hour to 20 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
(A) A) 5.61
(B) B) 8
(C) C) 10
(D) D) 17.19
(E) E) 24
Rationale: Old time in minutes to cross 9 miles stretch = 9*60/55 = 9*12/11 = 9.81
New time in minutes to cross 9 miles stretch = 9*60/20 = 9*3/1 = 27
Time difference = 17.19
Ans:D
Answer: (D) D) 17.19
Question: Find the odd man out
2, 5, 11, 23, 48, 95
(A) 5
(B) 11
(C) 23
(D) 48
(E) 28
Rationale: 2*2+1 = 5
5*2+1 = 11
11*2+1 = 23
23*2+1 = 47
47*2+1 = 95
ANSWER:D
Answer: (D) 48
Question: If 0 < a < 1, what is the median of the values a, x^-1, a^2, a^1/2 and a^3?
(A) a
(B) a^-1
(C) a^2
(D) a^1/2
(E) a^3
Rationale: A. To make the problem less confusing, I picked a number between 0 and 1 such as a = 1/4 and calculate:
a = 1/4
a^-1 = 4
a^2 = 1/16
a^(1/2) = 1/2
a^3 = 1/8.
From this, rearrange the number and the median is 1/4, which is a. Answer A
Answer: (A) a
Question: Rahim and his uncle differ in their ages by 30 years. After 7 years, if the sum of their ages is 66, what will be the age of the uncle ?
(A) 41 years
(B) 36
(C) 48
(D) 33
(E) 44
Rationale: A
41
Let uncle’s present age = x
Rahim's present age = y
y– x= 30 ...(i)
After 7 year
(x + 7) + (y+ 7) = 66
x + y + 14 = 66
x + y = 52 ...(ii)
combining (i) and (ii) we get
(x + y = 52) + (x – y = 30)
2x= 82
x= 41
Uncle's age is 41
Answer: (A) 41 years
Question: 4 dice are thrown simultaneously on the board. Find the probability show the same face.
(A) 1/115
(B) 3/113
(C) 1/216
(D) 3/119
(E) 1/119
Rationale: The total number of elementary events associated to the random experiments of throwing four dice simultaneously is:
=6×6×6×6=64=6×6×6×6=64
n(S)=64n(S)=64
Let XX be the event that all dice show the same face.
X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}
n(X)=6n(X)=6
Hence required probability,
=n(X)n(S)=664=n(X)n(S)=664
=1/216
C
Answer: (C) 1/216
Question: Find the value of x if the mean of the series 245,564,458,125,36,x is 250
(A) 50
(B) 72
(C) 36
(D) 45
(E) 112
Rationale: mean = 245+564+458+125+36+x / 6 = 250
1428+x = 1500
x = 72
Answer is B
Answer: (B) 72
Question: If 6 is one solution of the equation x^2 + 3x + k = 10, where k is a constant, what is the other solution?
(A)  -7
(B)  -4
(C)  -3
(D)  -9
(E)  6
Rationale: The phrase “6 is one solution of the equation” means that one value of x is 6. Thus, we first must plug 6 for x into the given equation to determine the value of k. So we have
6^2 + (3)(6) + k = 10
36 + 18 + k = 10
54 + k = 10
k = -44
Next we plug -44 into the given equation for k and then solve for x.
x^2 + 3x – 44 = 10
x^2 + 3x – 54 = 0
(x+9)(x-6) = 0
x = -9 or x = 6
Thus, -9 is the other solution. Answer D.
Answer: (D)  -9
Question: The volume of a cube is 3375 cc. Find its surface.
(A) 864
(B) 556
(C) 255
(D) 287
(E) 1350
Rationale: a3 = 3375 => a = 15
6a2 = 6 * 15 * 15 = 1350
Answer:E
Answer: (E) 1350
Question: How many liters of water must be evaporated from 50 liters of a 3-percent sugar solution to get a 2-percent solution?
(A) 35
(B) 33 1/3
(C) 27
(D) 16 2/3
(E) 18
Rationale: How many liters of water must be evaporated from 50 liters of a 3-percent sugar solution to get a 2-percent solution?
3% of a 50 liter solution is 1.5L. So you are trying to determine how many liters must a solution be for the 1.5L to represent 2% of the solution. Set up an inequality and solve for x:
1.5/x = 1/2
x = 3
Since you need a 15L solution, you must evaporate 18 of the original 50L solution to get a 2% solution.
Answer is E.
Answer: (E) 18
Question: A certain company retirement plan has arule of 70provision that allows an employee to retire when the employee's age plus years of employment with the company total at least 70. In what year could a female employee hired in 1990 on her 32nd birthday first be eligible to retire under this provision?
(A) 2003
(B) 2009
(C) 2005
(D) 2006
(E) 2007
Rationale: She must gain at least 70 points, now she has 31 and every year gives her two more points: one for age and one for additional year of employment, so 32 + 2*(# of years) = 70 --> (# of years) = 19 --> 1990+19=2009.
Answer: B.
Answer: (B) 2009
Question: The concentration of spirit in three different vessels A, B and C are 45%, 30% and 12% 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) 32.80%
(B) 26.80%
(C) 34%
(D) 24.62%
(E) 36%
Rationale: Quantity of spirit in new solution=(4*45/100)+(5*30/100)+(6*12/100)=1.8+1.5+0.72=4.02 liters
So % concentration of spirit=100*4.02/(4+5+6)=26.80%
ANSWER:B
Answer: (B) 26.80%
Question: Two trains start from P and Q respectively and travel towards each other at a speed of 50 km/hr and 40 km/hr respectively. By the time they meet, the first train has traveled 100 km more than the second. The distance between P and Q is?
(A) 237
(B) 278
(C) 277
(D) 900
(E) 261
Rationale: At the time of meeting, let the distance traveled by the second train be x km. Then, distance covered by the first train is (x + 100) km.
x/40 = (x + 100)/50
50x = 40x + 4000 => x = 400
So, distance between P and Q = (x + x + 100)km = 900 km.
Answer: D
Answer: (D) 900
Question: In a Pvt Company 15 staffs are working. Salary for 10 Staffs @ 15000/- and 5 staffs @ 9000/- per month. Owner deducted amount of 15 leaves from every one. Then how much amount will be given in total for One month?
(A) 195000
(B) 202000
(C) 192000
(D) 188000
(E) 188500
Rationale: Salary for 10 Staffs @ 15000/- : 1,50,000/-
Salary for 5 Staffs @ 9000/- : 45,000/-
Total Salary : 195000/-
Salary cutting 1 day for 10 Staffs: 5000/-
Salary cutting 1 days for 5 staffs : 1500/-
Total salary for one month : 195000/- - 6500/ =
Answer is E
Answer: (E) 188500
Question: What is the length of the longest pole which can be kept in a room 10 m long, 4 m broad and 3 m high?
(A) 7
(B) 9
(C) 11.18
(D) 13
(E) None
Rationale: Explanation:
d2 = 102 + 42 + 32 = 11.18
C)
Answer: (C) 11.18
Question: The area of a triangle will be when a = 1m, b = 2m, c = 3m, a, b, c being lengths of respective sides.
(A) 0 sq m
(B) 3 sq m
(C) 2 sq m
(D) 6 sq m
(E) 8 sq m
Rationale: Explanation:
S = (1 + 2 + 3)/2 = 3
=> No triangle exists
ANSWER IS A
Answer: (A) 0 sq m
Question: The set S consists of 5 numbers: {1,2,3,4,5}. If all possible subsets including the null set are created and one subset is chosen at random, what is the probability that the subset has 2 as its largest number?
(A) 1/2
(B) 1/4
(C) 1/8
(D) 1/16
(E) 1/32
Rationale: The set S has 2^5 = 32 subsets.
The number 2 is the largest number in the subset {1,2} and the subset {2}.
Thus 2 is the largest number in 2 subsets of S.
The probability that 2 is the largest number is 2/32 = 1/16.
The answer is D.
Answer: (D) 1/16