mathewhe/aqua_rat huggingface dataset:
Question: If p is the smallest positive integer that is not prime and not a factor of 50!, what is the sum of the factors of p?
(A) 51
(B) 54
(C) 162
(D) 72
(E) 50!+2
Rationale: In fact 51=3*17 IS a factor of 50!.
The smallest positive integer that is NOT prime and NOT a factor of 50! is 106=2*53. The sum of the factors of 106 is 162.
Answer: C.
Answer: (C) 162
Question: A heap of coconuts is divided into groups of 2, 5 and 9 and each time one coconut is left over. The least number of Coconuts in the heap is?
A. 31 B. 41 C. 51 D. 61
(A) A)31
(B) B)41
(C) C)51
(D) D)61
(E) E)91
Rationale: LCM = 90
=> 90 + 1 = 91
ANSWER:E
Answer: (E) E)91
Question: In a certain sequence, each term except for the first term is one less than twice the previous term. If the first term is 0.8, then the 3rd term is which of the following?
(A) −1.5
(B) −1
(C) 0
(D) 0.2
(E) 2
Rationale: First = 0.8
Second = 2*0.8-1 = 0.6
Second = 2*0.6-1 = 0.2
Answer: option D
Answer: (D) 0.2
Question: If the side of the regular hexagon above is 2, what is the circumference of the inscribed circle?
(A) 2∏√3
(B) 3∏
(C) 4∏/√3
(D) 2∏/√3
(E) ∏√3
Rationale: Now AC will be 1 because circle is touching the midpoints of the circle.
Then we get kite ACBO.
We have AC = 1 and CB = 1, now we need to find BO which is radius
from triplets we get 30:60:90 = 1:√3:2
Now CBO is right angled triangle, then we get BO as √3.
r = √3...circumference is 2∏r is 2∏√3.
Answer :option A.
Answer: (A) 2∏√3
Question: Three numbers are in the ratio 4 : 5 : 6 and their average is 39 . The largest number is:
(A) 28
(B) 32
(C) 36
(D) 42
(E) 46.8
Rationale: Explanation:
Let the numbers be 4x, 5x and 6x. Therefore,
(4x+5x+6x)/3 = 39
15x = 117
x = 7.8
Largest number = 6x = 46.8.
ANSWER E
Answer: (E) 46.8
Question: Out of 12 persons working on a project, 4 are graduates. If 3 are selected, what is the probability that there is at least one graduate among them?
(A) 5/55
(B) 21/55
(C) 51/55
(D) 41/55
(E) 31/55
Rationale: P(at least one graduate) = 1 - P(no graduates)
= 1 - 8C₃/12C₃ = 1 - (8 * 7 * 6)/(10 * 11 *12)
= 41/55
Answer: D
Answer: (D) 41/55
Question: The speed of a railway engine is 74 Km per hour when no compartment is attached, and the reduction in speed is directly proportional to the square root of the number of compartments attached. If the speed of the train carried by this engine is 24 Km per hour when 9 compartments are attached, the maximum number of compartments that can be carried by the engine is:
(A) 49
(B) 18
(C) 16
(D) 17
(E) 19
Rationale: the reduction in speed is directly proportional to the square root of the number of compartments attached
Doesreductionmean amount subtracted? or percentage decrease? There are at least two interpretations, and the wording does not provide a clear interpretation between them.
Evidently what the question intends is the subtraction interpretation. What is subtracted from the speed is directly proportional to the square root of the number of compartments attached.
In other words, if S = speed, and N = number of compartments, then
S = 74 - k*sqrt(N)
wherekis a constant of the proportionality. In general, if A is directly proportional to B, we can write A = k*B and solve for k.
If N = 9, then S = 24
24 = 74 - k*sqrt(9) = 74 - 3k
k = 16.67
Now, we need to know: what value of N makes S go to zero?
0 = 74 - 16.67*sqrt(N)
16.67*sqrt(N) = 74
sqrt(N) = 4.44
n = 4.44^2 > 19
With 20 compartments, the train does not budge. Therefore, it would budge if there were one fewer cars. Thus, 19 is the maximum number of cars the engine can pull and still move.
E
Answer: (E) 19
Question: If cost of sugar increases by 25%. How much percent consumption of sugar should be decreased in order to keep expenditure fixed?
(A) 20
(B) 10
(C) 15
(D) 25
(E) 30
Rationale: 100
125
-----
125 ----- 25
100 ------ ? => 20%
ANSWER A
Answer: (A) 20
Question: A grocer has 400 pounds of coffee in stock, 20 percent of which is decaffeinated. If the grocer buys another 100 pounds of coffee of which 70 percent is decaffeinated, what percent, by weight, of the grocer’s stock of coffee is decaffeinated?
(A) 28%
(B) 30%
(C) 32%
(D) 34%
(E) 36%
Rationale: 1. 20% of 400=80 pounds of decaffeinated coffee
2. 70% of 100=70 pounds of decaffeinated coffee
3. Wt have 150 pounds of decaffeinated out of 500 pounds, that means 150/500*100%=30%. The correct answer is B.
Answer: (B) 30%
Question: In a kilometer race, A beats B by 50 meters or 10 seconds. What time does A take to complete the race?
(A) 180 sec
(B) 190 sec
(C) 290 sec
(D) 490 sec
(E) 390 sec
Rationale: Time taken by B run 1000 meters = (1000 * 10)/50
= 200 sec.
Time taken by A = 200 - 10
= 190 sec.
Answer:B
Answer: (B) 190 sec
Question: If 6th March, 2005 is Monday, what was the day of the week on 6th March, 2004?
(A) Wednesday
(B) Tuesday
(C) Sunday
(D) Monday
(E) Friday
Rationale: The year 2004 is a leap year. So, it has 2 odd days.
Feb 2004 not included because we are calculating from March 2004 to March 2005. So it has 1 odd day only.
The day on 6th March, 2005 will be 1 day beyond the day on 6th March, 2004.
Given that, 6th March, 2005 is Monday.
6th March, 2004 is Sunday
Answer: C
Answer: (C) Sunday
Question: Two persons A and B take a field on rent. A puts on it 21 horses for 3 months and 15 cows for 2 months; B puts 15 cows for 6months and 40 sheep for 7 1/2 months. If one day, 3 horses eat as much as 5 cows and 6 cows as much as 10 sheep, what part of the rent should A pay?
(A) 1/3
(B) 1/9
(C) 2/8
(D) 6/4
(E) 5/7
Rationale: 3h = 5c
6c = 10s
A = 21h*3 + 15c*2
= 63h + 30c
= 105c + 30c = 135c
B = 15c*6 + 40s*7 1/2
= 90c + 300s
= 90c + 180c = 270c
A:B = 135:270
27:52
A = 27/79 = 1/3
Answer: A
Answer: (A) 1/3
Question: If it is 7:19 in the evening on a certain day, what time in the morning was it exactly 2,880,705 minutes earlier? (Assume standard time in one location.)
(A) 7:25
(B) 7:34
(C) 7:43
(D) 7:47
(E) 7:52
Rationale: 7:19 minus 2,880,705 must end with 4, the only answer choice which ends with 4 is B.
Answer : B.
Answer: (B) 7:34
Question: A person walking at 4 Kmph reaches his office 8 minutes late. If he walks at 6 Kmph, he reaches there 16 minutes earlier. How far is the office from his house?
(A) 4 4/5 Km
(B) 4 1/7 Km
(C) 3 1/5 Km
(D) 3 1/7 Km
(E) 3 2/5 Km
Rationale: Formula = S1*S2/S2-S1 * T1+T2/60
= 4*6/2 * 24/6
= 24/2 * 24/60
= 12 * 2/5
= 24/5 = 4 4/5 Km
A)
Answer: (A) 4 4/5 Km
Question: A train covers a distance in 50 min, if it runs at a speed of 48kmph on an average. The speed at which the train must run to reduce the time of journey to 40min will be
(A) 45 min
(B) 60 min
(C) 55 min
(D) 70 min
(E) 75 min
Rationale: Time = 50/60 hr = 5/6hr
Speed = 48mph
distance = S*T = 48 * 5/6 = 40km
time = 40/60hr = 2/3hr
New speed = 40* 3/2 kmph = 60kmph
Answer : B
Answer: (B) 60 min
Question: Given that a is the average (arithmetic mean) of the first five positive multiples of six and b is the median of the first twelve positive multiples of six, what is the ratio of a to b?
(A) 3:4
(B) 6:13
(C) 5:6
(D) 13:10
(E) 4:3
Rationale: The first nine positive multiples of six are {6, 12, 18, 24,30}
The first twelve positive multiples of six are {6, 12, 18, 24, 30,36,42, 48, 54, 60, 66, 72}
Both sets are evenly spaced, thus their median=mean:
a=18 and b=(36+42)/2=39 --> a/b=18/39=6/13.
Answer: B.
Answer: (B) 6:13
Question: A group of medical interns at Bohemus Medical School want to go on dates. There are 5 girls and 7 guys. Assuming girls go on dates with guys, how many possible ways can these 10 medical interns date each other?
(A)  10
(B)  25
(C)  60
(D)  2520
(E)  2320
Rationale: 1st girl can go with 7 guys
2nd girl can go with remaining 6
3rd girl can go with remaining 5 and so on
so the total ways are 7 * 6 * 5 * 4 * 3
D should be the answer
Answer: (D)  2520
Question: If the numbers 1 to 95 are written on 95 pieces of paper, (one on each) and one piece is picked at random, then What is the probability that the number drawn is neither prime nor composite?
(A) 1/50
(B) 1/25
(C) 1/95
(D) 1
(E) 2
Rationale: There are 25 primes, 69 composite numbers from 1 to 95. The number
which is neither prime nor composite is 1.
Therefore, required probability = 1/95.
ANSWER:C
Answer: (C) 1/95
Question: 852.68 − 4.5 + 108.98 = ? − 2132.54
(A) 6078.58
(B) 5225.9
(C) 6258.58
(D) 6088.58
(E) None
Rationale: Option 'A'
Answer: (A) 6078.58
Question: If 10 crates have 99 apples each and how many apples more is required in order to make 100 apples in each crate?
(A) 5
(B) 10
(C) 15
(D) 20
(E) 0
Rationale: Each crate requires 1 apples and totally there are 10 crates so required apples = 10 * 1 = 10
Answer: B
Answer: (B) 10
Question: The distance between two cities A and B is 330 km. A train starts from A at 8 a.m. and travels towards B at 60 km/hr. Another train starts from B at 9 a.m. and travels towards A at 75 km/hr. At what time do they meet?
(A) 10 a.m
(B) 07 a.m
(C) 11 a.m
(D) 03 a.m
(E) 06 a.m
Rationale: Suppose they meet x hrs after 8 a.m. Then,
(Distance moved by first in x hrs) + [Distance moved by second in (x - 1) hrs] = 330
60x + 75(x - 1) = 330 => x = 3
So, they meet at (8 + 3) i.e., 11 a.m.
Answer: C
Answer: (C) 11 a.m
Question: Rs.6160 were divided among B, C & D in such a way that B had Rs.320 more than C and D had Rs 240 more than B . How much was Câ€™s share?
(A) Rs.2300
(B) Rs.2310
(C) Rs.2320
(D) Rs.2330
(E) Rs.2340
Rationale: Let C gets Rs x. Then We can say B gets Rs (x + 320 ) and D gets Rs ( x + 280) .
x + 320 + x + x + 560 = 6160
3x = 5280
x = 1760 .
Câ€™s share = Rs ( 1760+560 ) = Rs.2320
C
Answer: (C) Rs.2320
Question: What is the smallest positive integer nn such that √6,480∗n is a perfect cube?
(A) 5
(B) 5^2
(C) 30
(D) 30^2
(E) 30^4
Rationale: Sol: Let's factorize 6480 and we get 6480= 3^4*2^4*5
Now we need to see for what minimum value of n√n*6480= a^3 where a is an Integer
So from 6480 we already have 2^4*3^4*5*n√n = (2^2)^3* (3^2)^3*(5)^3 why cause a is an integer which will need to be have the same factors which are in LHS
solving for n√n = (2^6*3^6*5^3)/ 2^4*3^4*5 and we get
n√n= 2^2*3^2*5^2
Or n = 2^4*3^4*5^4 or 30^4
Answer is E
Answer: (E) 30^4
Question: The H.C.F of 1.75, 5.6 and 7 is?
(A) 0.07
(B) 0.7
(C) 3.5
(D) 0.35
(E) None of these
Rationale: Given numbers with two decimal place are: 1.75, 5.60 and 7.00. Without decimal places, these numbers are: 175, 560 and 700, whose H.C.F. is 35.
H.C.F. of given numbers = 0.35.
Correct Option : D
Answer: (D) 0.35
Question: The average height of 50 pupils in a class is 150 cm. Five of them whose height is 146 cm, leave the class and five others whose average height is 156 cm, join. The new average height of the pupils of the class (in cm) is?
(A) 288
(B) 151
(C) 177
(D) 282
(E) 277
Rationale: :
Total height = 150 * 50 = 7500 cm.
New average = [7500 - 5 * 146 + 5 * 156 ] / 50 = 151 cm.
Answer: B
Answer: (B) 151
Question: A work crew of 5 Men takes 6 days to complete one-half of a job. If 7 men are then added to the crew and the men continue to work at the same rate, how many days will it take the enlarged crew to do the rest of the job?
(A) 2 1/2
(B) 3
(C) 3 1/3
(D) 4
(E) 4 4/5
Rationale: Suppose 1 man can do work in X days..
so 5 men will do in ..
5/X=1/6*1/2 as half job is done
X=60
now 7 more are added then
12/60=1/2*1/d for remaining half job
d=2 1/2 Number of days
A
Answer: (A) 2 1/2
Question: 20% of a number is more than 30% of 120 by 80. Find the number?
(A) 520
(B) 560
(C) 580
(D) 620
(E) 610
Rationale: (20/100) * X – (30/100) * 120 = 80
1/5 X = 116
X = 580
Answer:C
Answer: (C) 580
Question: A bag contains an equal number of one rupee, 50 paise and 25 paise coins respectively. If the total value is 105, how many coins of each type are there?
(A) 20 coins
(B) 30 coins
(C) 40 coins
(D) 60 coins
(E) None of these
Rationale: Let number of each type of coin = x. Then,
1 × x + .50 × x + .25x = 105
⇒ 1.75x = 105 ⇒ x = 60 coins
Answer D
Answer: (D) 60 coins
Question: If the radius of a sphere is increased by 50%, find the increase percent in
volume and the increase percent in the surface area.
Sol.
(A) 100%
(B) 120%
(C) 90%
(D) 115%
(E) 125%
Rationale: Let original radius = R. Then, new radius = (150/100)R=(3R/2)
Original volume = (4/3)R3, New volume = (4/3)(3R/2)3 =(9R3/2)
Increase % in volume=((19/6)R3)*(3/4R3)*100))% = 237.5%
Original surface area =4R2. New surface area = 4(3R/2)2=9R2
Increase % in surface area =(5R2/4R2) * 100) % = 125%.
ANSWER E 125%
Answer: (E) 125%
Question: Out of a classroom of 6 boys and 4 girls the teacher picks a president for the student board, a vice president and a secretary. What is the probability that only girls will be elected?
(A) 8/125.
(B) 2/5.
(C) 1/30.
(D) 1/720.
(E) 13/48.
Rationale: probability that only girls will be elected = 4C3/10C3 = 1/30
Answer C.
Answer: (C) 1/30.
Question: 70 91 120
14 13 24
5 7 ?
What number should replace the question mark?
(A) 2
(B) 5
(C) 3
(D) 19
(E) 68
Rationale: B
5
70 Ã· 14 = 5;
91 Ã· 13 = 7,
120 Ã· 24 = 5;
Answer: (B) 5
Question: Mohan's salary was first increased by 20% and then decreased by 20%. If his present salary is Rs. 7200, then what was his original salary?
(A) 188
(B) 7500
(C) 2788
(D) 1277
(E) 2771
Rationale: Let Mohan's salary be Rs.100.
When increased by 20%, Mohan's salary = Rs.120
Again when decreased by 20%, Mohan's salary = 120 - 24 = Rs. 96.
But present salary is Rs. 7200
for, 96 ---> 100 ; 7200 ---> ?
Required salary is 7200/96 * 100 = Rs. 7500
Answer: B
Answer: (B) 7500
Question: How many times the keys of a typewriter have to be pressed in order to write first 400 counting numbers?
(A) 1092
(B) 1300
(C) 1500
(D) 1125
(E) 1234
Rationale: 1 to 9 = 9 * 1 = 9
10 to 99 = 90 * 2 = 180
100 to 400 = 301 * 3 = 903
=====> 1092
ANSWER A
Answer: (A) 1092
Question: Increasing the original price of an article by 10 percent and then increasing the new price by 10 percent is equivalent to increasing the original price by
(A) 20%
(B) 20.5%
(C) 20.8%
(D) 21%
(E) 21.8%
Rationale: 1.1*1.1*x = 1.21*x
The answer is D.
Answer: (D) 21%
Question: How many different sets of positive square integers M, each greater than 1, add up to 75?
(A)  1
(B)  4
(C)  7
(D)  11
(E)  13
Rationale: E = 13 is the correct answer.
Answer: (E)  13
Question: A jar contains 3 red marbles and 7 green marbles.If a marble is drawn from a jar at random,what is the probability that this marble is green?
(A) 3/10
(B) 7/10
(C) 1
(D) 4/10
(E) 6/10
Rationale: Total number of marbles = 7+3 = 10
no. of green marbles = 7
probability of drawn a green marble= 7/10
Answer is B
Answer: (B) 7/10
Question: The equal amounts of money are deposited in two banks each at 15% per annum for 3.5 years and 5 years respectively. If the difference between their interests is Rs.144, find the each sum?
(A) 337
(B) 640
(C) 297
(D) 276
(E) 912
Rationale: (P*5*15)/100 - (P*3.5*15)/100 = 144
75P/100 – 52.5P/100 = 144
22.5P = 144 * 100
=> P = Rs.640
Answer:B
Answer: (B) 640
Question: A batsman in his 12th inning makes a score of 60 and their by increasing his average by 4. What is his average after the 12th inning?
(A) 12
(B) 16
(C) 20
(D) 24
(E) 28
Rationale: 11x + 60 = 12(x + 4)
x = 12 + 4 = 16
Answer:B
Answer: (B) 16
Question: If books bought at prices ranging from Rs. 130 to Rs. 320 are sold at prices ranging from Rs. 210 to Rs 310, what is the greatest possible profit that might be made in selling 18 books ?
(A) Rs. 2500
(B) Rs. 3000
(C) Rs. 3500
(D) Rs. 3240
(E) Rs. 3600
Rationale: The greatest profit is possible only if the cost price of the books are minimum and selling prices are maximum.
Let lowest cost price of the 18 books = 130*18 = Rs. 2,340
Maximum selling price of 18 books = 310 *18 = Rs. 5,580
So, maximum profit = 5580 - 2340 = Rs. 3,240
ANSWER : OPTION D
Answer: (D) Rs. 3240
Question: In a simultaneous throw of two dice , what is the probability of getting to total of 10 or 11?
(A) 15/66
(B) 4/9
(C) 7/36
(D) 3/5
(E) 5/36
Rationale: n(S)36
n(E)=5
P(E)=5/36
Ans: E
Answer: (E) 5/36
Question: The average of the five numbers is 6.8. If one of the numbers is multiplied by 3, the average of the numbers increases to 9.2. Which of the five numbers is multiplied by 3?
(A) 1.5
(B) 3.0
(C) 3.9
(D) 4.0
(E) 6.0
Rationale: Initial avg is 6.8
So the summation of the nos is 6.8*5 = 34
Now the new avg is 9.2
So summation will be 9.2*5 = 46.
So change in summation is 12.
This comes when a number is multiplied by 3.
In the original sum we already have that number added once. To bring additional 12 increment by multiplying by 3, we get a total increase of 18. Thus, 6 is multiplied by 3.
ANSWER:E
Answer: (E) 6.0
Question: You have found a mutant algae that doubles in size every hour. It takes 18 hours for one algae plant to take up half of a certain lake.
How long would it take for two of these plants to take up half of the same lake?
(A) 7
(B) 17
(C) 27
(D) 37
(E) 47
Rationale: At 17 hours the one plant will take up 1/4 of the lake (1/2 of 1/2). At 17 hours the two plants would be double the size of the one plant and double 1/4 is one half.
Answer: (B) 17
Question: The difference of two numbers is 1385. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number ?
(A) 274
(B) 270
(C) 295
(D) 360
(E) 252
Rationale: Let the smaller number be x. Then larger number = (x + 1385).
x + 1385 = 6x + 15
5x = 1370
x = 274
Smaller number = 274.
ANSWER A
Answer: (A) 274
Question: At what price must an article costing Rs.47.50 be marked in order that after deducting 5% from the list price. It may be sold at a profit of 25% on the cost price?
(A) 62.5
(B) 62.0
(C) 62.6
(D) 62.1
(E) 62.2
Rationale: CP = 47.50
SP = 47.50*(125/100) = 59.375
MP*(95/100) = 59.375
MP = 62.5
Answer: A
Answer: (A) 62.5
Question: A and B together can do a piece of work in 10 days. B alone can finish it in 20 days. In how many days can A alone finish the work ?
(A) 20
(B) 10
(C) 15
(D) 5
(E) 7
Rationale: Time taken by A to finish the work = XY/(Y-X)
= 10 x 20 / (20-10)
= 200/10
= 20 days
Answer: A
Answer: (A) 20
Question: A train moves fast a telegraph post and a bridge 264 m long in 8 sec and 40 sec respectively. What is the speed of the train?
(A) 89
(B) 29.7
(C) 56
(D) 79.2
(E) 67
Rationale: Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 8 => x = 8y
(x + 264)/40 = y
y = 8.25 Speed = 8.25 m/sec = 8.25 * 18/5 = 29.7 km/hr.
Answer: Option B
Answer: (B) 29.7
Question: Three numbers are in the ratio 3:4:5 and their L.C.M is 2400. Their H.C.F is:
(A) 40
(B) 80
(C) 120
(D) 200
(E) 220
Rationale: Let the numbers be 3x, 4x and 5x.
Then, their L.C.M = 60x. So, 60x = 2400 or x = 40.
The numbers are (3 * 40), (4 * 40) and (5 * 40).
Hence, required H.C.F = 40.
ANSWER:A
Answer: (A) 40
Question: Three students appear at an examination of Mathematics. The probability of their success are 1/2, 1/4, 1/5 respectively. Find the probability of success of at least two.
(A) 1/60
(B) 2/50
(C) 9/40
(D) 3/40
(E) 4/50
Rationale: The probability of success of at least two students will involve the following possibilities.
The first two students are successful, the last two students are successful, the first and third students are successful and all the three students are successful.
Therefore, the required probability = 1/2 x 1/4 x 4/5 + 1/4 x 1/5 x 1/2 + 1/2 x 1/5 x 3/4 + 1/2 x 1/4 x 1/5 = 9/40
ANSWER:C
Answer: (C) 9/40
Question: A shipment of 1500 heads of cabbage, each of which was approximately the same size was purchased for $600.The day the shipment arrived 2/3 of the heads were sold, each at 25% above the cost per head.The following day the rest were sold at a price per head equal to 10% less than the price each head sold for the day before.what was the gross profit V on this shipment?
(A) a) $100
(B) b) $115
(C) c) $125
(D) d) $130
(E) e) $135
Rationale: I recommend one should use fractions to solve this one rather than converting it into decimals
Sol:
1500 heads -> $600
1 head -> $600/1500
1 head -> $(2/5)
25% more of (2/5) -> 125/100 * 2/5 = $(1/2)
He sold 2/3*1500 = 1000 heads for $(1/2) per head
Total revenue by selling 1000 heads = 1000 * 1/2 = $500
Heads left: 500
Cost per head: 90% of the previous price: 90/100 * 1/2 = $(9/20)
Total revenue by selling 500 heads = 9/20 * 500 = 225
Total revenue after selling 1500 cabbage heads - 225+500 = $725
Money spent on the purchase: $600
Profit V= 725-600 = $125
Ans:C
Answer: (C) c) $125
Question: How long does a train 110 m long running at the speed of 72 km/hr takes to cross a bridge 132 m length?
(A) 11
(B) 12.1
(C) 13
(D) 14
(E) 15
Rationale: Speed = 72 * 5/18 = 20 m/sec
Total distance covered = 110 + 132 = 242 m.
Required time = 242/20 = 12.1 sec.
Answer: Option B
Answer: (B) 12.1
Question: John purchased a fridge & a mobile for Rs. 15000&Rs. 8000 respectively. He sold the fridgeat a loss of 4% and the mobile phone at a profit of 10%. Overall how much he make a profit.
(A) Rs. 100
(B) Rs. 150
(C) Rs. 200
(D) Rs. 300
(E) Rs. 350
Rationale: Let the SP of the refrigerator and the mobile phone be Rs. r and Rs. m respectively.
r = 15000(1 - 4/100) = 15000 - 600
m = 8000(1 + 10/100) = 8000 + 800
Total SP - Total CP = r + m - (15000 + 8000) = -600 + 800 = Rs. 200
As this is positive, an overall profit of Rs. 200 was made.
C
Answer: (C) Rs. 200
Question: If –1 < x < 1 and x ≠ 0, which of the following inequalities must be true?
I. x^3 < x
II. x^2 < |x|
III. x^4 – x^5 > x^3 – x
(A)  I only
(B)  II only
(C)  III only
(D)  II and III only
(E)  I, II, and III
Rationale: Answer is D. Let's look at the statements one by one
Stmt I. x^3 < x
if 0<x<1 then x^3< x but if -1<x<0 then x^3>x
So this statement is not always true
Stmt II. x^2 < |x|
Because we know that x is a number less than one but not equal to zero then x^2 will always be less than |x|.
Why? think of positive fractions (and you can think in terms of positive fractions because the inequality is in regards to |x|). Lets set x = 1/2, then x^2 = 1/4 and 1/4<1/2
So Stmt II is always true
Stmt III. x^4 – x^5 > x^3 – x^2
This one may seem tricky but lets break it down. x^4 – x^5 > x^3 – x^2 = x^4(1-x)>x^2(x-1).
Because lets concentrate on (1-x) and (x-1). We are given that -1<x<1 which means that (1-x)>0 and (x-1)<0. x^4 will always be positive and x^2 will always be positive so without doing any math we are looking at positive > negative... which is always true.
So Stmt III is always true
A
Answer: (A)  I only
Question: A woman is 18 years older than her son. In 4 years, her age will be twice the age of her son. The present age of her son is
(A) 12
(B) 14
(C) 16
(D) 18
(E) 20
Rationale: Explanation:
Let the son's present age be x years. Then, woman's present age = (x + 18) years
=> (x + 18) + 4 = 2(x + 4)
=> x + 22 = 2x +8
So, x = 14 Answer: B
Answer: (B) 14
Question: Excluding stoppages, the speed of a train is 45 kmph and including stoppages it is 33 kmph. Of how many minutes does the train stop per hour?
(A) E982
(B) 16
(C) 12
(D) 121
(E) 28
Rationale: Explanation:
T = 12/45 * 60 = 16
Answer: Option B
Answer: (B) 16
Question: Find the fourth proportional to 0.5, 1.12 and 1.3?
(A) 2.914
(B) 2.81
(C) 2.192
(D) 2.912
(E) None of these
Rationale: Explanation:
Formula = Fourth proportional = (b × c)/a
A = 0.5 , B = 1.12 and C = 1.3
(1.12 × 1.3)/0.5
1.456/0.5 = 2.912
Answer: Option D
Answer: (D) 2.912
Question: If number divisible by both 3 and 2 ,then the same number divisible by which number?
(A) 4
(B) 5
(C) 8
(D) 6
(E) 9
Rationale: Obviously,The answer is 6
Option D
Answer: (D) 6
Question: John bought 2 shares and sold them for $75 each. If he had a profit of 20% on the sale of one of the shares but a loss of 20% on the sale of the other share, then on the sale of both shares John had
(A) a profit of $10
(B) a profit of $6.25
(C) a loss of $6.25
(D) a loss of $10
(E) neither a profit nor a loss
Rationale: Loss% = (%age Profit or loss / 10)^2 = (20/10)^2 = 4% loss
Total Selling Price = 75*2 = $192
Total Cost Price = 150/(0.96) = $156.25
Loss = 156.25 - 150 = $6.25
Answer: Option C
Answer: (C) a loss of $6.25
Question: If a is the smallest positive integer such that 5,880 multiplied by a is the square of an integer, then ya must be
(A) 30
(B) 15
(C) 12
(D) 23
(E) 17
Rationale: 5880= 2*2*7*7*5*6, so we need one 5 and one 6 to make it a square of a number. so 5*6= 30
Ans: A
Answer: (A) 30