mathewhe/aqua_rat huggingface dataset:
Question: Kate and David each have $10. Together they flip a coin 5 times. Every time the coin lands on heads, Kate gives David $1. Every time the coin lands on tails, David gives Kate $1. After the coin is flipped 5 times, what is the probability that Kate has more than $10 but less than $15?
(A) 5 /16
(B) 15/ 32
(C) 1/ 2
(D) 2/32
(E) 11/ 16
Rationale: After 5 tries Kate to have more than initial sum of 10$ and less than 15$ must win 3 or 4 times (if she wins 2 or less times she'll have less than 10$ and if she wins 5 times she'll have 15$).
So the question becomes "what is the probability of getting 3 or 4 tails in 5 tries?".
P(t=3 or t=4)=P(t=3)+P(t=4)=C35∗(12)5+C45∗(12)5=1532P(t=3 or t=4)=P(t=3)+P(t=4)=C53∗(12)5+C54∗(12)5=1532
Answer: B.
Answer: (B) 15/ 32
Question: I. a3 - 988 = 343,
II. b2 - 72 = 49 to solve both the equations to find the values of a and b?
(A) If a > b
(B) If a ≥ b
(C) If a < b
(D) If a ≤ b
(E) If a = b or the relationship between a and b cannot be established.
Rationale: Explanation:
a3 = 1331 => a = 11
b2 = 121 => b = ± 11
a ≥ b
B)
Answer: (B) If a ≥ b
Question: In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 6 boys when a boy gets any no. of prizes?
(A) 55
(B) 230
(C) 224
(D) 216
(E) 70
Rationale: Ans.(D)
Sol. In this case, repetitions are allowed, so all the three prizes can be given in 4 ways, i.e. (6 x 6 x 6) ways = 63 ways = 216 ways Or nr ways = 63 ways = 216 ways
Answer: (D) 216
Question: x, y and z are consecutive positive integers such that x < y < z; which of the following must be true?
1. xyz is divisible by 6
2. (z-x)(y-x+1) = 4
3. xy is even
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I, II, and III
Rationale: Since x, y and z are consecutive integers such that x < y < z, we can say x = y-1 and Z = y+1
Statement 1 would be true as at least one of the three numbers is divisible by 2 and one by 3 so xyz would be divisible by 6.
Statement 2 can be simplified if we write everything in terms of y as ((y+1)-(y-1))*(y-(y-1)+1) = 2*2 = 4 So, always true
Statement 3 talks about xy Since x and y are consecutive integers one of them is odd and other is even so product would always be even and hence true.
So, I II and III are always true and hence answer is
E.
Answer: (E) I, II, and III
Question: Ranjeet purchased an item for Rs.3500 and sold it at the loss of 25%. From that amount he purchased another item and sold it at the gain of 20%. What is his overall gain/loss?
(A) Loss of Rs.240
(B) Gain of Rs.120
(C) Loss of Rs.350
(D) Neither gain nor loss
(E) None of these
Rationale: Explanation:
1st SP = Rs.3500 – 25% of 3500 = Rs.3500 – 875 = Rs.2625.
(24% = ¼)
2nd SP = Rs.2625 + 20% of 2625 = Rs.2625 + 525 = Rs.3150.
:. Overall loss = Rs.3500 – Rs.3150 = Rs.350.
Answer: Option C
Answer: (C) Loss of Rs.350
Question: Find the odd man out 3, 8, 38, 78, 158
(A) 28
(B) 8
(C) 128
(D) 18
(E) 158
Rationale: 3 x 2 + 2 = 8
8 x 2 + 2 =18
18 x 2 + 2 =38
38 x 2 + 2 =78
ANSWER:D
Answer: (D) 18
Question: From the answers select the option that is near to √5?
(A) 2.2
(B) 2.3
(C) 3.0
(D) 3.8
(E) 1.9
Rationale: 2.2 is nearly equal to the square root of 5.
2.2*2.2=4.4
2.3*2.3=5.29
Difference
5 - 4.4=0.6
5 - 5.3=0.7
Since 0.6 is lesser among both, 2.2 is closer.
Answer is A
Answer: (A) 2.2
Question: The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 55 kg. What might be the weight of the new person?
(A) 56 kg
(B) 90 kg
(C) 75 kg
(D) Data inadequate
(E) None of these
Rationale: C
75 kg
Total weight increased = (8 x 2.5) kg = 20 kg.
Weight of new person = (55 + 20) kg = 75 kg.
Answer: (C) 75 kg
Question: If x is divisible by 5, 20, and 125, which of the following must be the least multiple of x?
(A) 12500
(B) 1250
(C) 500
(D) 100
(E) 125
Rationale: If x is divisible by 5, 20, and 125, then x must be a multiple of 5,4and 25.
Hence,the least multiple of x will be 5*4*25=500.
ANSWER:C
Answer: (C) 500
Question: Which of the following has 21^20 as a factor?
(A) 15^60
(B) 30^20
(C) 40^80
(D) 42^20
(E) 90^80
Rationale: Here 21^20 = 3^20 * 7^20 Only Option D has both .
Smash D
Answer: (D) 42^20
Question: Mary and Mike enter into a partnership by investing $650 and $350 respectively. At the end of one year, they divided their profits such that a third of the profit is divided equally for the efforts they have put into the business and the remaining amount of profit is divided in the ratio of the investments they made in the business. If Mary received $600 more than Mike did, what was the profit made by their business in that year?
(A) $3000
(B) $3200
(C) $3300
(D) $3400
(E) $4000
Rationale: Explanatory Answer
Let the profit made during the year be $3x
Therefore, $x would have been shared equally and the remaining $2x would have been shared in the ratio 6.5 : 3.5
i.e., 65% of 2x would go to Mary and 35% of 2x would go to Mike.
Hence, Mary would get (65 - 35)% of 2x more than Mike
Or30% of 2x = $600
i.e.,(30/100)*2x = 600
or 2x = 2000.
Hence, the profit made by the company during the year $3x = $3000.
Answer : A
Answer: (A) $3000
Question: A can knit a pair of socks in 3 days. B can knit the same thing in 6 days. If they are knitting together, in how many days will they knit two pairs of socks?
(A) 4 days
(B) 2 days
(C) 4 1⁄2 days
(D) 3 days
(E) None of these
Rationale: ExplanationA’s one day’s work = 1⁄3 rd work.
B’s one day’s work = 1⁄6 rd work.
(A + B)’s one day’s work = 1⁄3 + 1⁄6 = 1⁄2 nd work.
∴ A and B together can complete the work (knit a pair of socks) in 2 days.
∴ They together knit two pair of socks in 4 days.
Answer A
Answer: (A) 4 days
Question: If 12 : 8 :: x : 16, then find the value of x
(A) 18
(B) 24
(C) 28
(D) 16
(E) 20
Rationale: Explanation:Treat 12:8 as 12/8 and x:16 as x/16, treat :: as = So we get 12/8 = x/16=> 8x = 192=> x = 24 Option B
Answer: (B) 24
Question: It takes Kannan 10 minutes to walk to the car park and 110 min to drive to work. At what time should he get out of the house in order to get to work at 9:00 a.m.?
(A) 8:50 a.m
(B) 5:50 a.m
(C) 7:50 a.m
(D) 6:50 a.m
(E) 7:00 a.m
Rationale: The time it takes Kannan to get to work: time to walk to car park + time to drive
10 + 110 = 120 minutes = 2 hours
Kannan needs to get out of the house 2 hours before 9:00 am at
9:00 - 2:00 = 7:00 a.m
correct answer E
Answer: (E) 7:00 a.m
Question: Reema can complete a piece of work in 12 days while Seema can the same work in 18 days. If they both work together, then how many days will be required to finish the work?
(A) 6 days
(B) 7.2 days
(C) 9.5 days
(D) 12 days
(E) 13 days
Rationale: EXPLANATION:
Hint:
A's one day work =	1/12
B's one day work =	1/18
(A + B)'s one day work =	1/12	+	1/18	=	(18 + 12)/(12 x 18)=	30/216=	1/7.2
Together, A & B will finish the work in 7.2 days.
ANSWER IS B
Answer: (B) 7.2 days
Question: Calculate the sum of first 39 natural numbers.
(A) 780
(B) 891
(C) 812
(D) 847
(E) 890
Rationale: Solution
We know that(1+2+3+.....+39)	= n(n+1)/2
Therefore (1+2+3+....+39)	=(39×40 / 2)
= 780.
Answer A
Answer: (A) 780
Question: In a class of 50 students, 3/5 went away do painting, 1/5 went to play in the field. How many students are left in the classroom?
(A) 20
(B) 30
(C) 5
(D) 8
(E) 10
Rationale: 3/5 + 1/5 are the students who have left the classroom
3/5 + 1/5 = (3 + 1)/5 , since denominator is same for both fractions
= 4/5
Remaining students in the classroom = 1 - 4/5 = 5/5 - 4/5 = (5-4)/5 = 1/5
1/5 of 50 = 10
Ans: E
Answer: (E) 10
Question: Which is largest prime number?
(A) 653
(B) 857
(C) 859
(D) 523
(E) 461
Rationale: Answer:C
Answer: (C) 859
Question: Excluding stoppages, the speed of a train is 45 kmph and including stoppages it is 42 kmph. Of how many minutes does the train stop per hour?
(A) 16
(B) 4
(C) 15
(D) 18
(E) 12
Rationale: T = 3/45 * 60
= 4
Answer: B
Answer: (B) 4
Question: A sum of money is to be distributed among A, B, C, D in the proportion of 6 : 2 : 4 : 3. If C gets $500 more than D, what is D's share?
(A) $2000
(B) $2500
(C) $3000
(D) $3600
(E) $4200
Rationale: Let the shares of A, B, C and D be 6x, 2x, 4x and 3x respectively.
Then, 4x - 3x = 500
x = $500
A's share = 6x = 6*$500 = $3000
The answer is C.
Answer: (C) $3000
Question: If A lends Rs.2000 to B at 10% per annum and B lends the same sum to C at 11.5% per annum then the gain of B in a period of 3 years is?
(A) 90
(B) 122.5
(C) 132.5
(D) 114.5
(E) 212.5
Rationale: (2000*1.5*3)/100 => 90
ANSWER:A
Answer: (A) 90
Question: Kim purchased n items from a catalog for $8 each. Postage and handling charges consisted of $6 for the first item and $1 for each additional item. Which of the following gives the total dollar amount for Kim’s purchase, including postage and handling, in terms of n ?
(A) 8n + 2
(B) 8n + 4
(C) 9n + 2
(D) 9n + 5
(E) 9n + 4
Rationale: its C
n items for $8 each
total price $8n
postage and handling of $3 for 1st item and $1 for the rest
total postage and handling = $ [6+ (n-1)]
= $ n+5
total cost
8n+n+5 = 9n+5
D
Answer: (D) 9n + 5
Question: Claire has a total of 92 pets consisting of gerbils and hamsters only. One-quarter of the gerbils are male, and one-third of the hamsters are male. If there are 25 males altogether, how many gerbils does Claire have?
(A) 39
(B) 68
(C) 54
(D) 57
(E) 60
Rationale: G+H =92 ...1 ; G/4 +H/3 =25 ....2 OR 3G +4H =25*12 =300
G =92-H OR 3(92-H) +4H =300 H = 300-276 =24 THEN G= 92-24 = 68
B
Answer: (B) 68
Question: A car driver travels from the plains to the hill station, which are 200 km apart at an average speed of 50km/hr. in return trip, he covers the same distance at an average speed of 20km/hr. the average speed of the car over the entire distance of 400 km is
(A) 8.95km/hr
(B) 26.7km/hr
(C) 27.8km/hr
(D) 28.5km/hr
(E) 8.45km/hr
Rationale: average speed = (2*50*20)/50+20 km/hr
=28.5 km/hr
Answer (D)
Answer: (D) 28.5km/hr
Question: The mass of 1 cubic meter of a substance is 400 kg under certain conditions. What is the volume in cubic centimeters of 1 gram of this substance under these conditions? (1 kg =1,000 grams and 1 cubic meter = 1,000,000 cubic centimeters)
(A) 1.5
(B) 2.5
(C) 3.5
(D) 4.5
(E) 5.5
Rationale: 400 kg - 1 cubic meter;
400,000 g - 1 cubic meter;
400,000 g - 1,000,000 cubic centimeters;
1 g - 1,000,000/400,000 = 10/4 = 2.5 cubic centimeters.
Answer: B.
Answer: (B) 2.5
Question: Manoj received Rs. 6000 as his share out of the total profit of Rs. 9000 which he and Ramesh earned at the end of one year. If Manoj invested Rs.120000 for 6 months, whereas Ramesh invested his amount for the whole year, what was the amount invested by Ramesh
(A) Rs. 2000
(B) Rs. 3000
(C) Rs. 4000
(D) Rs. 5000
(E) None of these
Rationale: Explanation:
Suppose Ramesh invested Rs. x. Then,
Manoj : Ramesh = 20000 * 6 : x * 12.
120000/12x : 6000/3000
=> x = 120000/24 = 5000
Option D
Answer: (D) Rs. 5000
Question: A cistern is normally filled in 8 hours but takes two hours longer to fill because of a leak in its bottom. If the cistern is full, the leak will empty it in?
(A) 87
(B) 09
(C) 40
(D) 42
(E) 76
Rationale: 1/8 - 1/x
= 1/10
x = 40
Answer:C
Answer: (C) 40
Question: Two trains 500 m and 750 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
(A) 10.6
(B) 45
(C) 10.4
(D) 10.8
(E) 10.1
Rationale: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other = 500 + 750 = 1250 m.
Required time = 1250 * 9/250 = 45 sec.
Answer: B
Answer: (B) 45
Question: Machine M, N, O working simultaneously Machine M can produce x units in 3/4 of the time it takes machine N to produce the same amount of units. Machine N can produce x units in 2/5 the time it takes machine O to produce that amount of units. If all three machines are working simultaneously, what fraction of the total output is produced by machine N?
(A) 1/2
(B) 5/11
(C) 4/13
(D) 8/29
(E) 6/33
Rationale: Now ultimately the speed of every machine is given with respect to Mach O.
So lets assume the speed of O, say 12 hrs to make x units (assuming 6 because we can see we will need to divide by 3 and 4
Mach O makes x units in 12 hrs
So, Mach N = 2/5 of O = 2/5*12 = 4.8 hrs to make x units
and Mach M = 3/4 of N = 3/4*4.8 = 6 hrs to make x units
No they are running simultaneously. Lets see how much each mach makes in 1 hr
Mach O = x/12 units
Mach N = 5x/24 units
Mach M = x/6 units
In 1 hr, together they make - x/12+5x/24+x/6 = 11/24
So what ratio of this has Mach N made?
(5x/24) / (11/24) = 5/11
Ans:B=5/11
Answer: (B) 5/11
Question: How many words can be formed from the letters of the word ‘DIRECTOR’ So that the vowels are always together?
(A) 1524
(B) 7845
(C) 2160
(D) 2541
(E) 5631
Rationale: In the given word, we treat the vowels IEO as one letter.
Thus, we have DRCTR (IEO).
This group has 6 letters of which R occurs 2 times and others are different.
Number of ways of arranging these letters = 6!/2! = 360.
Now 3 vowels can be arranged among themselves in 3! = 6 ways.
Required number of ways = (360x6) = 2160.
Ans: C
Answer: (C) 2160
Question: A box contains 2 red, 3 black and 4 blue balls. 3 balls are randomly drawn from the box. If two balls are found to be different, what is the probability that the third ball is blue?
(A) 8/3
(B) 9/3
(C) 5/3
(D) 2/3
(E) 1/3
Rationale: there are 6 ways to draw a blue ball at third attempt if first two balls are different. they are
1)RED BLACK BLUE
2)RED BLUE BLUE
3)BLACK RED BLUE
4)BLACK BLUE BLUE
5)BLUE RED BLUE
6)BLUE BLACK BLUE
Probability of 1st way is (2/9)*(3/8)*(4/7)
as at first attempt we got red which are two in number out of 9 and in second we got black which are 3 in number out of 8 (as first ball is removed)and in 3rd attempt we got blue which are 4 in number out of 7 balls left.
similarly probability of other ways is as follows
(2/9)*(4/8)*(3/7)
(3/9)*(2/8)*(4/7)
(3/9) *(4/8)*(3/7)
(4/9)*(2/8)*(3/7)
(4/9)*(3/8)*(3/7)
total probability of getting a blue ball is sum of all above ways so p=(2/9)*(3/8)*(4/7)+(2/9)*(4/8)*(3/7)+(3/9)*(2/8)*(4/7)+(3/9) *(4/8)*(3/7)+(4/9)*(2/8)*(3/7)+(4/9)*(3/8)*(3/7)=1/3
so probability of ball to be blue is 1/3
Answer E
Answer: (E) 1/3
Question: Ramu bought an old car for Rs. 42000. He spent Rs. 13000 on repairs and sold it for Rs. 60900. What is his profit percent?
(A) 10.7%
(B) 19%
(C) 18%
(D) 14%
(E) 16%
Rationale: Total CP = Rs. 42000 + Rs. 13000
= Rs. 55000 and SP
= Rs. 60900
Profit(%) = (60900 - 55000)/55000 * 100
= 10.7%
Answer: A
Answer: (A) 10.7%
Question: The length of the bridge, which a train 110 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
(A) 255
(B) 265
(C) 245
(D) 277
(E) 211
Rationale: Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (110 + x)/30 = 25/2 => 2(110 + x) = 750 => x = 265 m.
Answer:B
Answer: (B) 265
Question: A shopkeeper loses 15%,if an article is sold for Rs. 102. What should be the selling price of the article to gain 20%?
(A) Rs.148
(B) Rs.144
(C) Rs.120
(D) Rs.129
(E) Rs.126
Rationale: Given that SP = Rs. 102 and loss = 15%
CP = [100(SP)]/(100 - l%) = (100 * 102)/85 = 20 * 6 = Rs. 120.
To get 20% profit, New SP = [(100 + p%)CP]/100 = (120 * 120)/100
= Rs.144
Answer:B
Answer: (B) Rs.144
Question: 1907 x 1907 = ?
(A) A)3623216
(B) B)3624216
(C) C)3624316
(D) D)3636649
(E) E)3625216
Rationale: 1907 x 1907 = (1907)2
= (1900 + 7)2
= (1900)2 + (7)2 + (2 x 1900 x 7)
= 3610000 + 49 + 26600.
= 3636649.
D)
Answer: (D) D)3636649
Question: Given f(x) = 3x – 5, for what value of x does 2*[f(x)] – 19 = f(x – 4) ?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
Rationale: 2(3x-5)-19 = 3(x-4) - 5
3x = 12
x = 4
The answer is B.
Answer: (B) 4
Question: 3 person can fill tank in 25 min, a can fill in 30 min , b can fill in 35 min and c can empty the 5 gallon per min then what is the capacity of tank?
(A) 208.26 gallons
(B) 218.26 gallons
(C) 228.26 gallons
(D) 238.26 gallons
(E) 248.26 gallons
Rationale: A can fill the tank in 30 minutes
B can fill the same tank in 35 minutes
A B C together fill the tank in 25 minutes
Equating we get,
1050/23*5 = 228.26 gallons
ANSWER:C
Answer: (C) 228.26 gallons
Question: The edge of three cubes of metal is 3 dm, 4 dm and 5 dm. They are melted and formed into a single cube. Find the edge of the new cube?
(A) 1
(B) 9
(C) 4
(D) 6
(E) 3
Rationale: 33 + 43 + 53 = a3 => a
= 6
Answer: D
Answer: (D) 6
Question: A man gains 30% by selling an article for a certain price. If he sells it at double the price, the percentage of profit will be.
(A) 130%
(B) 140%
(C) 150%
(D) 260%
(E) 170%
Rationale: Explanation:
Let the C.P. = x,
Then S.P. = (130/100)x = 13x/10
New S.P. = 2(13x/10) = 26x/10
Profit = 26x/10 - x = 26x/10
Profit% = (Profit/C.P.) * 100
=> (26x/10) * (1/x) * 100 = 260 %
Option D
Answer: (D) 260%
Question: A doctor prescribed 20 cubic centimeters of a certain drug to a patient whose body weight was 120 pounds. If the typical dosage is 2 cubic centimeters per 15 pounds of the body weight, by what percent was the prescribed dosage greater than the typical dosage?
(A) 25%
(B) 9%
(C) 11%
(D) 12.5%
(E) 14.8%
Rationale: Typical dosage per 15 pound of the body weight = 2 c.c
Typical dosage per 120 pound of the body weight = 2 *(120/15)
= 2 * 8
= 16 c.c
Dosage prescribed by doctor for 120 pound patient = 20 c.c
% prescribed dosage greater than the typical dosage = (20-16/16) *100%
=(2/16) *100%
= 25%
Answer A
Answer: (A) 25%
Question: The price of lunch for 15 people was $208.00, including a 15 percent gratuity for service. What was the average price per person, EXCLUDING the gratuity?
(A)  $11.73
(B)  $12.60
(C)  $13.80
(D)  $14.00
(E)  $15.87
Rationale: Take the initial price before the gratuity is 100
The gratuity is calculated on the final price, so as we assumed the final bill before adding gratuity is 100 so gratuity is 15% of 100 is 15 so the total price of meals is 115 so the given amount i.e 208 is for 115 then we have to calculate for 100
for 115 208
for 100 x
so by cross multiplication we get 115x=100*208 => x=100*208/110 by simplifying we get x as 189 which is the price of lunch before gratuity so the gratuity is 19 so
as the question ask the average price person excluding gratuity is 189/15=12.6 so our answer is B)
Answer: (B)  $12.60
Question: An adventuring party consists of 4 white mages, 6 warriors, and 4 archers. In how many ways can 3 white mages, 2 warriors and 2 archers be selected from the given group?
(A) 987 ways
(B) 446 ways
(C) 360 ways
(D) 157 ways
(E) 134 ways
Rationale: The number of ways of selecting three white mages, two warriors and two archers is:
= ⁴C₃ * ⁶C₂ * ⁴C₂
= (4 * 3 * 2)/(3 * 2 * 1) * (6 * 5)/(2 * 1) * (4 * 3)/( 2 * 1)
= 4 * 15 * 6
= 360 ways.
Answer: C
Answer: (C) 360 ways
Question: Peter invests a sum of money and gets back an amount of $ 815 in 3 years . David invests an equal amount of money and gets an amount of $850 in 4 years. If both amounts were invested at the same rate (simple interest ) What was the sum of money invested ?
(A) 670
(B) 664
(C) 698
(D) 744
(E) 710
Rationale: Since both Peter and David invested the same amount of money at the same rate, they would earn same interest per year.
David invested for one year more than Peter and hence he got interest amount for one more year.
Interest earned per year = Amount received by David - Amount received by Peter = 850 - 815 = 35
Interest earned for 3 years = 35*3 =105
Amount invested = 815 - 105= 710
Answer: E
Answer: (E) 710
Question: If x is equal to the sum of the integers from 60 to 80, inclusive, and y is the number of even integers from 60 to 80, inclusive, what is the value of x + y?
(A) 1361
(B) 1481
(C) 1601
(D) 1721
(E) 1841
Rationale: x = 60 + 61 +...+ 80 = 21(70) = 1470
y = 11
x+y = 1481
The answer is B.
Answer: (B) 1481
Question: A and B rent a pasture for 10 months. A put in 80 cows for 7 months. How many can B put in for the remaining 3 months, if he pays half as much again as A?
(A) 299
(B) 277
(C) 281
(D) 280
(E) 267
Rationale: 80* 7: x* 3 = 1:1 1/2
560: 3x = 2: 3
x = 280
Answer: D
Answer: (D) 280
Question: If 2a – b = 3c, where a, b, and c are non-zero integers, which of the following could be the average (arithmetic mean) of a and b, if the average must itself be an integer?
(A) -2
(B) -1
(C) 1
(D) 10
(E) 12
Rationale: Let's say Average of a & b is c
a+b/2=c
a+b= 2c
2a-b=3c
a+b=2c
--------
3a = 5c
a=5c/3
we can plug in all answer choices for average - " c " and see which one gives us an integer as "a" is also an integer.
5(-2)/3 = -10/3
5(-1)/3 = -5/3
5(1)/3 = 5/3
5(10)/3 = 50/3
5(12)/3 = 60/3= 20 ( Hence 12 is the correct answer)
ANSWER:E
Answer: (E) 12
Question: A group of n students can be divided into equal groups of 4 with 2 student left over or equal groups of 5 with 2 students left over. What is the sum of the two smallest possible values of n?
(A) 33
(B) 46
(C) 49
(D) 64
(E) 86
Rationale: 4x+2 = 5y+2...........ie: 4x-5y = 0
x,y must be >1 and y is even ie ( 2,4,6,..etc)
if y = 2 thus x is fraction
if y = 4 thus x =5 n =22
if y = 6 thus x = not possible fraction
if y =8 thus x = 10 n =42
n= 22+42= 64
D
Answer: (D) 64
Question: What is the number which when multiplied by 13 is increased by 180?
(A) 13
(B) 15
(C) 23
(D) 35
(E) 45
Rationale: 13 × 15 = 195
Answer: B
Answer: (B) 15
Question: Over a three-week period, the price of an ounce of gold increased by 10% in the first week, decreased by 20% in the following week, and increased by 10% in the third week. If the price of gold was G dollars per ounce at the beginning of the three weeks, what was the price at the end of the three weeks?
(A) 0.968G
(B) 0.978G
(C) 0.988G
(D) 0.998G
(E) 1.008G
Rationale: After 3 weeks, the price was 1.1*0.8*1.1*G=0.968G
The answer is A.
Answer: (A) 0.968G
Question: A man can do a piece of work in 5 days, but with the help of his son he can do it in 3 days. In what
time can the son do it alone ?
(A) 712days
(B) 612days
(C) 512days
(D) 412days
(E) None of these
Rationale: Explanation:
In this type of question, where we have one person work and together work done. Then we can easily
get the other person work just by subtracting them. As
Son's one day work =
(13−15)=(5−315)=215
So son will do whole work in 15/2 days
which is =
712days
Answer: A
Answer: (A) 712days
Question: Solve the given two equations and find the inequality of X and Y. (a) 2x^2 + 11x + 14 = 0 and (b) 4y^2 + 12y +9 =0
(A) If x>y
(B) If x>=y
(C) If x<y
(D) If x<=y
(E) x=y or relationship cannot be established
Rationale: Solution:-
X=-7/2 or -2
Y=-3/2
If x<y
C)
Answer: (C) If x<y
Question: Present ages of Sameer and Anand are in the ratio of 5 : 4 respectively. Eight years hence, the ratio of their ages will become 11 : 9 respectively. What is Anand's present age in years?
(A) Can't be determined
(B) 40
(C) 27
(D) 64
(E) None of these
Rationale: Explanation:
Let the present ages of Sameer and Anand be 5x years and 4x years respectively.
Then, (5x+8)/(4x+8)=11/9
⇒ 45x + 72 = 44x + 88⇒ 9(5x + 8) = 11(4x + 8)
⇒ 45x - 44x = 88 - 72
⇒ x = 16.
Anand's present age = 4x = 64 years.
Answer: D
Answer: (D) 64
Question: An error 2% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is:
(A) 4.00%
(B) 4.14%
(C) 4.04%
(D) 4.26%
(E) 4.27%
Rationale: 100 cm is read as 102 cm.
A1 = (100 x 100) cm2 and A2 (102 x 102) cm2.
(A2 - A1) = [(102)2 - (100)2]
= (102 + 100) x (102 - 100)
= 404 cm2.
Percentage error = 404	x 100	%	= 4.04%
100 x 100
C
Answer: (C) 4.04%
Question: A man can row upstream at 25 kmph and downstream at 35 kmph, and then find the speed of the man in still water?
(A) 18 kmph
(B) 20 kmph
(C) 30 kmph
(D) 19 kmph
(E) 10 kmph
Rationale: US = 25
DS = 35
M = (35 + 25)/2 = 30
Answer:C
Answer: (C) 30 kmph