mathewhe/aqua_rat huggingface dataset:
Question: Arun borrowed a sum for 4 years on S.I. at 12%. The total interest paid was Rs. 360. Find the Principal.
(A) 120
(B) 360
(C) 480
(D) 560
(E) 750
Rationale: P=100×SI/RT=100×360/12×4
=100×30/4
=25×30
=750
Option E
Answer: (E) 750
Question: A and B can do a piece of work in 45 days and 40 days respectively. They began to do the work together but A leaves after some days and then B completed the remaining work in 23 days. The number of days after which A left the work was
(A) 5 days
(B) 6 days
(C) 7 days
(D) 9 days
(E) 8 days
Rationale: does the job in 40 days = 1/40
A & B together completes the job = ?
After A leaves, B completes the remaining job in 23 days.
i.e B's part of job in 23days = 23/40
Remaining part 17/40 is done by A & B together in x no.of days.
i.e (x/45) + (x/40) = 17/40
=> x = 9 days
ANSWER:D
Answer: (D) 9 days
Question: The ratio of the radius of two circles is 1: 3, and then the ratio of their areas is?
(A) 1: 5
(B) 1: 0
(C) 1: 9
(D) 1: 4
(E) 1: 2
Rationale: r1: r2 = 1: 3
Πr12: Πr22
r12: r22 = 1: 9
Answer: C
Answer: (C) 1: 9
Question: A group of four girls and three boys have tickets for seven adjacent seats in one row of a theater. If the three girls will not sit in three adjacent seats, how many possible different seating arrangements are there for these 7 theatre-goers?
(A) 7! – 2!3!2!
(B) 7! – 4!3!
(C) 7 × 2!3!2!
(D) 2!3!2!
(E) 7! – 5!3!
Rationale: There are 3 boys and 4 girls , we want to calculate the seating arrangements if three boys do not sit together, like MMM.
Let's calculate the # of arrangements when they SIT together and subtract from total # of arrangements of these 7 persons without restriction. Thus we'll get the # of arrangements asked in the question.
1. Total # of arrangements of 7 is 7!.
2. # of arrangements when 3 girls are seated together, like GGG;
Among themselves these 3 boys can sit in 3! # of ways,
Now consider these 3 boys as one unit like this {GGG}. We'll have total of 5 units: {GGG}{G}{B}{B}{B}. The # of arrangements of these 5 units is 5!.
Hence total # of arrangements when 3 men sit together is: 3!5!.
# of arrangements when 3 boys do not sit together would be: 7!-3!5!.
Answer: E.
Answer: (E) 7! – 5!3!
Question: Jose is uploading a file to the internet for a college project. The file weighs 160 megabytes. If Jose's internet speed for uploading tops 8 megabytes per minute, how long will it take until the upload is completed?
(A) 1 hour
(B) 45 minutes
(C) 20 minutes
(D) 5 minutes
(E) 1 hour and 10 minutes
Rationale: Answer is (C). Jose calculates that if the files weighs 160 megabytes, and his internet uploads at 8 megabytes per minute, it would take 20 minutes to upload as 160 divided by 8 megabytes per minute equals 20.
Answer: (C) 20 minutes
Question: If c is 14% of a and 40% of b, what percent of a is b?
(A)  2.5%
(B)  15%
(C)  25%
(D)  35%
(E)  250%
Rationale: Answer = D
14a/100 = 40b/100
b = 14a/40 = 35a/100 = 35%
Answer: (D)  35%
Question: Using all the letters of the word "TEN", how many words can be formed, which begin with N and end with A?
(A) 1
(B) 6
(C) 8
(D) 9
(E) 2
Rationale: There are five letters in the given word.
Consider 3 blanks ....
The first blank and last blank must be filled with T and N all the remaining three blanks can be filled with the remaining 1 letters in 1! ways.
The number of words = 1! = 1.
Answer: A
Answer: (A) 1
Question: Jo's collection contains US, Indian and British stamps. If the ratio of US to Indian stamps is 5 to 3 and the ratio of Indian to British stamps is 5 to 1, what is the ratio of US to British stamps?
(A) 5 : 1
(B) 10 : 5
(C) 15 : 2
(D) 20 : 2
(E) 25 : 2
Rationale: U/I = 5/3
I/B = 5/1
Since I is multiple of both 2 (as per first ratio) and 5 (as per second ratio) so let's assume that I = 10
i.e. Multiplying teh first ratio by 5 and second ration by 2 in each numerator and denominator
then, U : I : B = 25 : 15 : 2
i.e. U : B = 25 : 2
Answer: Option E
Answer: (E) 25 : 2
Question: What no. should be subtracted from x^3+4x^2−7x+12x^3+4x^2−7x+12, if it is to be perfectly divisible by x+3x+3?
(A) 40
(B) 42
(C) 45
(D) 46
(E) 49
Rationale: According to remainder theorem when dfracf(x)x+adfracf(x)x+a, then the remainder is f(−a)f(−a).
In this case, as x+3x+3 divides x3+4x2−7x+12–kx3+4x2−7x+12–k perfectly (kk being the number to be subtracted), the remainder is 0 when the value of xx is substituted by -3.
i.e., (−3)3+4(−3)2−7(−3)+12−k=0(−3)3+4(−3)2−7(−3)+12−k=0
or −27+36+21+12=k−27+36+21+12=k
or k=k= 42
B
Answer: (B) 42
Question: A city had 800 migrants in the year 2000. Since then, The number of migrants in a countrythe city has doubled every 2 years. If there were 800 migrants in the country in the year 2000, What was the increase in the population of migrants during the period from 2006 to 2008?
(A) 2800
(B) 4400
(C) 5400
(D) 6400
(E) 8800
Rationale: The population will increase in the following order:
2000: 800
2002: 1600
2004: 3200
2006: 6400
2008: 12800
Difference between 2006 and 2008 = 6400
Option D
Answer: (D) 6400
Question: On a map, 3 centimeters represents 33 kilometers. Two cities 209 kilometers apart would be separated on the map by how many centimeters?
(A) 19
(B) 7
(C) 13
(D) 110
(E) 180
Rationale: 1 centimeter represents 11 kilometers ( 33/3 )
X=209/11= 19
Answer: A
Answer: (A) 19
Question: The average of 25 result is 18.The average of 1st 12 of them is 14 & that of last 12 is 17.Find the 13th result.
(A) 57
(B) 48
(C) 36
(D) 78
(E) 52
Rationale: Clearly 13th result=(sum of 25 results)-(sum of 24 results)
=(18*25)-(14*12)+(17*12)
=450-(168+204)
=450-372
=78.
Ans: D
Answer: (D) 78
Question: The distance that light travels in one year is approximately 5,870,000,000,000 miles. The distance light travels in 10 years is:
(A) 111 × 1827 miles
(B) 999× 1238 miles
(C) 346 × 1012 miles
(D) 247 × 1012 miles
(E) 587 × 10^11 miles
Rationale: The distance of the light travels in 10 years is:
5,870,000,000,000 × 10 miles.
= 58,700,000,000,000 miles.
= 587 × 10^11 miles.
Answer :E
Answer: (E) 587 × 10^11 miles
Question: A 20% stock yielding 10% is quoted at :
(A) 83.33
(B) 110
(C) 200
(D) 120
(E) 160
Rationale: Solution
To earn Rs. 10, money invested = Rs. 100.
To earn Rs. 20, money invested = Rs.(100/10X20) = Rs. 200.
âˆ´ Market value of Rs. 100 stock =Rs. 200
Answer C
Answer: (C) 200
Question: The rate of inflation was 1000%. Then what will be the cost of an article, which costs 6 units of currency now, 2 years from now?
(A) 666
(B) 626
(C) 547
(D) 726
(E) None of these
Rationale: Explanation :
Let x be initial cost .
1000 % increase => x + (1000/100)x = 11x.
1st yr = 6 * 11 = 66
2nd year = 66 * 11 = 726.
Answer : D
Answer: (D) 726
Question: What is the perimeter of a regular polygon with sides of length 15 cm and internal angles measuring 130° each?
(A) 108 cm
(B) 118 cm
(C) 120 cm
(D) 132 cm
(E) 144 cm
Rationale: Sum of all interior angles is given by:
180(n-2) = n is number of sides
180(n-2) = 130*n
from here
n = 7.2
So perimeter becomes 15*7.2= 108
Answer: A
Answer: (A) 108 cm
Question: 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, (...)
(A) 53
(B) 67
(C) 48
(D) 59
(E) 45
Rationale: Explanation :
All are prime numbers in their order, starting from 23
Hence, next number is 67
Answer : B
Answer: (B) 67
Question: Mike weighs twice as much as Mary. Mike's weight is 150% of Michelle's weight. Alan weighs 20% more than Charlie. Charlie weighs 160% of Mary's weight. Which of these 5 people weighs the highest?
(A) Mary
(B) Mike
(C) Michelle
(D) Alan
(E) Charlie
Rationale: Mary < Michelle < Mike
Charlie < Alan
Let x be Mary's weight.
Mike's weight is 2x and Alan's weight is 1.2*1.6x = 1.92x.
The answer is B.
Answer: (B) Mike
Question: The diameter of the driving wheel of a bus in 140 cm. How many revolutions per minute must the wheel make in order to keep a speed of 11 kmph?
(A) 21.23
(B) 52.85
(C) 23.26
(D) 41.67
(E) 25.15
Rationale: distance covered in 1 min=(66*1000)/60=183.33cm
circumference of the wheel=(2*(22/7)*.70)=4.4m
no of revolution per min=183.33/4.4=41.67
ANSWER:D
Answer: (D) 41.67
Question: Anil invested a sum of money at a certain rate of simple interest for a period of five years. Had he invested the sum for a period of nine years for the same rate, the total intrest earned by him would have been sixty percent more than the earlier interest amount. Find the rate of interest p.a.
(A) 6%
(B) 9%
(C) 12.5%
(D) Cannot be determined
(E) None of these
Rationale: Let the sum be Rs.P. Let the rate of interest be R% p.a.
(P)(9)(R)/100 = [1 + 6/100][ (P)(5)(R) /100] = 1.6{5PR/100]
9PR/100 = 9PR/100 which is anyway true.
R cannot be found.
ANSWER:D
Answer: (D) Cannot be determined
Question: Two trains of equal are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 sec. The length of each train is?
(A) 50
(B) 88
(C) 77
(D) 66
(E) 45
Rationale: Let the length of each train be x m.
Then, distance covered = 2x m.
Relative speed = 46 - 36 = 10 km/hr.
= 10 * 5/18 = 25/9 m/sec.
2x/36 = 25/9 => x = 50.
Answer: A
Answer: (A) 50
Question: Which of the following is closer to √0.8+√0.1?
(A) 0.5
(B) 0.7
(C) 0.9
(D) 1.1
(E) 1.2
Rationale: √0.8+√0.1=approximately √0.81+√0.09=0.9+0.3=1.2. Hence, the correct answer is E.
Answer: (E) 1.2
Question: In an office, 60 percent of the workers have at least 5 years of service, and a total of 16 workers have at least 10 years of service. If 90 percent of the workers have fewer than 10 years of service, how many of the workers have at least 5 but fewer than 10 years of service?
(A)  96
(B)  64
(C)  50
(D)  144
(E)  160
Rationale: (10/100)Workers = 16 = > number of workers = 160
(60/100)*Workers = x+16 = > x = 96
Answer A
Answer: (A)  96
Question: The list price of a watch is 160. A retailer bought the same watch 122.40. He got two successive discounts one at 10% and the other at a rate which was not legible. What is the second discount rate?
(A) 12%
(B) 14%
(C) 15%
(D) 18%
(E) None of these
Rationale: Retailer price = list price (1−d1/100)(1−d2/100)
⇒ 122.40 = 160(1−10/100)(1−d2/100)
⇒ 1−d2/100=122.40×100/160×90=0.85
⇒ d2 = (1 - 0.85) × 100 = 15%
Answer C
Answer: (C) 15%
Question: Angela, Bernie, and Colleen can complete a job, all working together, in 4 hours. Angela and Bernie, working together at their respective rates, can complete the same job in 6 hours. How long would it take Colleen, working alone, to complete the entire job?
(A) 8 hours
(B) 10 hours
(C) 12 hours
(D) 16 hours
(E) 24 hours
Rationale: A+B+C complete the job in 4 hours.
A+B complete the job in 6 hours.
A+B and C complete the job in 4 hours -->1/(A+B) + 1/C = 1/4-->1/6+1/C=1/4 ----> C=24 hours. ANS E
Answer: (E) 24 hours
Question: If the price of an item is decreased by 20% and then increased by 20%, the net effect on the price of the item is
(A) A decrease of 4%
(B) No change
(C) A decrease of 1%
(D) A increase of 1%
(E) none
Rationale: initially assume 100 rupees
20% discount in 100 gives price of 80 rupees
then 20% raise in 80 is only 16 rupees.
therefore total price =96 rupees.
hence 4% is the loss
ANSWER:A
Answer: (A) A decrease of 4%
Question: If log 2 = 0.3010 and log 3 = 0.4771 then the value of log 4.5 is:
(A) 0.6532
(B) 0.7727
(C) 0.3266
(D) 0.3796
(E) none of these
Rationale: log 3 + log 3 = log (3*3) ->log 9 = 0.4771 + 0.4771 = 0.9542
now
log 9 - log 2 = log (9/2) =log 4.5
-> log 4.5 = 0.9542 - 0.3010 = 0.6532
ANSWER:A
Answer: (A) 0.6532
Question: The number 155 can be written as the sum of the squares of 3 different positive integers. What is the sum of these 3 integers?
(A) 17
(B) 16
(C) 15
(D) 14
(E) 21
Rationale: 7^2+5^2+9^2=49+25+81 = 155
7+5+9 =21
Hence answer is E
Answer: (E) 21
Question: A thief steels a car at 6a.m. and drives it at 60kmph. The theft is discovered at 7a.m. and the owner sets off in another car at 90 kmph. When will he overtake the thief?
(A) 9a.m.
(B) 9.30a.m.
(C) 10a.m.
(D) 11.45a.m.
(E) 10.15a.m.
Rationale: Suppose the thief overtakes x hours after 6a.m.
Distance covered by the thief in x hrs = distance covered by the owner in (x-1 hours)
60x = 90(x-1)
30x = 90
x = 3 hrs
Thief is overtaken at 9a.m.
Answer is A
Answer: (A) 9a.m.
Question: Find the C.I. on a sum of Rs.1800 for 6 months at 20% per annum, interest being compounded quarterly?
(A) 792
(B) 892
(C) 8920
(D) 802
(E) 9920
Rationale: C.I.= 1800(21/20)^2-1800
= 792
Answer: C
Answer: (C) 8920
Question: For what value of x, is |x – 2| + |x + 5| + |x| = 17?
(A)  0
(B)  3
(C)  -3
(D)  5
(E)  -5
Rationale: For what value of x, is |x – 2| + |x + 5| + |x| = 17?
It's easiest just to plug in answer choices:
(D): 5
|x – 2| + |x + 5| + |x| = 17?
|5 - 3| + |5 + 5| + |5| = 17?
|2| + |10| + |5| = 17
(D)
Answer: (D)  5
Question: There are three guys who have equal number of bullets. All of them shoot 4 bullets. The remaining bullets are equal to the total number of bullets remaining is equal to the bullets each had after division. What was the original number of bullets each one had?
(A) 18
(B) 19
(C) 20
(D) 21
(E) 22
Rationale: let initially each was having x bullets
they shot 4 bullets
so 3x-12=x
x=6
so each was having 6 bullets.
total was 18.
ANSWER:A
Answer: (A) 18
Question: A car was driving at 50 Km/h for 30 minutes, and then at 40 Km/h for another 30 minutes. What was its average speed?
(A) 80.
(B) 75.
(C) 70.
(D) 65.
(E) 54.
Rationale: driving at 50 Km/h for 30 minutes ,distance covered = 50*1/2=25 km
driving at 40 km/h for 30 minutes ,distance covered = 40*1/2=20 km
average speed = total distance/total time = 45/1 = 45 km/h
Answer : A
Answer: (A) 80.
Question: If after 300 grams of water were added to the 24%-solution of alcohol, the strength of the solution decreased by one-third, how much of the 24%-solution was used?
(A) 180 grams
(B) 220 grams
(C) 250 grams
(D) 350 grams
(E) 600 grams
Rationale: I too think 600 grams should be the answer.
My reasoning is
The h20 content in 300 gms of water is 1
h20 content in 24% solution is 0.76
Resulting new solution's concentration decreases by one third means. Now it becomes 16% solution which means h20 content is 0.84
Let amount of solution be X
Then the equation can be set up
300*1 + 0.76X = 0.84 (X+300)
0.08X = 48
8X = 4800
X = 600 (ans E)
Answer: (E) 600 grams
Question: The average of the two-digit numbers, which remain the same when the digits interchange their positions, is:
(A) 98
(B) 55
(C) 21
(D) 23
(E) 28
Rationale: Explanation:
Average = (11 + 22 + 33 + 44 + 55 + 66 + 77 + 88 + 99)/9
= [(11 + 99) + (22 + 88) + (33 + 77) + (44 + 66) + 55]/9
= [(4 * 110) + 55]/9 = 495/9 = 55.
Option B
Answer: (B) 55
Question: Eleven bags are bought for Rs.1000 and sold at 10 for Rs.1500. What is the gain or loss in percentage?
(A) 10%
(B) 21%
(C) 26%
(D) 20%
(E) None of these
Rationale: Explanation:
As selling price is Rs.1500 for 10 bags, each bag is sold at Rs.150.
Hence, the profit is Rs.100 after selling 10 bags plus the selling price of 1 bag = 100 + 150 = Rs.260.
%profit = 260/1000 *100
= 26%
ANSWER C
Answer: (C) 26%
Question: a number divided by 34 leaves remainder 37 what is the remainder when same number divided by 9
(A) 7
(B) 8
(C) 9
(D) 0
(E) 1
Rationale: add 34+37=72
now 72divided by 9 so we get 0 as reaminder
ANSWER:D
Answer: (D) 0
Question: 9.4 , 9.9 , 9.9 , 9.9 , 10.0 , 10.2 , 10.2 , 10.5
The mean and the standard deviation of the 8 numbers shown above is 10 and 0.3 respectively. What percent of the 8 numbers a re within 1 standard deviation of the mean?
(A) 90%
(B) 85%
(C) 80%
(D) 75%
(E) 70%
Rationale: D. 75% answer is D
Answer: (D) 75%
Question: The average age of 15 men of a group is 18 years. Out of these, the average age of 5 men is 14 years and that of the other 9 men is 16 years. The age of the 15th man is?
(A) 11 years
(B) 17 years
(C) 56 years
(D) 14 years
(E) 12 years
Rationale: Age of the 15th student
=[15 * 18 - (14 * 5 + 16 * 9)]
= (270- 214)
= 56 years.
Answer:C
Answer: (C) 56 years
Question: How many three letter words are formed using the letters of the word TIME?
(A) 22
(B) 28
(C) 27
(D) 24
(E) 91
Rationale: Explanation:
The number of letters in the given word is four.
The number of three letter words that can be formed using these four letters is â´Pâ‚ƒ = 4 * 3 * 2 = 24.
Answer: D
Answer: (D) 24
Question: Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even ?
(A) 3/4
(B) 1/4
(C) 7/4
(D) 1/2
(E) None of these
Rationale: Explanation:
Total number of cases = 6*6 = 36
Favourable cases = [(1,2),(1,4),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,2),(3,4),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,2),(5,4),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)] = 27
So Probability = 27/36 = 3/4
Option A
Answer: (A) 3/4
Question: A carpenter makes 4 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 = 4.7
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.
C
Answer: (C) 5.
Question: In the fifth grade at Parkway elementary school there are 420 students. 312 students are boys and 250 students are playing soccer. 82% of the students that play soccer are boys. How many girl student are in Parkway that is not playing soccer?
(A) 63.
(B) 73.
(C) 81
(D) 91
(E) 108
Rationale: Total students = 420
Boys = 312, Girls = 108
Total playing soccer = 250
82%of 250 = 205 are boys who play soccer.
Girls who play soccer = 45.
Total girls who do not play soccer = 108 - 45 = 63.
Correct option: A
Answer: (A) 63.
Question: A train 150 m long running at 72 kmph crosses a platform in 25 sec. What is the length of the platform?
(A) 271
(B) 266
(C) 350
(D) 277
(E) 232
Rationale: D = 72 * 5/18 = 25 = 500 – 150
= 350
Answer:C
Answer: (C) 350
Question: For one cake, a recipe calls for 3 cups of milk, 2 cups of sugar, and 2 cups of flour. Sally wants to bake as many cakes as possible and has 27 cups of milk and 18 cups of flour. How many cups of sugar does she need?
(A) 27
(B) 18
(C) 9
(D) 36
(E) 2
Rationale: First, we need to figure out how many cakes Sally can make with her milk and flour.
Both the amount of milk and flour she has is 9 times the amount needed for one cake, so she can make 9 cakes.
Since she needs sugar for 9 cakes, she needs 9 times 2 cups of sugar = 18 cups
Answer: B)
Answer: (B) 18
Question: A man sold 18 toys for Rs. 27300, gaining thereby the cost price of 3 toy find the cost price of a toy
(A) s. 600
(B) s. 800
(C) s.500
(D) s.900
(E) s. 1300
Rationale: Let the cost of one toy = X.
Then, cost of 18 toys = 18X.
Gain = 3X.
SP of 18 toys = Rs. 27300.
Gain = SP â€“ CP
3X = 27300 â€“ 18X
21X = 27300
X = Rs. 1300.
ANSWER : OPTION E
Answer: (E) s. 1300
Question: Mangala completes a piece of work in 20 days, Raju completes the same work in 30 days. If both of them work together, then the number of days required to complete the work is
(A) 4 days
(B) 6 days
(C) 8 days
(D) 10 days
(E) 12 days
Rationale: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days.
That is, the required No. of days = 20 × 30/50 = 12 days.
Answer : E
Answer: (E) 12 days
Question: 27 is a perfect cube. When x is perfect cube which is added to the prime factor of 27, the result is not a prime number. What is the square root of x?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
Rationale: 27 is 3*3*3
2*2=4, 3+4=7
4*4=16, 3+16=17
6*6=36, 3+36=39
8*8=64, 3+64=67
10*10=100, 3+100=103
here C is the only addition that is not a prime number.
so the answer is C
Answer: (C) 6
Question: A rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.2 per sq m?
(A) 675, Rs.1350
(B) 575, Rs.1350
(C) 1350, Rs.675
(D) 1450, Rs.775
(E) 1550, Rs.875
Rationale: Area = (l + b +2d) 2d
= (75 + 55 +2.5 * 2) 2*2.5 => 675
675 * 2 = Rs.1350
ANSWER:A
Answer: (A) 675, Rs.1350
Question: From the integer n, if n*n*n is odd, then what is true from below options?
(A) n is odd
(B) n*n is even
(C) n is odd and n*n is even
(D) n is even
(E) None
Rationale: n is odd and n*n is even
Option C
Answer: (C) n is odd and n*n is even
Question: In how many different ways can the letters of the word ‘I’ be arranged?
(A) 7
(B) 2
(C) 3
(D) 1
(E) 5
Rationale: D
1
The word SMART has 1 distinct letters.
Number of arrangements = 1!
= 1 x 1 = 1
Answer is D
Answer: (D) 1
Question: On dividing a number by 5, we get 3 as remainder. What will the remainder when the square of the this number is divided by 5 ?
(A) 0
(B) 5
(C) 8
(D) 9
(E) 4
Rationale: Explanation:
Let the number be x and on dividing x by 5, we get k as quotient and 3 as remainder.
x = 5k + 3
x^2 = (5k + 3)^2
= (25k^2 + 30k + 9)
= 5(5k^2 + 6k + 1) + 4
On dividing x2 by 5, we get 4 as remainder.
E)
Answer: (E) 4
Question: Five years ago the average of the ages of A and B was 40 years and now the average of the ages of B and C is 44 years. What will be the age of the B ten years hence?
(A) 22
(B) 88
(C) 26
(D) 96
(E) 51
Rationale: Let the present ages of A, B and C be a, b and c respectively.
Given, [(a - 5) + (b - 5)] / 2 = 40 => a + b = 90 --- (1)
(b + c)/2 = 44 => b + c = 88 --- (2)
From (1) and (2), we cannot find b.
Answer: B
Answer: (B) 88
Question: Two trains are moving in opposite directions @ 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is:
(A) 36
(B) 45
(C) 48
(D) 49
(E) 50
Rationale: Relative speed=60+90=150*5/18=(125/3)m/s
Total Distance covered=(1.10+0.9)= 2 km = 2000m
Required time = (2000*3/125) = 48sec
ANSWER:C
Answer: (C) 48
Question: A woman goes shopping during a door buster sale at JcPenney's. You are given a ticket with a random number on it when you arrive at the store. The number on the ticket is the pecent you get to take off of your total bill. The woman bought a shirt for $9.99, a pair of jeans for 19.99 and a jacket for $36.00. Her total was 65.98 before her secret door buster discount. If she paid 59.38 after her discount, What number did the woman have on her ticket?
(A) 10
(B) 5
(C) 15
(D) 20
(E) 25
Rationale: 65.98-59.38= 6.50 = amount of money saved
65.98÷6.50=9.999 = percent of the total bill
9.99 is rounded up to 10.
The answer is A
Answer: (A) 10
Question: Which of the following number is divisible by 4 and 9?
(A) 2368
(B) 2736
(C) 3954
(D) 3814
(E) None of these
Rationale: For a number to be divisible by 4, the number formed by the last two digits of that number must be divisible by 4.
For a number to be divisible by 9, the sum of its digits must be divisible by 9.
Among the choices, choices (a) and (b) are divisible by 4 but of the first two choices, only choice (b) is divisible by 9.
Hence choice (b) is divisible by both 4 and 9.
ANSWER:B
Answer: (B) 2736
Question: A girl is organizing her jellybean collection in which each color has its own row. In each row, there are as many jellybeans as the number of jellybean colors. Her little brother chops each jellybean into the same number of peices as the number of jellybean colors. If the final number of jellybean pieces is m, then:
(A) m is a perfect square
(B) m is an odd number
(C) m is an even number
(D) m is a perfect cube.
(E) None
Rationale: For example, if there were 4 jellybean colors, the girl would have made a 4x4 arrangement. The boy chopped up each jellybean into 4, the number of pieces would be (4*4)*4 = 64 pieces, which is a cube of 4.
Answer: D
Answer: (D) m is a perfect cube.