mathewhe/aqua_rat huggingface dataset:
Question: A certain list of 300 test scores has an arithmetic mean of 70 and a standard deviation of d, where d is positive. Which of the following two test scores, when added to the list, must result in a list of 302 test scores with a standard deviation less than d?
(A)  70 and 70
(B)  80 and 85
(C)  70 and 75
(D)  75 and 75
(E)  70 and 80
Rationale: Deviation means spreading of the numbers from one median point value..
as the set is already established and we need to add only two numbers, this means we can only add numbers which are closer to the median to reduce the deviation.
so 70 and 70 are the most close numbers and they will increase the number of elements in the set without changing the median value.
A
Answer: (A)  70 and 70
Question: A windmill is taking advantage of strong air currents in order to produce electrical energy. On a typical day the wind speed is around 20 mph and in that speed the windmill produces 400 kw/h (kilowatts per hour). On a stormy day a windmill produces 20% more energy. How much kw/h can three windmills produce in two hours on a stormy day?
(A) 2880.
(B) 4860.
(C) 5780
(D) 5760
(E) 6380.
Rationale: Normal Day = 400 kw/h
Stormy Day = 400*1.2=480 kw/h
3 windmills for 2 hours on stormy day
480*3*2=2880
Answer: A
Answer: (A) 2880.
Question: Mike had 200 watermelons. Sally came over and took some. After Sally left mike had 136 watermelons. How many watermelons did Sally take?
(A) 33
(B) 87
(C) 264
(D) 5
(E) 64
Rationale: 200-X=136
X=200-136
X=64
Sally took 64 watermelons
E.64
Answer: (E) 64
Question: You have a pair of unbiased dices. You throw them together till you get a sum of 4 or 7.
What is the probability that you get a sum of 4 before the sum of 7?
(A) 1/6
(B) 5/7
(C) 2/8
(D) 3/7
(E) 2/5
Rationale: E
2/5
Explanation:
This problem can be solved with different approaches. Let us not go into the complicated generic stuff to avoid confusion and try to solve it with simpler means.
Let us find the results separately. There can be 4 different results that give the sum of 5 and there can be 6 different results that give the sum of 7.
Thus, the probability that we get the sum of 4 before the sum of 7 will be:
4/(4+6) = 4/10 = 2/5.
Answer: (E) 2/5
Question: How many 3 digit positive integers T exist that when divided by 7 leave a remainder of 5?
(A) 128
(B) 142
(C) 143
(D) 141
(E) 129
Rationale: Minimum three digit number is 100 and maximum three digit number is 999.
The first three digit number that leaves remainder 5 when divided by 7 is 103.
14 * 7 = 98 +5 = 103
The second three digit number that leaves remainder 5 when divided by 7 is 110.
15 * 7 = 105 +5 =110
The third three digit number that leaves remainder 5 when divided by 7 is 117
and so on
The last three digit number that leaves remainder 5 when divided by 7 is 999
142 * 7 = 994 + 5 = 999
Therefore, we identify the sequence
103,110,117.....999
use the formula of last term
Last term = first term + (n - 1) * common difference
you will get the answer 129 that is definitely E.
Answer: (E) 129
Question: A and B start a business with Rs.6000 and Rs.8000 respectively. Hoe should they share their profits at the end of one year?
(A) 3:9
(B) 3:4
(C) 3:2
(D) 3:1
(E) 3:6
Rationale: Explanation:
They should share the profits in the ratio of their investments.
The ratio of the investments made by A and B =
6000 : 8000 => 3:4
Answer: B
Answer: (B) 3:4
Question: A technician makes a round-trip to and from a certain service center by the same route. If the technician completes the drive to the center and then completes 30 percent of the drive from the center, what percent of the round-trip has the technician completed?
(A) 60
(B) 65
(C) 55
(D) 50
(E) 55
Rationale: round trip means 2 trips i.e.to and fro. He has completed one i.e 50% completed. then he traveled another 30% of 50% i.e 15%. so he completed 50 +15 =65 % of total trip.
B
Answer: (B) 65
Question: A shopkeeper sold 15 articles at the cost price of 20 articles. Then find the profit% or lost%
(A) 30%
(B) 31%
(C) 20%
(D) 33.33%
(E) 40%
Rationale: here 15 articles selling price = 20 articles cost price
so the difference = 20-15 = 5
% of profit = 5*100/15 = 33.33%
correct option is D
Answer: (D) 33.33%
Question: the stock price of xyz inc. has suffered a decline of 18% in the last 6 months. Financial Analysts believe that the shares will bounce back and gain 5% in the next 3 months. this gain will bring the share value to $700. What was the approximate price of the stock 6 months ago?
(A) 706
(B) 750
(C) 760
(D) 900
(E) 813
Rationale: -18+5-(18*5)/100=-13.9% net decrease
let initial price be Y
Y(1-13.9/100)=700
Y=700/0.861 = ~813
Ans is E)
Answer: (E) 813
Question: The number of permutations of the letters of the word 'MESMERISE' is?
(A) 9!/(2!)2 3!
(B) 9!/(2!)7 3!
(C) 9!/(2!)9 3!
(D) 9!/(2!)2 8!
(E) 9!/(2!)1 3!
Rationale: n items of which p are alike of one kind, q alike of the other, r alike of another kind and the remaining are distinct can be arranged in a row in n!/p!q!r! ways.
The letter pattern 'MESMERISE' consists of 10 letters of which there are 2M's, 3E's, 2S's and 1I and 1R.
Number of arrangements = 9!/(2!)2 3!
Answer:A
Answer: (A) 9!/(2!)2 3!
Question: The mean age of john,william,sam and katy is 25.the age of jhon is 22,age of sam is 30 and age of katy is 24.then tell me the age of william.
(A) 23
(B) 24
(C) 25
(D) 26
(E) 27
Rationale: solution
let age of william be x.
now, the mean of four age=(22+x+30+24)/4=25
76+x=100
so x=24.
answer B
Answer: (B) 24
Question: Q-1) Of the 64 parents who attended a meeting at a
school, 35 volunteered to supervise children during
the school picnic and 11 volunteered both to supervise
children during the picnic and to bring refreshments to
the picnic. If the number of parents who volunteered
to bring refreshments was 1.5 times the number of
parents who neither volunteered to supervise children
during the picnic nor volunteered to bring
refreshments, how many of the parents volunteered to
bring refreshments?
(A) 24
(B) 36
(C) 38
(D) 42
(E) 45
Rationale: i used the following formula: total = group1 + group2 + neither - both
using the information from the question stem, we have:
64 total people
35 who supervise (group1)
x who neither supervise nor bring refreshments
1.5x people who bring refreshments (group2)
11 who supervise AND bring refreshments (both)
therefore...
64 = 35 + 1.5x + x - 11
solving, we get x = 16
since we want the value of those who bring refreshments AND supervise:
1.5(16) = 24
answer is A
Answer: (A) 24
Question: A customer pays 70 dollars for a coffee maker after a discount of 20 dollars
What is the original price of the coffe maker?
(A) 50
(B) 40
(C) 90
(D) 60
(E) 20
Rationale: Let x be the original price.
x - 20 = 70
x - 20 + 20 = 70 + 20
x + 0 = 90
x = 90
Answer is C
Answer: (C) 90
Question: Fresh grapes contain 70% by weight while dried grapes contain 10% water by weight. What is the weight of dry grapes available from 100 kg of fresh grapes?
(A) 18.33 kg
(B) 21.50 kg
(C) 25.00 kg
(D) 33.33 kg
(E) 40.39 kg
Rationale: From the question we know: 100kg * 70% = 70kg of water in the fresh grapes
100kg - 70kg of water = 30kg of non-water mass
We are looking for the weight of the dry grapes (X).
Since the question tells us that 10% of the weight of the dry graps is water and we know that 30kg is non-water mass we can set up the following equation:
X = 1/10(X) + 30kg
9/10(X) = 30kg
X = 33.33 kg
Answer- D
Answer: (D) 33.33 kg
Question: The area of a triangle is with base 2m and height3m?
(A) 11
(B) 10
(C) 787
(D) 3
(E) 12
Rationale: 1/2 * 2 * 3 = 3 m2
Answer: D
Answer: (D) 3
Question: It costs $6 for the first 1/4 hour to use the copier at Kinkos. After the first ¼ hour it costs $8 per hour. If a certain customer uses the copier for 4 hours and 25 minutes, how much will it cost him?
(A) $23.45
(B) $65.33
(C) $40
(D) $38.27
(E) $39.33
Rationale: 4 hrs 25 min = 265 min
First 15 min ------> $6
Time left is 250 min...
Now, 60 min costs $ 8
1 min costs $ 8/60
250 min costs $ 8/60*250 => $ 33.33
So, Total cost will be $33.33 + $6 => $ 39.33
The answer will be (E) $ 39.33
Answer: (E) $39.33
Question: A merchant purchased a jacket for $56 and then determined a selling price that equalled the purchase price of the jacket plus a markup that was 30 percent of the selling price. During a sale, the merchant discounted the selling price by 20 percent and sold the jacket. What was the merchant’s gross profit on this sale?
(A)  $0
(B)  $8
(C)  $4
(D)  $12
(E)  $15
Rationale: Actual Cost = $56
SP = Actual Cost + Mark up
= Actual Cost + 30% SP
= 56*100/70
on sale SP = 80/100(56*100/70) = 64
Gross profit = $8
Answer is B
Answer: (B)  $8
Question: An order was placed for a carpet whose length and width were in the ratio of 3 : 2. Subsequently, the dimensions of the carpet were altered such that its length and width were in the ratio 2 : 1 but were was no change in its perimeter. What is the ratio of the areas of the carpets?
(A) 7:5
(B) 12:11
(C) 17:15
(D) 22:17
(E) 27:25
Rationale: Let the length and width of one carpet be 3x and 2x.
Let the length and width of the other carpet be 2y and y.
2(3x + 2x) = 2(2y + y)
5x = 3y
(5/3) * x = y
The ratio of the areas of the carpet in both cases:
= 3x * 2x : 2y * y
= 6x^2 : 2y^2
= 6x^2 : 2*(25/9) * x^2
= 54 : 50
= 27:25
The answer is E.
Answer: (E) 27:25
Question: A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is:
(A) 2477
(B) 387
(C) 698
(D) 377
(E) 212
Rationale: Explanation:
S.I. for 1 year = Rs. (854 - 815) = Rs. 39.
S.I. for 3 years = Rs.(39 x 3) = Rs. 117.
Principal = Rs. (815 - 117) = Rs. 698
Answer: C) 698
Answer: (C) 698
Question: Sum of the squares of 3 no. is 149 and the sum of their products taken two at a time is 70. Find the sum?
(A) 17
(B) 19
(C) 21
(D) 13
(E) 18
Rationale: (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 149 + 2* 70
a + b + c = âˆš289 = 17
Answer A
Answer: (A) 17
Question: A wheel that has 8 cogs is meshed with a larger wheel of 16 cogs. When the smaller wheel has made 24 revolutions, then the number of revolutions mad by the larger wheel is:
(A) 10
(B) 11
(C) 15
(D) 14
(E) 12
Rationale: E
12
Let the required number of revolutions made by larger wheel be x.
Then, More cogs, Less revolutions (Indirect Proportion)
16 : 8 :: 24 : x <-> 16 x x = 8 x 24
x = (8x 24)/16
x = 12
Answer: (E) 12
Question: Gopi gives Rs. 90 plus one turban as salary to his servant for one year. The servant leaves after 9 months and receives Rs. 40 and the turban. Find the price of the turban.
(A) 27
(B) 36
(C) 29
(D) 10
(E) 110
Rationale: Let the price of turban be x.
Thus, for one year the salary = (90 + x)
For 9 months he should earn 3434 (90 + x).
Now he gets one turban and Rs. 40.
Thus, 3434 (90 + x) = 40 + x or 270 + 3x = 160 + 4x or x = 110
Answer:E
Answer: (E) 110
Question: If AB=3, BC=6, CD=7 and DE=9, what are the coordinates of point E in the figure above?
A.
B.
C.
D.
E.
(A) (−8,8)
(B) (4,−4)
(C) (5,−5)
(D) (2,−2)
(E) (−4,4)
Rationale: Co-ordinates of Point B = (2, 2) (Same x co-ordinate as that of A and Y co ordinate 3 units up than y co ordinate of A)
Co-ordinates of Point C = (-4, 2) (Same Y co-ordinate as that of B and X co-ordinate 6 units Left than X co-ordinate of B)
Co-ordinates of Point D = (-4, -5) (Same x co-ordinate as that of C and Y co-ordinate 7 units Down than Y co-ordinate of C)
Co-ordinates of Point E = (5, -5) (Same Y co-ordinate as that of D and X co-ordinate 9 units Right than X co-ordinate of D)
Answer: Option C
Answer: (C) (5,−5)
Question: Find the area of the quadrilateral of one of its diagonals is 20 cm and its off sets 9 cm and 6 cm?
(A) 189 cm2
(B) 150 cm2
(C) 127 cm2
(D) 177 cm2
(E) 187 cm2
Rationale: 1/2 * 20(9 + 6)
= 150 cm2
Answer: B
Answer: (B) 150 cm2
Question: If x and y are integers, what is the least positive number of 24x+16y?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 8
Rationale: 24x+16y = 8(3x+2y) which will be a minimum positive number when 3x+2y = 1.
3(1) + 2(-1) = 1
Then 8(3x+2y) can have a minimum positive value of 8.
The answer is E.
Answer: (E) 8
Question: A certain company reported that the revenue on sales increased 15 % from 2000 to 2003, and increased 30 % from 2000 to 2005. What was the approximate percent increase in revenue for this store from 2003 to 2005?
(A) 50 %
(B) 40 %
(C) 35 %
(D) 32 %
(E) 13 %
Rationale: Assume the revenue in 2000 to be 100. Then in 2003 it would be 115 and and in 2005 130, so from 2003 to 2005 it increased by (130-115)/115=15/115=13%.
Answer: E.
Answer: (E) 13 %
Question: What is the greatest prime factor of 1+2+3+。。。+70?
(A) 71
(B) 69
(C) 31
(D) 59
(E) 101
Rationale: find the sum from direct formula = n(n+1)/2 = 70(70+1)/2 = 35*71...
71 is a PRIME number, so ans is 71..
A is the answer
Answer: (A) 71
Question: A canoe has two oars, left and right. Each oar either works or breaks. The failure or non-failure of each oar is independent of the failure or non-failure of the other. You can still row the canoe with one oar. The probability that the left oar works is 3/5. The probability that the right oar works is also 3/5. What is the probability Y that you can still row the canoe?
(A) 9/25
(B) 10/25
(C) 6/10
(D) 2/3
(E) 21/25
Rationale: Simply look at the question from the other side. What is the probability that you can’t row the canoe? This would be 2/5 x 2/5 = 4/25.
Using the idea that the probability of something happening is 1 – the probability that it doesn’t happen, you can use the following equation to reach the right answer Y: 1 – 4/25 = 21/25.Answer choice E.
Answer: (E) 21/25
Question: How many three digit numbers can be formed using the digits {1, 3, 4, 5, 7,8, 9}(repetition of digits is not allowed)?
(A) 360
(B) 210
(C) 278
(D) 279
(E) 274
Rationale: The given digits are six.
The number of four digit numbers that can be formed using six digits is
7P3 = 7* 6 * 5 = 210
Answer: B
Answer: (B) 210
Question: For the past n days, the average (arithmetic mean) daily production at a company was 50 units. If today's production of 90 units raises the average to 58 units per day, what is the value of n ?
(A) 30
(B) 18
(C) 10
(D) 9
(E) 4
Rationale: (average production for n days) * n = (total production for n days) --> 50n=(total production for n days);
(total production for n days) + 90 = (average production for n+1 days) * (n+1) --> 50n + 90 = 58 * (n+1) --> n=4.
Or as 40 extra units increased the average for n+1 days by 8 units per day then 40/(n+1)=8 --> n=4.
Answer: E.
Answer: (E) 4
Question: A certain auto manufacturer sold 4% fewer vehicles in 2007 than in 2006. If the manufacturer sold 2.4 million vehicles in 2006, how many vehicles, to the nearest 10,000, did the manufacturer sell in 2007?
(A) 20,00,000
(B) 21,00,000
(C) 23,00,000
(D) 23,90,000
(E) 24,00,000
Rationale: Let's assume in 2006 the manufacturer sold X.
In 2007 he sold X-4/100(X)
If sales in 2006,X= 2.4 million find X-4/100(X)
(2.4 x 10^6)-4/100(2.4 x 10^6)
2400000-96000=23,04,000-----> 23,00,000(approx)
Answer-C
Answer: (C) 23,00,000
Question: A customer pays 30 dollars for a coffee maker after a discount of 20 dollars
What is the original price of the coffe maker?
(A) A)$50
(B) B)$60
(C) C)$70
(D) D)$80
(E) E)$90
Rationale: Let x be the original price.
x - 20 = 30
x - 20 + 20 = 30 + 20
x + 0 = 50
x = 50
correct answer is A)$50
Answer: (A) A)$50
Question: Which number need to add to 859622 to get a number exactly divisible by 456?
(A) 478900
(B) 435390
(C) 656899
(D) 675668
(E) 859622
Rationale: Dividend = Quotient * Divisor + Reminder
859622 / 456 gives quotient = 1885 and reminder = 62.
So, the next number divisible by 456 is 456 places infront of 456 * 1885
Which means 456 – 62 = 394 should be added to 859622.
E
Answer: (E) 859622
Question: In a dairy farm, 20 cows eat 20 bags of husk in 20 days. In how many days one cow will eat one bag of husk?
(A) 1
(B) 40
(C) 20
(D) 26
(E) 30
Rationale: Explanation :
One bag of husk = 20 cows per day
⇒ 20 × 1 × 20 = 1 × 20 × x
For one cow = 20 days
Answer : C
Answer: (C) 20
Question: 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?
(A) 28 days
(B) 76 days
(C) 16 days
(D) 18 days
(E) 19 days
Rationale: 8/12 + 6/x = 1
X = 18 days
Answer:A
Answer: (A) 28 days
Question: Two different primes may be said torhymearound an integer if they are the same distance from the integer on the number line. For instance, 3 and 7 rhyme around 5. What integer W between 1 and 20, inclusive, has the greatest number of distinct rhyming primes around it?
(A) 12
(B) 15
(C) 17
(D) W=18
(E) 20
Rationale: Since we are concerned with integers W between 1 and 20, write down the primes till 40.
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37
(you should be very comfortable with the first few primes... )
2, 3, 5, 7, 11,12, 13, 17, 19, 23, 29, 31, 37 - Three pairs (11,13), (7,17), (5, 19)
2, 3, 5, 7, 11, 13,15,17, 19, 23, 29, 31, 37 - Three pairs (13, 17), (11, 19), (7, 23)
2, 3, 5, 7, 11, 13,17, 19, 23, 29, 31, 37 - Three pairs (11, 23), (5, 29), (3, 31)
2, 3, 5, 7, 11, 13, 17,18,19, 23, 29, 31, 37 - Four pairs (17, 19), (13, 23), (7, 29), (5, 31)
2, 3, 5, 7, 11, 13, 17, 19,20,23, 29, 31, 37 - definitely cannot be more than 4 since there are only 4 primes more than 20. So must be less than 4 pairs. Ignore.
Answer (D).
Answer: (D) W=18
Question: The average of first five prime numbers greater than 20 is?
(A) 32.2
(B) 32.98
(C) 32.3
(D) 32.8
(E) 32.4
Rationale: 23 + 29 + 31 + 37 + 41
= 161/5
= 32.2
Answer: A
Answer: (A) 32.2
Question: An eccentric casino owner decides that his casino should only use chips in $4 and $7 denominations. Which of the following amount cannot be paid out using these chips?
(A) $26
(B) $29
(C) $28
(D) $25
(E) $21
Rationale: Yes, the number of 4 or/and 7 dollar chips can be zero, however both being zero mean that the casino is paying out $0, which is not realistic.
Each option but C can be represented as the sum of a multiple of 4 and a multiple of 7:
A. $29 = 7*3 + 4*2
B. $26 = 7*2 + 4*3
C. $25 = 7*3 + 4*1
E. $21 = 7*3
Answer: C.
Answer: (C) $28
Question: On a two-dimensional coordinate plane, the line q = x^2 - x^3 touches the x-axis in how many places?
(A)  0
(B)  1
(C)  2
(D)  3
(E)  4
Rationale: Apparently it's q = x^2 - x^3 instead of q = x^2 - q^3.
In this case: the x-intercept is the value(s) of x for q = 0.
0 = x^2 - x^3;
0 = x^2(1 - x);
x = 0 or x = 1.
Answer: C.
Answer: (C)  2
Question: A train running at the speed of 60 km/hr crosses a pole in 18 sec. What is the length of the train?
(A) 356
(B) 278
(C) 300
(D) 279
(E) 150
Rationale: Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 18 = 300 m
Answer: C
Answer: (C) 300
Question: There are 5,260 feet in 1 mile and 12 inches in one foot. How many inches are in a mile?
(A) 5,280 - 12
(B) 5,280/12
(C) 12(5,260)
(D) 12^2(5,280)
(E) 12/5,280
Rationale: 1 feet = 12 inches
1 mile = 5260 feet
1 mile = 5260*12 inches
Ans: C
Answer: (C) 12(5,260)
Question: The annual interest rate earned by an investment increased by 10 percent from last year to this year. If the annual interest rate earned by the investment this year was 12.5 percent, what was the annual interest rate last year?
(A) 1%
(B) 1.1%
(C) 9.1%
(D) 11.36%
(E) 10.8%
Rationale: 12.5=1.1*x
X=11.36%
Answer D)
Answer: (D) 11.36%
Question: If (c-5)(y+2) = 0 which of the following must be true?
(A)  c = y
(B)  c > y
(C)  c < y
(D)  cy = -10
(E)  None of the above
Rationale: From (c-5)(y+2) = 0 it follows that either c=5 or y=-2.
(A) c = y --> not necessarily true. Consider c=5 and y=0.
(B) c > y --> not necessarily true. Consider c=5 and y=10.
(C) c < y --> not necessarily true. Consider c=5 and y=0.
(D) cy = -10 --> not necessarily true. Consider c=5 and y=0.
Thus, none of the statements must be true.
Answer: E.
Answer: (E)  None of the above
Question: Find the nest term in series ?
25 16 9 4 1 0 ?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: the series is in the form of perferct square series
5,4,3,2,1,0, then comes 1
the answer is 1
ANSWER:B
Answer: (B) 1
Question: A man can row upstream at 30 kmph and downstream at 60 kmph, and then find the speed of the man in still water?
(A) 27
(B) 29
(C) 30
(D) 20
(E) 45
Rationale: US = 30
DS = 60
M = (30 + 60)/2
= 45
Answer:E
Answer: (E) 45
Question: The greatest possible length which can be used to measure exactly the length 7m, 3m 85cm, 12 m 95 cm is
(A) 15 cm
(B) 25 cm
(C) 35 cm
(D) 42 cm
(E) None of these
Rationale: Solution
Required length	= H.C.F of 700 cm, 385 cm and 1295 cm
‹=› 35 cm.
Answer C
Answer: (C) 35 cm
Question: If two positive numbers are in the ratio 1/8 : 1/5, then by what percent is the second number more than the first?
(A) 40%
(B) 33 1/3%
(C) 60%
(D) 66 2/3%
(E) None of these
Rationale: Given ratio = 1/8 : 1/5 = 5 : 8
Let first number be 5x and the second number be 8x.
The second number is more than first number by 3x.
Required percentage = 3x/5x * 100 = 60%.
ANSWER:C
Answer: (C) 60%
Question: In how many ways can 5 boysand 2 girls be arranged at a table if 2 girls are never together?
(A) 200
(B) 240
(C) 250
(D) 260
(E) 480
Rationale: Total ways of arranging 7 person in a circle = 6! = 720 ways
If we consider two women as one, then we have 5+1=6 persons. Arranging these six persons in circle will take = 5! = 120 ways
And two women can arrange themselves in 2! ways
Total ways in which two women sit together in circle = 5!*2! = 240 ways
Total ways in which two women doesn’t sit together in circle = 6! - 5!*2! = 720 - 240 = 480 ways
E
Answer: (E) 480
Question: A garrison of 400 men had a provision for 31 days. After 28 days 280 persons re-enforcement leave the garrison. Find the number of days for which the remaining ration will be sufficient?
(A) 17 days
(B) 19 days
(C) 10 days
(D) 16 days
(E) 12 days
Rationale: 400 --- 31
400 --- 3
120 --- ?
400*3 = 120*x => x =10 days
Answer: C
Answer: (C) 10 days
Question: In a recent election, Ms. Robbins received 7,200 votes cast by independent voters, that is, voters not registered with a specific political party. She also received 10 percent of the votes cast by those voters registered with a political party. If N is the total number of votes cast in the election and 40 percent of the votes cast were cast by independent voters, which of the following represents the number of votes that Ms. Robbins received?
(A) 0.06N + 3,200
(B) 0.1N + 7,200
(C) 0.06N + 7,200
(D) 0.1N + 8,000
(E) 0.06N + 8,000
Rationale: total vote = N
vote cast by independent voters = 0.4 N
vote cast by registered voters = 0.6 N
vote received by Ms. Robbins = 7200 + 10% of vote be registered voters = 7200 + 0.06 N
Answer choice C
Answer: (C) 0.06N + 7,200
Question: Look at this series: 53, 53, 48, 48, 43, 43, ... What number should come next?
(A) A)12
(B) B)14
(C) C)38
(D) D)53
(E) E)86
Rationale: In this series, each number is repeated, then 5 is subtracted to arrive at the next number.
Answer: C
Answer: (C) C)38
Question: A worker is paid x rupees for painting every 20 metres of a wall and y rupees for painting every extra metre. During one week, he painted 20 metres on Monday, 22 metres on Tuesday, 24 metres on Wednesday, 26 metres on Thursday and 28 metres on Friday. What is his average daily earning rupees for the five day week?
(A) x + (8/5)y
(B) (5x + 9y)/5
(C) x+4y
(D) None of these
(E) Cannot be determined
Rationale: Explanation :
On Monday, the payment = Rs x
On Tuesday, the payment = Rs (x + 2y)
On Wednesday, the payment = Rs (x + 4y)
On Thursday, the payment = Rs (x + 6y)
On Friday, the payment = Rs (x + 8y)
Average daily earning during the five-day week = (5x +20y)/5
= x + 4y
Answer : C
Answer: (C) x+4y
Question: How many 4 digit numbers are there, if it is known that the first digit is even, the second is odd, the third is prime, the fourth (units digit) is divisible by 3, and the digit 3 can be used only once?
(A) 20
(B) 150
(C) 225
(D) 250
(E) 316
Rationale: 4 options for the first digit: 2, 4, 6, 8;
5 options for the second digit: 1, 3, 5, 7, 9;
4 options for the third digit: 2, 3, 5, 7;
4 options for the fourth digit: 0, 3, 6, 9.
Four digit # possible without the restriction (about the digit 6): 4*5*4*4=320
Numbers with three 3-s, 3X3X3 4*1*1*1=4
Thus there are 320-4=316 such numbers.
Answer: E.
Answer: (E) 316