mathewhe/aqua_rat huggingface dataset:
Question: A cargo ship carrying four kinds of items, doohickies, geegaws, widgets, and yamyams, arrives at the port. Each item weighs 2, 11, 5, and 7 pounds, respectively, and each item is weighed as it is unloaded. If, in the middle of the unloading process, the product of the individual weights of the unloaded items equals 1,043,504,000 pounds, how many widgets have been unloaded?
(A) 2
(B) 3
(C) 4
(D) 625
(E) 208,700,800
Rationale: We need to know the number of widgets (which weigh 5 pounds each). The number of times that 5 divides the number is related to the number of times that 10 divides the number.
When we divide 1,043,504,000 by 1000, we get 1,043,504,000 = 1,043,504 * 5^3 *2^3.
1,043,504 is not divisible by 5, thus there are 3 widgets.
The answer is B.
Answer: (B) 3
Question: The digit in units place of the product 81 x 82 x ..... x 89 is
(A) 0
(B) 2
(C) 6
(D) 8
(E) 9
Rationale: Sol.
Required digit = unit digit in (1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9) = 0.
Answer A
Answer: (A) 0
Question: In how many different ways can the letters of the word 'DETAIL' be arranged in such a way that the vowels occupy only the odd positions?
(A) 32
(B) 48
(C) 36
(D) 60
(E) 120
Rationale: 3 vowels can be arranged in odd positions in 6 ways
and
3 consonants can be arranged in even positions in 6 ways.
so total 6*6= 36 ways
ANSWER:C
Answer: (C) 36
Question: If a particular is never chosen, in how many ways can a cricketbe chosen out of 15 players?
(A) 234
(B) 256
(C) 364
(D) 378
(E) 398
Rationale: A particular players is never chosen, it means that 11 players are selected out of 14 players.
=> Required number of ways = 14C11
= 14!/11!x3! = 364
C
Answer: (C) 364
Question: 80% of the population of a village is 23040. The total population of the village is ?
(A) 28800
(B) 24000
(C) 24936
(D) 25640
(E) None
Rationale: Answer
∵ 80% of P = 23040
∴ P = (23040 x 100) / 80 = 28800
Correct Option: A
Answer: (A) 28800
Question: If A,B,C are three integers and AB+C is even ; which of the following must be true? A)C is even B)B is even C)AB is Odd
(A) None of the above
(B) I only
(C) II only
(D) III only
(E) I,II only
Rationale: If AB is Odd then C will not even. O+E = O
If B is even AB is even always. But If C is Odd E+O = O
None of the above are true.
Answer : A
Answer: (A) None of the above
Question: 21 ball numbered 1 to 21. A ballis drawn and then another ball is drawn without replacement.
(A) 2/17
(B) 3/37
(C) 9/42
(D) 8/97
(E) 12/31
Rationale: The probability that first toy shows the even number,
=1021=1021
Since, the toy is not replaced there are now 9 even numbered toys and total 20 toys left.
Hence, probability that second toy shows the even number,
=920=920
Required probability,
=(1021)×(920)=(1021)×(920)
=9/42
C
Answer: (C) 9/42
Question: If x > 0.3, which of the following could be the value of x?
(A) √0.005
(B) √0.0005
(C) √0.3
(D) √0.006
(E) √0.007
Rationale: Answer : C
Answer: (C) √0.3
Question: Find the simple interest on $10000 at 5% per annum for 12 months?
(A) $410
(B) $500
(C) $650
(D) $710
(E) $1000
Rationale: P = $10000
R = 5%
T = 12/12 YEARS = 1 YEAR
S.I. = P*R*T/100 = 10000*5*1/100 = $500
Answer is B
Answer: (B) $500
Question: A 600 meter long train crosses a signal post in 50 seconds. How long will it take to cross a 3 kilometer long bridge, at the same speed?
(A) 4 min
(B) 2 min
(C) 8 min
(D) 9 min
(E) 5 min
Rationale: S = 600/50 = 12 mps
S = 3600/12 = 300 sec = 5 min
Answer: E
Answer: (E) 5 min
Question: How much is 80% of 40 is greater than 4/5 of 25?
(A) 29
(B) 776
(C) 66
(D) 12
(E) 99
Rationale: (80/100) * 40 – (4/5) * 25
32 - 20 = 12
Answer: D
Answer: (D) 12
Question: The average of non zero number and its square is 5 times the number. The number is?
(A) 5
(B) 7
(C) 9
(D) 10
(E) 12
Rationale: Let the number be x
(x+x^2)/2 = 5x
x^2 - 9x = 0
x(x-9) = 0
x = 0 or x = 9
So the number is 9
Answer is C
Answer: (C) 9
Question: Carolina has 1 nickel and 5 pennies in her pocket. If she pulls 2 coins out of her pocket simultaneously and randomly, what is the probability that she will be holding exactly 6 cents?
(A) 1/3
(B) 4/15
(C) 5/6
(D) 6/10
(E) 2/15
Rationale: The probability is equal to the number of desired choices divided by the total number of possibilities.
Probability = Favorable/Total
Total = 6C2 = 6*5/2 = 15
Favorable:
Pick 1 penny out of 5 pennies
AND
Pick the 1 nickel
5C1*1C1 = 5*1 = 5
P = 5/15 = 1/3
When you use combination method, it is picking all possible cases and the order doesn't matter. Whereas, upon choosing probability method to solve, order matters.
Thus,
Total Probability:
Probability of choosing a penny first AND Probability of choosing the nickel
OR
Probability of choosing the nickel first AND Probability of choosing a penny
Answer: A
Answer: (A) 1/3
Question: A pipe can fill a cistern in 20 minutes whereas the cistern when fill can be emptied by a leak in 30 minutes. When both pipes are opened, find when the cistern will be full?
(A) 17 minutes
(B) 87 minutes
(C) 60 minutes
(D) 27 minutes
(E) 11 minutes
Rationale: 1/20 - 1/30 = 1/60
60 minutes
Answer:C
Answer: (C) 60 minutes
Question: The average marks obtained by 120 candidates in a certain examinationis 35.if the average marks of passed candidate is 39 and that of the failed candidates is 15,what is the no. of candidates who passed the examination?
(A) 880
(B) 100
(C) 110
(D) 109
(E) 107
Rationale: Let No. of passed candidates are x
So, x * 39 + (120 – x) 15= 120 * 35
x = 100
B
Answer: (B) 100
Question: The cost of an article is decreased by 15%. If the original cost is $80, find the decrease cost.
(A) 33
(B) 11
(C) 68
(D) 36
(E) 91
Rationale: Original cost = $80
Decrease in it = 15% of $80
= 15/100 × 80
= 1200/100
= $12
Therefore, decrease cost = $80 - $12 = $68
Answer:C
Answer: (C) 68
Question: If the average (arithmetic mean) of x + 1, x + 3, and x + 5 is 0, then x =
(A) –4
(B) –3
(C) –2
(D) –1
(E) 0
Rationale: (x+1 + x+3 + x+5)/3 = 0
=>3x + 9 = 0
=>x = -3
Answer B
Answer: (B) –3
Question: Which of the following is a prime number
(A) 13
(B) 14
(C) 15
(D) 16
(E) 18
Rationale: Clearly, 13 is a prime number.
Option A
Answer: (A) 13
Question: Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 14 cm.
(A) 335 cm2
(B) 885 cm2
(C) 285 cm2
(D) 825 cm2
(E) 266 cm2
Rationale: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)
= 1/2 (20 + 18) * (14)
= 266 cm2
Answer: E
Answer: (E) 266 cm2
Question: The current of a stream at 1 kmph. A motor boat goes 35 km upstream and back to the starting point in 12 hours. The speed of the motor boat in still water is?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 2
Rationale: S = 1
M = x
DS = x + 1
US = x - 1
35/(x + 1) + 35/(x - 1) = 12
x = 6
Answer:A
Answer: (A) 6
Question: The price of lunch for 15 people was $207.00, including a 15 percent gratuity for service. What was the average price per person, EXCLUDING the gratuity?
(A) $11.73
(B) $12.00
(C) $13.80
(D) $14.00
(E) $15.87
Rationale: If the amount spent excluding the gratuity was x, then x(1.15) = 207
=> x = 207/1.15 = 180
Then the average price per person = 180/15 = 12
Option (B)
Answer: (B) $12.00
Question: Divide Rs. 2379 into 3 parts so that their amounts after 2, 3 and 4 years respectively may be equal, the rate of interest being 5% per annum at simple interest. The first part is?
(A) 239
(B) 77
(C) 998
(D) 828
(E) 972
Rationale: Let the parts be x, y and [2379 - (x + y)]
x + (x * 2 * 5/100) = y + (y * 3 * 5/100) = z + (z * 4 * 5/100)
11x/10 = 23y/20 = 6z/5 = k
x = 10k/11, y = 20k/23, z = 5k/6
But x + y + z = 2379
10k/11 + 20k/23 + 5k/6 = 2379
k = (2379 * 11 * 23 * 6)/3965 = (3 * 11 * 23 * 6)/5
x = [10/11 * (3 * 11 * 23 * 6)/5] = 828
Hence, the first part is Rs. 828.
Answer: D
Answer: (D) 828
Question: A man has Rs. 512 in the denominations of one-rupee notes, five-rupee notes and ten rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has?
(A) 45
(B) 60
(C) 75
(D) 90
(E) 96
Rationale: Let number of notes of each denomination be x.
Then x + 5x + 10x = 512
16x = 512
x = 32.
Hence, total number of notes = 3x = 96
Answer: Option E
Answer: (E) 96
Question: A and B’s salaries together amount to Rs. 2,000. A spends 95% of his salary and B spends 85% of his. If now their savings are the same, what is A’s salary?
(A) 1888
(B) 2676
(C) 1297
(D) 1500
(E) 1678
Rationale: (5/100) A = (15/100) B
A = 3B
A + B = 2000
4B = 2000 => B = 500
A = 1500
Answer: D
Answer: (D) 1500
Question: If (x^2 + x - 8)/2 ≤ x + 1, then x could be represented by which of the following?
(A) − 4 ≤ x ≤ − 3
(B) − 4 ≤ x ≤ 3
(C) − 3 ≤ x ≤ 4
(D) − 3 ≤ x ≤ 3
(E) 3 ≤ x ≤ 4
Rationale: IMO C is correct answer
solving through eqautions
x^2 +x-8<= 2x+2
(x+3)(x-4)<=0
Answer: (C) − 3 ≤ x ≤ 4
Question: Average of five numbers is 12, and the sum of three of the numbers is 39, what is the average of the other 2 numbers?
(A) 9.5
(B) 8.5
(C) 7.5
(D) 11.5
(E) 10.5
Rationale: Let the five numbers be a, b, c, d, e. Then their average is (a+b+c+d+e)/5=12a+b+c=39(39+d+e)/5=1239+d+e=60d+e=21average=21/2=10.5Ans E
Answer: (E) 10.5
Question: A cube with its sides numbered 1 through 6 is rolled twice, first landing on a and then landing on b. If any roll of the cube yields an equal chance of landing on any of the numbers 1 through 6, what is the probability E that a + b is prime?
(A)  0
(B)  1/12
(C)  5/12
(D)  7/18
(E)  4/9
Rationale: Total # of outcomes is 6*6=36;
Favorable outcomes:
a-b --> prime
1-1 --> 2;
1-2 --> 3;
2-1 --> 3;
1-4 --> 5;
4-1 --> 5;
2-3 --> 5;
3-2 --> 5;
1-6 --> 7;
6-1 --> 7;
2-5 --> 7;
5-2 --> 7;
3-4 --> 7;
4-3 --> 7;
6-5 --> 11;
5-6 --> 11.
Total of 15 favorable outcomes
E=15/36.
Answer: C.
Answer: (C)  5/12
Question: During a special promotion, a certain filling station is offering a 10 percent discount on gas purchased after the first 10 gallons. If Kim purchased 20 gallons of gas, and Isabella purchased 25 gallons of gas, then Isabella‟s total per-gallon discount is what percent of Kim‟s total per-gallon discount?
(A) 80%
(B) 100%
(C) 116.7%
(D) 120%
(E) 140%
Rationale: Kim purchased 20 gallons of gas. She paid for 10 + 0.9*10 = 19 gallons, so the overall discount she got was 1/20 = 5%.
Isabella purchased 25 gallons of gas. She paid for 10 + 0.9*15 = 23.5 gallons, so the overall discount she got was 1.5/25 = 6%.
6 is 6/5*100 = 120% of 5.
Answer: D.
Answer: (D) 120%
Question: In a queue if 30 children were made to stand in a column, 16 columns could be formed. If 24 children were made to stand in a column, how many columns could be formed?
(A) 15
(B) 20
(C) 22
(D) 26
(E) 29
Rationale: Sol. Required number = 16 *^30 = 20
B
Answer: (B) 20
Question: A boat having a length 3 m and breadth 2 m is floating on a lake. The boat sinks by 1 cm when a man gets into it. The mass of the man is :
(A) 50 kg
(B) 60 kg
(C) 70 kg
(D) 80 kg
(E) None of these
Rationale: Explanation:
In this type of question, first we will calculate the volume of water displaces then will multiply with the density of water.
Volume of water displaced = 3*2*0.01 = 0.06 m cube
Mass of Man = Volume of water displaced * Density of water
= 0.06 * 1000 = 60 kg
Option B
Answer: (B) 60 kg
Question: X and Y run a 300m race,where X beats Y by 30m. To do a favor to Y, X starts 30m behind the starting line in a second 100m race. Both run at the same previous speed. Which of the following is true?
(A) X Beats Y by 2m
(B) X Beats Y by 0.5 m
(C) X Beats Y by 4 m
(D) Y Beats X by 10m
(E) X Beats Y by 3 m
Rationale: Let's suppose that the speed of X is 30m/s and that the speed of Y is 27m/s.
So, in the first race, the results are the following:
X crosses the finish line in 10s. In other words, X has run 300m in 10 s.
In 10s, Y has run 270 meters.
Therefore, there is the difference of 30 meters mentioned in the question.
Now, let's review the second race.
In 11 seconds, X can complete the 300 meters race. We have to remember that X is 30 meters behind the starting line.
But in 11 seconds, Y has covered (270+27) =297 meters. Also, it is important to notice that in 11 seconds Y cannot arrive to the finish line.
So, 300 - 297 = 3 meter
Answer: E
Answer: (E) X Beats Y by 3 m
Question: A boat goes 100 km downstream in 10 hours, and 60 km upstream in 15 hours. The speed of the stream is?
(A) 3km/h
(B) 4km/h
(C) 6km/h
(D) (1/2) km/h
(E) E)None
Rationale: 100 --- 10 DS = 10
? ---- 1
60 ---- 15 US = 4
? ----- 1 S = (10 - 4)/2
= 3 kmph
ANSWER:A
Answer: (A) 3km/h
Question: In a urban village of india named "owlna" , 70% people have refrigerator , 75% people have television , 80% people got computers and 80% got Air-conditionor. how many people(minimum) got all these luxury.
(A) 23%
(B) 17%
(C) 11%
(D) 10%
(E) 15%
Rationale: D
10%
100 - [ (100-85)+(100-80)+(100-75) +(100-70)]
=100-(15+20+25+30)
=100-90
Answer: (D) 10%
Question: A carpenter makes 6 bunk beds every day. A military school needs to organize a place to sleep for 143 soldiers. If there are 5 carpenters working on the job, how many whole days in advance should they receive the order and start working in order to finish the right number of beds assuming that each bunk- bed is used by two soldiers?
(A) 3.
(B) 4.
(C) 5.
(D) 6.
(E) 7.
Rationale: I believe it is C because if 1C makes 3 beds in 1 day then:
1C's rate = 3/1
So 5c's = 3/1 * 5 = 15/1 = 15 beds in a day.
Since we have 173 soldiers who need beds and bunk beds come in pairs, 72 is the least amount of beds needed.
Time = Amount / Rate
Time = 72 / (15/1) = 72/15, simplifying we get 72/15 = 24/5 = 5.7
So, in order for the carpenters to be able to finish they need 5 whole days. At first I made the mistake of thinking how many whole days it took them to finish (as in ignore the partial day) but the prompt clarifiesdays in advance, meaning how many days would they need to finish so even if they finish early, theyusedthat day.
D
Answer: (D) 6.
Question: Which of the following is not divisible by 4?
(A) 10236
(B) 21792
(C) 47816
(D) 91232
(E) 72034
Rationale: Divisibility rule of 4: Last two digits of the number should be divisible by 4
Option A: 10236, last two digits = 36. Divisible by 4
Option B: 21792, last two digits = 92. Divisible by 4
Option C: 47816, last two digits = 16. Divisible by 4
Option D: 91232, last two digits = 32. Divisible by 4
Option E: 72034, last two digits = 34. Not divisible by 4. Hence 72034 is not divisible by 4
Answer: (E) 72034
Question: There are 15 players in a chess group, and each player plays each of the others once. Given that each game is played by two players, how many total games will be played?
(A) 110
(B) 130
(C) 105
(D) 60
(E) 190
Rationale: 10 players are there.
two players play one game with one another.
so 15C2=15*14/2
=105
SO OPTION C is correct
Answer: (C) 105
Question: The parameter of a square is equal to the perimeter of a rectangle of length 24 cm and breadth 16 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places)
(A) 77.14 cm
(B) 47.14 cm
(C) 84.92 cm
(D) 94.94 cm
(E) 31.42 cm
Rationale: Let the side of the square be a cm.
Parameter of the rectangle = 2(24 + 16) = 80 cm Parameter of the square = 80 cm
i.e. 4a = 80
A = 20
Diameter of the semicircle = 20 cm
Circimference of the semicircle
= 1/2(∏)(20)
= 1/2(22/7)(20) = 440/14 = 31.42 cm to two decimal places
ANSWER:E
Answer: (E) 31.42 cm
Question: Rohan's income doubles after every one year. If the initial income was Rs. 4 lakhs, What would be the income after 6 years?
(A) Rs. 2.76 crores
(B) Rs. 2.51 crores
(C) Rs. 2.56 crores
(D) Rs. 2.57 crores
(E) Rs. 2.36 crores
Rationale: Explanation:
Income after 1 year = Rs. (4 * 21) lakhs
Income after 2 years = Rs. (4 * 2 * 2) lakhs = Rs. (4 x 22) lakhs
Income after 6 years = Rs. (4 * 26) lakhs = Rs. 256 lakhs = 2.56 crores.
ANSWER: C
Answer: (C) Rs. 2.56 crores
Question: Evaluate: 6702.5 + 670.25 + 67.025 + 6.7025 + 0.67025
(A) 7447.14775
(B) 6981.59775
(C) 6918.59775
(D) 6198.59775
(E) 6891.59775
Rationale: 6702.5
670.25
67.025
6.7025
+ 0.67025
---------------
7447.14775
Answer is A.
Answer: (A) 7447.14775
Question: The difference of two numbers is 1365. on dividing the larger number by the smaller, we get 6 as quotient and 15 as remainder. What is the smaller number?
(A) 240
(B) 270
(C) 295
(D) 360
(E) None of these
Rationale: Let the smaller number be x. Then larger number = (x+1365).
x+1365=6x+15, 5x=1350, x=270
Smaller number=270.
Correct Option: B
Answer: (B) 270
Question: A shopkeeper buys two articles for Rs.1000 each and then sells them, making 50% profit on the first article and 50% loss on second article. Find the net profit or loss percent?
(A) 500
(B) 768
(C) 276
(D) 280
(E) 279
Rationale: Profit on first article = 50% of 1000 = 500.
This is equal to the loss he makes on the second article. That, is he makes neither profit nor loss.
Answer: A
Answer: (A) 500
Question: In a graduating class, the difference between the highest and lowest salaries is $100,000. The median salary is $50,000 higher than the lowest salary and the average salary is $20,000 higher than the median. What is the minimum number of students R in the class?
(A) A)10
(B) B)12
(C) C)15
(D) D)20
(E) E)25
Rationale: the difference between the highest and lowest salaries is $100,000.
So there are at least 2 people - say one with salary 0 and the other with 100k. No salary will be outside this range.
Median = 50k more than lowest. So median is right in the center of lowest and highest since lowest and highest differ by 100k. In our example, median = 50k. Since there are more than 2 people, there would probably be a person at 50k.
Mean = 20k more than median so in our example, mean salary = 70k
On the number line,
0........50k (median)........100k
Mean = 70k
So there must be people more toward 100k to bring the mean up to 70k. Since we want to add minimum people, we will add people at 100k to quickly make up the right side deficit. 0 and 50k are (70k + 20k) = 90k away from 70k. 100k is 30k away from 70k. To bring the mean to 70k, we will add two people at 100k each to get:
0....50k.....100k, 100k, 100k
But when we add more people to the right of 70k, the median will shift to the right. We need to keep the median at 50k. So every time we add people to the right of 70k, we need to add people at 50k too to balance the median. 50k is 20k less than 70k while 100k is 30k more than 70k. To keep the mean same, we need to add 2 people at 100k for every 3 people we add at 50k. So if we add 3 people at 50k and 2 people at 100k, we get:
0, ... 50k, 50k, 50k, 50k, ... 100k, 100k, 100k, 100k, 100k
the median is not at 50k yet.
Add another 3 people at 50k and another 2 at 100k to get
0, 50k, 50k, 50k, 50k, 50k, 50k, 50k, 100k, 100k, 100k, 100k, 100k, 100k, 100k
Now the median is 50k and mean is 70k.
Total number of people is 15.
Answer (C)
Answer: (C) C)15
Question: If 2^4, 3^3, and 13^3 are factors of the product of 1,452 and w, where w is a positive integer, what is the smallest possible value of w?
(A) 198
(B) 288
(C) 363
(D) 396
(E) 468
Rationale: I will go with E (pending elements to match is 2^2*3^2*13^1 = 468
Answer: (E) 468
Question: A person incurs loss for by selling a watch for Rs1140.at what price should the watch be sold to earn a 5% profit ?
(A) 1542
(B) 3645
(C) 7845
(D) 1260
(E) 3654
Rationale: let the new sp be Rsx.then
(100-loss%) : (1st sp)=(100+gain%) (2nd sp)
	{(100-5)/1400}={(100+5)/x}=> x={(105*1140)/95} =1260.
Ans: D
Answer: (D) 1260
Question: Find the odd man out
864, 420, 200, 94, 40, 16, 6
(A) 420
(B) 200
(C) 16
(D) 94
(E) 6
Rationale: 6x2+4=16
16x2+8=40
40x2+12=92
92x2+16=200.. and so on. 94
ANSWER:D
Answer: (D) 94
Question: The time on a clock is 20 minutes past 5. What is the angle between the hands of the clock?
(A) 60 degrees
(B) 20 degrees
(C) 30 degrees
(D) 50 degrees
(E) 40 degrees
Rationale: The hour hand rotates 360 degrees in twelve hours.
The hour hand rotates 30 degrees in one hour.
The hour hand rotates 5 degrees in ten minutes.
At this time, the hour hand has rotated 160 degrees.
The minute hand rotates 360 degrees in 60 minutes, or 60 degrees in ten minutes.
At this time, the minute hand has rotated 120 degrees.
The difference is 160 - 120 = 40 degrees.
The answer is E.
Answer: (E) 40 degrees
Question: Working simultaneously and independently at an identical constant rate, 6 machines of a certain type can produce a total of x units of product P in 5 days. How many of these machines, working simultaneously and independently at this constant rate, can produce a total of 4x units of product P in 10 days?
(A) 9
(B) 10
(C) 12
(D) 14
(E) 18
Rationale: The rate of 6 machines is rate=job/time=x/5 units per day --> the rate of 1 machine 1/6*(x/5)=x/30 units per day;
Now, again as {time}*{combined rate}={job done}
then 10*(m*x/30)=4x --> m=12.
Answer: C.
Answer: (C) 12
Question: A person's present age is two-fifth of the age of his mother. After 6 years, he will be one - half of the age of his mother. How old is the mother at present ?
(A) A)25
(B) B)40
(C) C)32
(D) D)45
(E) E)30
Rationale: Let the mother's present age be x years
Then the person's present age = 2x/5
(2x/5)+6 = 1/2(x+6)
2(2x+30) = 5 (x+6)
x = 30
Answer is E
Answer: (E) E)30
Question: A salt manufacturing company produced a total of 5000 tonnes of salt in January of a particular year. Starting from February its production increased by 100 tonnes every month over the previous months until the end of the year. Find its average monthly production for that year?
(A) 5520
(B) 2789
(C) 5550
(D) 2889
(E) 2788
Rationale: Total production of salt by the company in that year = 5000 + 5100 + 5200 + .... + 6100 = 66600.
Average monthly production of salt for that year = 66600/12 = 5550.
Answer: C
Answer: (C) 5550
Question: The positive integers a and b leave remainders of 2 and 3, respectively, when divided by 6. a > b.
What is the remainder when a – b is divided by 6?
(A) 4
(B) 3
(C) 5
(D) 2
(E) 1
Rationale: Let's test out some values of m and n that satisfy the given information.
a leaves are remainder of 2 when divided by 6
So, a COULD equal 8
b leaves are remainder of 3 when divided by 6
So, b COULD equal 3
What is the remainder when a – b is divided by 6?
So, a - b = 8 - 3 = 5, and when we divide 5 by 6, we get 0 with remainder 5
Answer: C
Answer: (C) 5
Question: What percent is 120 of 70?
(A) 133 1/3 %
(B) 134 1/3 %
(C) 135 1/3 %
(D) 140 1/3 %
(E) 171 3/7 %
Rationale: 120/70 = 12/7
12/7 × 100 = 1200/7 = 171 3/7 %
E
Answer: (E) 171 3/7 %
Question: Given that f(x) = x×f(x - 1) for any natural number x. If f(x + 2) = 20*f(x), then what is the value of x?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 98
Rationale: Given:f(x) = x××f(x - 1) ....(a)
and f(x + 2) = 20××f(x) ....(b)
Substitute x = x + 1 in (a)
Then, f(x + 1) = (x + 1)××f(x) .........(c)
Substitute x = x + 2 in (a)
Then, f(x + 2) = (x + 2)××f(x + 1) ......(d)
From (b), 20××f(x) = f(x + 2) = (x + 2)××f(x + 1)= (x + 2)(x + 1)××f(x)
⇒⇒ 20××f(x) = (x + 2) (x + 1)××(f(x)
Cancelling f(x) on both sides and upon simplification we get
or x2x2+ 3x - 18 = 0
or (x + 6)(x - 3) = 0
or x = -6 or 3. Hence the answer is option (e).
Answer:B
Answer: (B) 6
Question: In 1995 a total of 250 earthquakes occurred worldwide, some but not all of which occurred in Asia. If 100 of these earthquakes occurred in Asia, which of the following represents the ratio of the number of earthquakes that occurred in Asia to the number that did NOT occur in Asia?
(A) 2/3
(B) 1/3
(C) 1/4
(D) 3/4
(E) 5/8
Rationale: We're given a couple of facts to work with:
1) There were a total of 250 earthquakes
2) Of those earthquakes, 100 of them occurred in Asia
We're asked for the ratio of the number of earthquakes that occurred IN ASIA to the number of earthquakes that DID NOT occur in Asia.
Thus, there were 150 earthquakes that DID NOT occur in Asia....
The answer to the question is 100/150 = 2/3
Answer : A
Answer: (A) 2/3