mathewhe/aqua_rat huggingface dataset:
Question: A certain tire company can produce tires at a cost of $22,500 per batch plus $6 per tire. The company can sell tires to the wholesaler at a cost of $20 per tire. If a batch of 15,000
tires is produced and sold, what is the company’s profit per tire?
(A) $9.00
(B) $9.50
(C) $11.00
(D) $13.50
(E) $12.50
Rationale: CP(15000 tires) = $22500 +($6×15000) =$112500
SP (15000 tires) = $20×15000 = $300000
Profit = SP-CP
= $300000-$112500= $187500
PROFIT/TIRE = $187500/15000 = $12.50
Answer E
Answer: (E) $12.50
Question: A rower can row 5 km/h in still water. When the river is running at 2 km/h, it takes the rower 1 hour to row to Big Rock and back. How many kilometers is it to Big Rock?
(A) 1.5
(B) 1.8
(C) 2.1
(D) 2.4
(E) 2.7
Rationale: Let x be the distance to Big Rock.
time = x/3 + x/7 = 1
x = 21/10 = 2.1 km
The answer is C.
Answer: (C) 2.1
Question: A garrison of 3300 men has provisions for 32 days when supplied at the rate of 850 g per head. At the end of 7 days, a reinforcement arrives, and it is found that the provisions can last for 17 days more when supplied at the rate of 825 g per head. What is the strength of the reinforcement?
(A) 1700
(B) 1000
(C) 3000
(D) 2700
(E) 2600
Rationale: 825*17*x=850*25*3300
=> 5000
strength of reinforcement = (5000-1300)= 1700
final answer 1700.
ANSWER:A
Answer: (A) 1700
Question: 4, 8, 16, 28, 44, ?
(A) 64
(B) 56
(C) 74
(D) 57
(E) 32
Rationale: The pattern is + 4, + 8, + 12, + 16, +20
Answer : A.
Answer: (A) 64
Question: Priya and her father differ in their ages by 31 years. After 8 years. if the sum of their ages will be 69, their present ages are
(A) 11, 42
(B) 12, 24
(C) 15, 42
(D) 16, 19
(E) 33, 44
Rationale: A
11, 42
Let the age of Priya = x years
Then, the age of her father = (x+ 31) years
ATQ,
(x+ 8) + (x+ 31 + 8) = 69
2x+ 47 = 69
2x= 69 – 47 = 22
x= 11
The age of Priya = 11 years
The age of her father = 11 + 31 = 42 years
Answer: (A) 11, 42
Question: A reduction of 10% in the price of tea enables a dealer to purchase 25 kg more tea for Rs. 22500. What is the reduced price per kg of tea?
(A) Rs. 70
(B) Rs. 80
(C) Rs. 90
(D) Rs. 100
(E) None
Rationale: Solution: 1st Method:
Let the original price of tea be Rs. x/kg.
After reduction the price becomes = x -10% of x = 9x/10 per kg.
Now,
(22500/(9x/10))-22500/x = 25
Or, 22500[10/9x- 1/x] = 25
Or, 25*9x = 22500;
Or, x = (22500/2589) = Rs. 100.
Hence, new price = 90 per kg.
Thought process Method:
Let the original price be Rs. 100 per kg, he get tea = 22500/100 = 225 kg.
After reduction the price becomes = 90 per kg, he get tea = 22500/90 = 250 kg.
So, reduction price is Rs. 90 per kg as it enables him to buy 25 kg of more tea.
Answer: Option C
Answer: (C) Rs. 90
Question: Find (7x + 4y ) / (x-2y) if x/2y = 3/2 ?
(A) 24
(B) 25
(C) 26
(D) 27
(E) 29
Rationale: x/2y=3/2
=>x=6y/2=3y
=>(7x+4y)/(x-2y)=((7*(3y))+4y)/(3y-2y)
=>25y/y=25
ANSWER:B
Answer: (B) 25
Question: In how many ways can the letters of word IMAGINATION be arranged such that all the vowels as well as all the Consonants always appear together?
(A) 9!
(B) 5!*4!
(C) 5!*5!
(D) 5!*4!*2!
(E) 6!*5!*2!
Rationale: Since all the vowels and consonants have to be together there can only be there are 6! way to order the vowels and 5! to order the consonants. But they must be together either vowels come first or consonants so you multiply by 2.
So 6!5!2! (E)
Answer: (E) 6!*5!*2!
Question: When positive integer N is divided by positive integer J, the remainder is 18. If N/J = 134.03, what is value of J?
(A) 22
(B) 56
(C) 78
(D) 112
(E) 600
Rationale: 1) We know that
decimal part of decimal quotient ={remainder/divisor}
So 0.03, the decimal part of the decimal quotient, must equal the remainder, 18, divided by the divisor J.
0.03 = 18/J
0.03*J = 18
J = 18/0.03 = 1800/3 = 600
So J = 600, answer = E.
Answer: (E) 600
Question: The rate of spin of a certain gyroscope doubled every 15 seconds from the moment a particular stopwatch started. If after a minute and a half the gyroscope reached a speed of 400 meters per second, what was the speed, in meters per second, when the stopwatch was started?
(A) 25/2
(B) 25/4
(C) 25/8
(D) 25/16
(E) 25/32
Rationale: Let x be the original speed when the stopwatch was started.
In 90 seconds, the speed doubled 6 times.
2^6 * x = 400
x = (2^4 * 25) / 2^6 = 25/4
The answer is B.
Answer: (B) 25/4
Question: A train covers a distance of 15 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?
(A) m
(B) m
(C) m
(D) m
(E) m
Rationale: Speed = (15/10 * 60) km/hr
= (90 * 5/18) m/sec = 25 m/sec.
Length of the train = 25 * 6
= 150 m.
Answer:C
Answer: (C) m
Question: A man purchases the milk at Rs. x/litre and sells it at Rs. 2x/liter stillhe mixes 2liters waterwith every 6liters of pure milk. What is the profit %?
(A) 123%
(B) 134%
(C) 145%
(D) 166.66%
(E) 186.66%
Rationale: Let the cost price of 1 litre pure milk be Re.1, then
\inline{6litres(milk)→CP=Rs.62litres(water)→CP=Rs.0}{6litres(milk)→CP=Rs.62litres(water)→CP=Rs.0}\rightarrow CP=Rs.6 only
and 8 litre mixture \rightarrow SP \rightarrow 8 x 2 = Rs.16
Profit %= 166.66%
D
Answer: (D) 166.66%
Question: In the xy-plane, line k passes through point (3,-2) and intersect perpendicularly with line n that passes through points (0,3) and (3,5). What is the equation of line k?
(A) 3x+2y-5=0
(B) 3x+2y+5=0
(C) 2x-3y-12=0
(D) 2x+3y=0
(E) 4x+3y-6=0
Rationale: If two lines intersect perpendicularly, we get -1 when we multiply two slopes together. The slope of a line n is (5-3)/(3-0)=2/3. Hence, the slope of a line k should be -3/2. Since it crosses (3,-2), if we calculate we get 3x+2y=5. Hence, the correct answer is A.
Answer: (A) 3x+2y-5=0
Question: A can build up a wall in 8 days while B can break it in 3 days. A has worked for 4 days and then B joined to work with A for another 2 days only. In how many days will A alone build up the remaining part of wall?
(A) 13 1⁄3 days
(B) 7 1⁄3 days
(C) 6 1⁄3 days
(D) 7 days
(E) None of these
Rationale: A’s one day’s work = 1⁄8th work.
B’s one day’s work = 1⁄3rd work.
∴ A’s 4 day’s work = 4 × 1⁄8 = 1⁄2nd work
∴ In next two days, total wall = 1⁄2 + 2(1⁄8) - 2(1⁄3) = 1⁄12th wall
Remaining wall = 1 - 1⁄12 = 11⁄12th
Now, 1⁄8th wall is built up by A in one day.
∴ 11⁄12th wall is built up by A in 8 × 11⁄12 = 71⁄3 days.
Answer B
Answer: (B) 7 1⁄3 days
Question: The probability that A speaks truth is 7/9 and that of B speaking truth is 9/13. What is the probability that they agree in stating the same fact?
(A) 18/35
(B) 111/117
(C) 157/195
(D) 192/235
(E) None of these
Rationale: If both agree stating the same fact, either both of them speak truth of both speak false.
Probability = 7/9 * 9/13 + 6/9 * 8/13
= 63/117 + 48/117 = 111/117
ANSWER:B
Answer: (B) 111/117
Question: Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
(A) 60
(B) 50
(C) 48
(D) 76
(E) 34
Rationale: Relative speed = 45 + 30 = 75 km/hr.
75 * 5/18 = 125/6 m/sec.
Distance covered = 500 + 500 = 1000 m.
Required time = 1000 * 6/125 = 48 sec.
Answer: Option C
Answer: (C) 48
Question: James have 10 parrots, 4 fishes, 9 rabbits and 6 dogs.How many pets does he have in all?
(A) 17
(B) 11
(C) 9
(D) 15
(E) 29
Rationale: 10+4+9+6=29. Answer is E
Answer: (E) 29
Question: Scott's average (arithmetic mean) golf score on his first four rounds was 58.What score does he need on his fifth round to drop his average score by 2 points?
(A) 48
(B) 72
(C) 78
(D) 88
(E) 312
Rationale: Average score for first 4 rounds = 58
Average score after 5 rounds = 56
Score Scott needs on his 5th round to drop average score by 2 points = 58 - (2*5) = 48
Answer A
Answer: (A) 48
Question: Find the odd man out. 18, 7, 12, 24, 48, 34, 46
(A) 16
(B) 46
(C) 24
(D) 11
(E) 7
Rationale: Explanation :
7 is the only odd number in the given series
Answer : Option E
Answer: (E) 7
Question: In what ratio must rice at Rs.7.10 be mixed with rice at Rs.9.20 so that the mixture may be worth
Rs.8 per Kg?
(A) 5 : 4
(B) 2 : 1
(C) 3 : 2
(D) 4 : 3
(E) None of these
Rationale: Explanation :
By the rule of alligation, we have
CP of 1 kg Rice of 1st kind CP of 1 kg Rice of 2nd kind
7.1 9.2
Mean Price
8
9.2 - 8 = 1.2 8 - 7.1 = .9
Required ratio = 1.2 : .9 = 12 : 9 = 4 : 3
Answer : Option D
Answer: (D) 4 : 3
Question: A man buys Rs. 20 shares paying 9% dividend. The man wants to have an interest of 12% on his money. The market value of each share is:
(A) 12
(B) 13
(C) 14
(D) 15
(E) 18
Rationale: Dividend on Rs 20 = 9/100*20 = 9/5
is 12 income 100
9/5 is an income on Rs (100/12*9/5) = Rs 15
ANSWER D
Answer: (D) 15
Question: Taps A and B can fill a bucket in 10 minutes and 15 minutes respectively. If both are opened and A is closed after 3 minutes, how much further time would it take for B to fill the bucket?
(A) 7 min. 30 sec.
(B) 8min. 20 sec.
(C) 7min. 25 sec
(D) 7 min.35 sec.
(E) 8min. 20 sec.
Rationale: Explanation:
Part filled in 3 minutes =
3∗(1/10+1/15)=3∗5/30=5/10
Remaining part =1−5/10=5/10
=>1/15:5/10=1:X
=>X=15/2
=>X=7.5mins.
So it will take further 7 mins 30 seconds to fill the bucket.
OptionA
Answer: (A) 7 min. 30 sec.
Question: For what value of â€œkâ€ will the equation (2kx2 + 4kx +2)=0 have equal roots?
(A) 1
(B) 9/4
(C) 16/25
(D) 7/1
(E) 7/2
Rationale: for a 2nd degree equation ax2+bx_c=0 has equal roots the condition is b2-4ac =0
in the given equation
(4k)^2-4*2k*2=0
by solving this equation
we get k=0, k=1
ANSWER:A
Answer: (A) 1
Question: Which of the following numbers should not be included in the set?
331, 482, 551, 263, 386, 242, 111
(A) 263
(B) 386
(C) 242
(D) 111
(E) None of these
Rationale: Solution
In each number except 386,the product of first and third digits is the middle one. Answer B
Answer: (B) 386
Question: If x is an integer such that 5 < x < 21, 7 < x < 18, 13 > x > 2, 12 > x > 9, and x + 1 < 13, then x is
(A) 3
(B) 5
(C) 7
(D) 9
(E) 11
Rationale: 5 < x < 21,
7 < x < 18,
2 < x < 13
9 < x < 12
x<13
From above: 10< x < 12 --> x = 11.
Answer: E.
Answer: (E) 11
Question: How long does a train 110 m long traveling at 60 kmph takes to cross a bridge of 170 m in length?
(A) 16.8
(B) 17.8
(C) 15.9
(D) 13.2
(E) 12.4
Rationale: D = 110 + 170 = 280 m
S = 60 * 5/18 = 50/3
T = 280 * 3/50 = 16.8 sec
ANSWER A
Answer: (A) 16.8
Question: The average of first 11 prime numbers is?
(A) 14.55
(B) 11.11
(C) 12.11
(D) 13.11
(E) 14.11
Rationale: Sum of 11 prime no. = 160
Average = 160/11 = 14.55
ANSWER: A
Answer: (A) 14.55
Question: On flipping 3 coins together what is the outcomes for at least three TAILl?
(A) 1/7
(B) 3/8
(C) 1/8
(D) 4/13
(E) 5/13
Rationale: Sample space, S = {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT}
Favorable outcomes for at least two heads
= favorable outcomes for exactly two heads and favorable outcomes for more than two heads
= {TTT}
1/8
C
Answer: (C) 1/8
Question: If 12!/3^x is an integer, what is the greatest possible value of x?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: This question is asking how many power of 3 exists in 12!
easiest way is to identify factor of three
12 -> 4*3 => 1 power of 3
9 -> 3*3=> 2 power of 3
6 -> 2*3=> 1 power of 3
3 -> 1*3=> 1 power of 3
Total equal 5
ANSWER:C
Answer: (C) 5
Question: Number of prime numbers between 70 and 100 is
(A) 4
(B) 5
(C) 6
(D) 7
(E) 9
Rationale: total 6=71, 73, 79, 83, 89, 97
ANSWER:C
Answer: (C) 6
Question: Carl is facing very difficult financial times and can only pay the interest on a $10,000 loan he has taken. The bank charges him a quarterly compound rate of 4%. What is the approximate interest he pays annually?
(A) $1750
(B) $2000
(C) $2150
(D) $2500
(E) $12000
Rationale: An easy way too attempt this is by approximation:
For the first quarter, he pays 4% of 10,000 which is $400.
So for the four quarters in the year, he will approximately play 400*4=1600 over the entire year.
Because of compound interest it will be more than 1600. Approx. option A is correct.
Answer : A
Answer: (A) $1750
Question: If x ≠ 0 and y/x=y+x, which of the following expressions is equal to its opposite?
(A) x^2
(B) x^2 – y^2
(C) y^2
(D) x^2 + xy - y^2
(E) (x – y)^2
Rationale: y/x=(y+x)/y
=> y^2 = xy +x^2
=> x^2 + xy - y^2= 0
Answer D
Answer: (D) x^2 + xy - y^2
Question: In a renowned city, the average birth rate is 5 people every two seconds and the death rate is 3 people every two seconds. Estimate the size of the population net increase that occurs in one day.
(A)  85,400
(B)  86,400
(C)  87,400
(D)  88,400
(E)  89,400
Rationale: This question can be modified so that the birth rate is given every m seconds and the death rate is given every n seconds.
For this particular question : Increase in the population every 2 seconds = 5-3 = 2 people.
Total 2 second interval in a day = 24*60*60/2 = 43,200
Population increase = 43,200 * 2 = 86,400. Hence B.
Answer: (B)  86,400
Question: A bag contains a certain number of 50 paise coins, 20 paise coins and 10 paise coins inthe ratio 3:4:5. If the total value of all the coins in the bag is Rs.350, find the number of 50 paise coins ?
(A) 498
(B) 488
(C) 375
(D) 528
(E) 418
Rationale: 50*3k + 20*4k + 10*5k = 35000
280k = 35000 => k = 125
50p coins = 3k = 3*125 = 375
ANSWER:C
Answer: (C) 375
Question: The cost price of three varieties of oranges namely A, B and C is Rs 20/kg, Rs 40/kg and Rs 50/kg. Find the selling price of one kg of orange in which these three varieties of oranges are mixed in the ratio of 2 : 3 : 5 such that there is a net profit of 20%?
(A) Rs 48
(B) Rs 48.6
(C) Rs 49.2
(D) Rs 49.8
(E) Rs 48.8
Rationale: Cost price of one kg of orange in which the three varieties of oranges are mixed in the ratio 2 : 3 : 5 is equal to S where
S = 0.2 x 20 + 0.3 x 40 + 0.5 × 50
= 4 + 12 + 25
= Rs 41
Selling price per kg of oranges to ensure there is a net profit of 20%
= 1.2 x 41
= Rs 49.2
ANSWER:C
Answer: (C) Rs 49.2
Question: A certain class of students is being divided into teams. The class can either be divided into 8 teams with an equal number of players on each team or 24 teams with an equal number of players on each team. What is the lowest possible number of students in the class?
(A) 6
(B) 36
(C) 48
(D) 24
(E) 72
Rationale: Let total no of students in the class be N
So, we are told that N is divisible by both 8 24
So, Lets find the least common multiple of 8 24 , ie 24
So our answer is (D) 24
Answer: (D) 24
Question: The compound ratio of 5:6, 3:4 and 4:5?
(A) 1:1
(B) 1:87
(C) 1:6
(D) 1:9
(E) 1:2
Rationale: 5/6 * 3/4 * 4/5 = 1/2
1:2
Answer: E
Answer: (E) 1:2
Question: A 8000 liter tank, half-full of water is being filled from a pipe with a flow rate of 1 kiloliter every 2 minutes. At the same time, the tank is losing water from two drains at a rate of 1 kiloliter every 4 minutes and every 6 minutes. How many minutes does it take to fill the tank completely?
(A) 8
(B) 12
(C) 18
(D) 24
(E) 48
Rationale: In: we have: 1,000/2min = 500 litres per minute
Out: we have: 1,000/4 + 1,000/6
Then do: IN - OUT to figure out the net inflow per minute (you get 83.3). Then divide the total number of litres you need (4,000 by that net inflow to get the minutes) - 48 min. Answer E.
Answer: (E) 48
Question: If x = -3/7 and y = -2/3, what is the value of the expression -2x – y^2?
(A) -33/22
(B) 23/85
(C) 26/63
(D) 58/41
(E) -26/63
Rationale: x = -3/7 and y = -2/3
==> -2(-3/7) - (2/3)^2 = 6/7 - 4/9 = 26/63
Ans: C
Answer: (C) 26/63
Question: Find the simple interest on $2500 for 3 years at 10% per annum?
(A) $250
(B) $300
(C) $750
(D) $600
(E) $1000
Rationale: SI = PTR/100
= 2500*3*10/100 = $750
Answer is C
Answer: (C) $750
Question: A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. If the speed of the boat in still water is 10 mph, the speed of the stream is
(A) 2 mph
(B) 2.5 mph
(C) 3 mph
(D) 4 mph
(E) 5 mph
Rationale: Let the speed of the stream x mph.
Speed downstream = (10 + x) mph.
Speed upstream = (10 - x) mph.
36/(10-x)-36/(10+x)=90/60
72x x 60 = 90(100-x2)
x2+48x-100 = 0
(x+ 50)(x - 2) = 0
x = 2 mph.
ANSWER:A
Answer: (A) 2 mph
Question: What is the remainder when 6990990900032 is divided by 32 ?
(A) 5
(B) 0
(C) 4
(D) 2
(E) 3
Rationale: Though i was unaware of the divisibility test for 32 but i guessed the pattern!!
divisibility rule for 4- last two digits must be divisible by 4
divisibility rule for 8- last three digits must be divisible by 8
similarly, divisibility rule for 32 - last five digits must be divisible by 32
Hence, Ans B
Answer: (B) 0
Question: Which of the following points is closest to line y=x
(A) (2, -1)
(B) (2, 4)
(C) (-1, 1)
(D) (1, 2)
(E) (-2, 0)
Rationale: Attachment:
m12-20.pngAs you can see point (1, 2) is the closest to line y=x.
Answer: D.
Answer: (D) (1, 2)
Question: What is the average (arithmetic mean) of the numbers 2, 4, 6, 8, 10, 12, 14 and 16?
(A) 9
(B) 10
(C) 15
(D) 12
(E) 14
Rationale: avg = sum of observations/number of observations
avg =(2+4+6+8+10+12+14+16)/8 = 9
Answer is A
Answer: (A) 9
Question: What is the greatest integer that will always evenly divide the sum of three consecutive integers?
(A) 2
(B) 3
(C) 4
(D) 6
(E) 12
Rationale: Let the three consecutive integers be x , x + 1 , x + 2
Sum = x + x + 1 + x + 2
= 3x+3 = 3(x+1)
Therefore , 3 will always be a factor .
Answer B
Answer: (B) 3
Question: A delegation of 5 members has to be formed from 3 ladies and 5 gentlemen. In how many ways the delegation can be formed, if 2 particular ladies are always included in the delegation?
(A) 20
(B) 82
(C) 82
(D) 25
(E) 27
Rationale: Explanation:
There are three ladies and five gentlemen and a committee of 5 members to be formed.
Number of ways such that two ladies are always included in the committee = ⁶C₃ = (6 * 5 * 4)/6 = 20.
Answer:A
Answer: (A) 20
Question: A ship sails out to a mark at the rate of 15 kmph. and sails back at the rate of 10 kmph. The average rate of sailing is ?
(A) 5 km/hr
(B) 12 km/hr
(C) 12.5 km/hr
(D) 25 km/hr
(E) None
Rationale: Answer
Average = ( 2uv / u +v ) km/hr
= ( 2 x 15 x 10 ) / (15 +10 ) km/hr.
= 12 km/hr.
Correct Option: B
Answer: (B) 12 km/hr
Question: The unit digit in the product (594 * 897* 929 * 462) is:
(A) 2
(B) 5
(C) 6
(D) 4
(E) 10
Rationale: Explanation:
Unit digit in the given product = Unit Digit in (4*7*9*2) = 4
ANSWER: D
Answer: (D) 4
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 18% less than the price each head sold for the day before.what was the gross profit on this shipment?
(A) $105
(B) $115
(C) $125
(D) $130
(E) $135
Rationale: 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: 82% of the previous price: 82/100 * 1/2 = $(16/39)
Total revenue by selling 500 heads = 16/39 * 500 = 205
Total revenue after selling 1500 cabbage heads - 205+500 = $705
Money spent on the purchase: $600
Profit = 705-600 = $105
Ans: A
Answer: (A) $105
Question: How much time will it take for an amount of 450 to yield 81 as interest at 4.5% per annum of simple interest?
(A) 3 years
(B) 4 years
(C) 6 years
(D) 5 years
(E) 7 years
Rationale: Time = (100 x 81)/(450 x 4.5) years = 4 years.
answer B
Answer: (B) 4 years
Question: Ramu bought an old car for Rs. 40000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent?
(A) A)14%
(B) B)16%
(C) C)18%
(D) D)21.6%
(E) of these
Rationale: Total CP = Rs. 40000 + Rs. 13000 = Rs. 53000 and SP = Rs. 64900
Profit(%) = (64900 - 53000)/55000 * 100 = 21.6%
ANSWER:D
Answer: (D) D)21.6%
Question: If the sum of a set of 5 different positive prime numbers is 94, what is the difference between largest and smallest prime numbers between them?
(A) 53
(B) 51
(C) 47
(D) 41
(E) 31
Rationale: All prime numbers apart from 2 are odd.
Even + Even = Even
Odd + Even = Odd
Odd + Odd = Even
We are given 5 different prime numbers, whose sum is 94 i.e even
If we include 2, we will have 4 odd prime numbers and one even.
This sum would be odd
If we exclude 2, we will have 5 odd numbers.
This sum would be even
Hence 2 is included.
The possible 5 no. are = 11+7+2+43+31 = 94
the difference between largest and smallest prime numbers between them = 43 - 2 = 41
Ans - D
Answer: (D) 41
Question: The ratio of investments of two partners P and Q is 7:5 and the ratio of their profits is 7:10. If P invested the money for 5 months, find for how much time did Q invest the money?
(A) 28
(B) 10
(C) 288
(D) 277
(E) 211
Rationale: 7*5: 5*x = 7:10
x = 10
Answer: B
Answer: (B) 10
Question: Ms. Mary sold two properties, X and Y, for $40,000 each. She sold property X for 20 % more than she paid for it and sold property Y for 20% less than she paid for it. If expenses are disregarded , what was her total net gain or loss, if any, on the two properties ?
(A) $3233.33
(B) $3433.33
(C) $3333.33
(D) $3533.33
(E) $3633.33
Rationale: There is a property to solve such questions withCommon Selling PriceandCommon %gain and loss. such cases always result in a loss and...
Total %Loss = (Common Gain% or Loss%/10)^2
Hence Here Loss% = (20/10)^2 = 4%
which means he recovered only 96% of his investment which amount to a total revenue = 40000 + 40000 = 80000
i.e. 96% of cost = 80000
therefore, 4% of cost (Loss) = $3333.33
Answer: C
Answer: (C) $3333.33
Question: In a recent election, Ms. Robbins received 8,000 votes cast by independent voters, that is, voters not registered with a specific political party. She also received 5 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) 0.4N + 7,200
(D) 0.1N + 8,000
(E) 0.03N + 8,000
Rationale: I will go with option E
According to question 40 percent of total votes (N) cas were cast by independent voters. This implies 60 percent of N are voters that belong to political party. And she received 8000 votes from independent voters and 5 percent from registered voters (i.e 0.05 * 0.6 * N = 0.03N). Hence total votes = 8000 + 0.03N ....option E
Answer: (E) 0.03N + 8,000
Question: The jogging track in a sports complex is 850 m in circumference. Rakesh and his wife start from the same point and walk in opposite directions at 4.2 km/hr and 3.3 km/hr respectively. They will meet for the first time in?
(A) 5.9 min
(B) 6.8 min
(C) 7.2 min
(D) 8.5 min
(E) 9.0 min
Rationale: Clearly, the two will meet when they are 850m apart.
To be (4.2 + 3.3) =7.5 km apart, they take 1 hour.
To be 850 m apart, they take
= (850/7500 * 60) min
= 6.8 min.
Answer: B
Answer: (B) 6.8 min
Question: Three partners shared the profit in a business in the ratio 5 : 7 : 8. They had partnered for 14 months, 8 months and 7 months respectively. What was the ratio of their investments?
(A) 5 : 7 : 8
(B) 20 : 49 : 64
(C) 38 : 28 : 21
(D) 3:7:9
(E) None of these
Rationale: Let their investments be Rs. x for 14 months, Rs. y for 8 months and Rs. z for 7 months respectively.
Then, 14x : 8y : 7z = 5 : 7 : 8.
Now,	14x/8y=5/7
then 98x = 40y
then y =	49/20x
And,	14x/7z=5/8
then112x= 35z
and z =(112/35 )x =(16/5 )x.
x : y : z = x :	(49/20)x	:(16/20)x	= 20 : 49 : 64
ANSWER:B
Answer: (B) 20 : 49 : 64
Question: A person purchases 90 clocks and sells 40 clocks at a gain of 10% and 50 clocks at a gain of 20%. If he sold all of them at a uniform profit of 15%, then he would have got Rs. 40 less. The cost price of each clock is?
(A) 26
(B) 28
(C) 80
(D) 26
(E) 21
Rationale: Let C.P. of clock be Rs. x.
Then, C.P. of 90 clocks = Rs. 90x.
[(110% of 40x) + (120% of 50x)] - (115% of 90x) = 40
44x + 60x - 103.5x = 40
0.5x = 40 => x = 80
Answer: C
Answer: (C) 80