mathewhe/aqua_rat huggingface dataset:
Question: A man said to his son, "I was two-third of your present age when you were born". If the present age of the man is 48 years, find the present age of the son?
(A) 28.9
(B) 28.7
(C) 28.2
(D) 28.8
(E) 28.1
Rationale: Present age of the son be P, he was born P years ago.
The age of the man was: (48 - P).
His age when the son was born should be equal to 2/3 of P.
(48 - P) = 2/3 P
5P = 144 => P = 28.8.Answer: D
Answer: (D) 28.8
Question: In an election between the two candidates, the candidates who gets 70% of votes polled is winned by 320 vote’s majority. What is the total number of votes polled?
(A) 750
(B) 700
(C) 800
(D) 850
(E) None of these
Rationale: Explanation:
Note: majority (40 %) = difference in votes polled to win (70 %) & defeated candidates (30 %)
40 % = 70 % - 30 %
40% -----> 320 (40*8 = 320)
100% -----> 800 (100*8 = 800)
Answer: Option C
Answer: (C) 800
Question: According to a recent survey report issued by the Commerce Ministry, Government of India, 30% of the total FDI goes to Gujarat and 20% of this goes to rural areas. If the FDI in Gujarat, which goes to urban areas, is $72 m, then find the size of FDI in rural Andhra Pradesh, which attracts 50% of the FDI that comes to Andhra Pradesh, which accounts For 20% of the total FDI?
(A) 30m
(B) 40m
(C) 35m
(D) 38m
(E) 50m
Rationale: 30% of total FDI given to Gujarat is $90m.
so,100% is $300m.
20%of 300m=60m.
50%of 60m=30m.
ANSWER:A
Answer: (A) 30m
Question: How many of the factors of 1000 are divisible by 2?
(A) 5
(B) 6
(C) 8
(D) 12
(E) 15
Rationale: 1000 = 2^3*5^3
The total number of factors is (3+1)(3+1) = 16
The odd factors are 1, 5, 25, and 125.
The number of even factors is 16-4 = 12
The answer is D.
Answer: (D) 12
Question: The average of 11 numbers is 22. Average of the first 6 of them is 19 and that of the last 6 is 27. Find the 6th number?
(A) 12
(B) 25
(C) 34
(D) 29
(E) 27
Rationale: Sum of all the 11 numbers = 11 * 22 = 242Sum of the first 6 of them = 6 * 19 = 114Sum of the last 6 of them = 6 * 27 = 162So, the 8th number = 242 + 114 - 162= 34.Answer: C
Answer: (C) 34
Question: A shopkeeper purchased 70 kg of potatoes for Rs. 420 and sold the whole lot at the rate of Rs. 6.50 per kg. What will be his gain percent?
(A) 8 1/7 %
(B) 2 1/3 %
(C) 8 1/3 %
(D) 8 1/8 %
(E) 8 1/9 %
Rationale: C.P. of 1 kg = 420/7 = Rs. 6
S.P. of 1 kg = Rs. 6.50
Gain % = 0.50/6 * 100 = 25/3
= 8 1/3 %
Answer:C
Answer: (C) 8 1/3 %
Question: If f(f(n)) + f(n) = 2n+3, f(0) = 1 then f(2016) = ?
(A) 2017
(B) 2088
(C) 270
(D) 1881
(E) 1781
Rationale: f (f(0)) + f(0) = 2(0) + 3 ⇒⇒ f(1) = 3-1 = 2, f(1) = 2
f(f(1)) + f(1) = 2(1) + 3 ⇒⇒ f(2) = 5-2 = 3, f(2) = 3
f(f(2)) + f(2) = 2(2) + 3 ⇒⇒ f(3) = 7-3 = 4, f(3) = 4
..............
f(2016) = 2017
Ans: A
Answer: (A) 2017
Question: What is the difference between the C.I. on Rs. 5000 for 1 1/2 years at 4% per annum compounded yearly and half-yearly?
(A) Rs. 2.04
(B) Rs. 2.02
(C) Rs. 2.10
(D) Rs. 2.11
(E) Rs. 2.21
Rationale: Explanation:
C.I. when interest is compounded yearly
= [5000 * (1 + 4/100) * (1 + (1/2 * 4)/100]
= 5000 * 26/25 * 51/50 = Rs. 5304
C.I. when interest is compounded half-yearly
= [5000 * (1 + 2/100)2]
= (5000 * 51/50 * 51/50 * 51/50) = Rs. 5306.04 Difference = (5306.04 - 5304) = Rs. 2.04.
Answer: A
Answer: (A) Rs. 2.04
Question: There are 4 copies of 5 different jeans. In how many ways can they be arranged on a shelf?
(A) 20!/4!
(B) 20!/5(4!)
(C) 20!/(4!)^5
(D) 20!
(E) 5!
Rationale: There are 4 copies of 5 different jeans.20!/((4!)^5)
Answer - C
Answer: (C) 20!/(4!)^5
Question: What will be the compound interest on a sum of Rs. 24,000 after 3 years at the rate of 12% p.a.?
(A) Rs. 9718.27
(B) Rs. 9750
(C) Rs. 10123.20
(D) Rs. 10483.20
(E) None
Rationale: Amount = [24000 * (1 + 12/100)3]
= 24000 * 28/25 * 28/25 * 28/25 = Rs. 33718.27
C.I. = (33718.27 - 24000) = Rs. 9718.27
ANSWER:A
Answer: (A) Rs. 9718.27
Question: In a certain appliance store, each model of television is uniquely designated by a code made up of a particular ordered pair of letters. If the store has 30 different models of televisions, what is the minimum number of letters that must be used to make the codes?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: If n is the number of distinct letters used to create the two lettered codes, then a total of n∗n=n^2 different codes can be created. We need n2≥30. The smallest n which fulfills this condition is n = 6.
Answer A
Answer: (A) 6
Question: The approximation of √0.8-√0.1 is between?
(A) 1/5 and 1/4
(B) 1/4 and 1/3
(C) 1/3 and 1/2
(D) 1/2 and 2/3
(E) 2/3 and 1
Rationale: √(0.8 )– √0.1
Let’s square this expression: 0.8 + 2√0.08 + 0.1 = 9/10+(4√2)/10
√2 is approximately 1.4 and we have (9-5,6)/10=3,4/10=34/100
Now take root of this: √(34/100)
√34 is close to 6 and our expression lies between 1/2 and 3/5
3/5 = 0.6 < 2/3 (0.66666…)
Answer D
Answer: (D) 1/2 and 2/3
Question: A group of 5 students bought movie tickets in one row next to each other. If Bob and Lisa are in this group, what is the probability that Bob and Lisa will each sit next to only one of the four other students from the group?
(A) 5%
(B) 10%
(C) 15%
(D) 20%
(E) 25%
Rationale: Bob and Lisa are students too. Given the above conditions, there are 2 possible seating arrangments:
scenario 1: LXXXB or
scenario 2: BXXXL
there are 5(4)3(2)1 = 120 total seating arrangements. in scenario 1, bob must be seated on the far right and lisa on the far left. this leaves 6 different possible seating arrangements among the other 3 students: 3(2)1 = 6. 6/120 = 1/20.
the prob of scenario 2 happening is also 1/20. either scenario 1 or 2 will occur so we sum the probs of 1 or 2 happening, 1/20 + 1/20 + 2/20 = 1/10 = .10.
answer is B.
Answer: (B) 10%
Question: A alone can finish a work in 10 days which B alone can finish in 15 days. If they work together and finish it, then out of a total wages of Rs.3000, A will get:
(A) Rs.1200
(B) Rs.1500
(C) Rs. 1800
(D) Rs.2000
(E) None of these
Rationale: Explanation:
Ratio of working days of A : B = 10 : 15
Therefore, their wages ratio = reverse ratio = 15 : 10
Therefore, A will get 15 units of ratio
Total ratio = 25
1 unit of ratio =3000/25 = 120
So, A’s amount = 120 × 15 = Rs.1800.
Answer: Option C
Answer: (C) Rs. 1800
Question: A carnival card game gives the contestant a one in three probability of successfully choosing the right card and thereby winning the game. If a contestant plays the game repeatedly, what is the minimum number of times that he must play the game so that the probability that he never loses is less than 1%?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Probability of Choosing Right card hence winning = 1/3
i.e. Probability of NOT Choosing Right card hence Losing = 2/3
We want that the probability that he never loses should be < 1%
i.e. We want that the probability that he never loses should be < 1/100
The probability of him losing can be calculated by taking the case that the right card is never picked
i.e. Probability of first card being the Right card = (1/3)
i.e. Probability of first as well as second card NOT being the Right card = (1/3)*(1/3)
i.e. i.e. Probability of all n attempts being the Right card (i.e. Never Losing) = (1/3)^n
and (1/3)^n<1/100
But(1/3)^4=1/81
And (1/3)^5=1/243
i.e. (1/3)^5<1/100
i.e. Minimum value of 'n' can be = 5
Answer:C
Answer: (C) 5
Question: A sum of Rs. 1360 has been divided among A, B and C such that A gets of what B gets and B gets of what C gets. B's share is:
(A) 240
(B) 120
(C) 300
(D) 160
(E) 270
Rationale: Let C's share = Rs. x
Then, B's share = Rs.	x/4,
A's share = Rs.(2/3)	x (x/4)= Rs.x/6
(x/6)	+(x/4)+ x = 1360
17x/12= 1360
x =1360 x (12/17)= Rs. 960
Hence, B's share = Rs.960/4= Rs. 240.
Answer is A.
Answer: (A) 240
Question: Combine terms: 5a + 26b -4b – 16a.
(A) 4a + 22b
(B) -28a + 30b
(C) -11a + 22b
(D) 28a + 30b
(E) 5a + 30b
Rationale: Solution:
5a + 26b -4b – 16a.
= 5a – 16a + 26b – 4b.
= -11a + 22b.
Answer: (C)
Answer: (C) -11a + 22b
Question: Mohit sold an article for Rs. 18000. Had he offered a discount of 13% on the selling price, he would have earned a profit of 8%. What is the cost price of the article?
(A) 14500
(B) 27767
(C) 16688
(D) 26678
(E) 19987
Rationale: Let the CP be Rs. x.
Had he offered 13% discount, profit = 8%
Profit = 8/100 x and hence his SP = x + 8/100 x = Rs. 1.08x = 18000 - 13/100(18000) = Rs. 15660
=> 1.08x = 15660
=> x = 14500
\Answer: A
Answer: (A) 14500
Question: If -5 < x < 7 and -6 < y < 3, which of the following specifies all the possible values of xy?
(A) -42 < xy < 30
(B) -42 < xy < 24
(C) -28 < xy < 18
(D) -24 < xy < 21
(E) -24 < xy < 24
Rationale: The least value of xy is a bit more than 7*(-6)=-42 and the largest value of xy is a bit less than (-5)*(-6)=30.
Therefore -42 < xy < 30.
Answer: A.
Answer: (A) -42 < xy < 30
Question: To celebrate a colleague's retirement, the T coworkers in an office agreed to share equally the cost of a catered lunch. If the lunch costs a total of R dollars and S of the coworkers fail to pay their share, which of the following represents the additional amount, in dollars, that each of the remaining coworkers would have to contribute so that the cost of the lunch is completely paid?
(A) R/T
(B) R/(T-S)
(C) SR/(T-S)
(D) SR/T(T-S)
(E) R(T-S)/T
Rationale: Since no absolute values are given in the question we can replace the given parameters with assumed numbers,
Let Total colleagues be 100 (T)
Let total contribution be 500 (R) (point to note is that its total cost not per person)
Those who dont pay are S (30)
Per person cost = R/T = 800/100 = 8
So cost for those who failed to pay = (R/T) * S = SR/T = 30*8=240
The equation for people who would bear the total cost after S people fail = (T-S)=70
There fore the solution is (SR/T)/ (T-S) = SR/T(T-S) = 240/70
Answer D
Hope this helps !!!
Answer: (D) SR/T(T-S)
Question: A train moves fast a telegraph post and a bridge 264 m long in 8 sec and 20 sec respectively. What is the speed of the train?
(A) 79.5
(B) 79.0
(C) 79.3
(D) 79.2
(E) 79.1
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)/20 = y
y = 22
Speed = 22 m/sec = 22 * 18/5 = 79.2 km/hr.Answer:D
Answer: (D) 79.2
Question: Set A consists of the integers from 4 to 15, inclusive, while set B consists of the integers from 6 to 20, inclusive. How many distinct integers do belong to the both sets at the same time?
(A) 5
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: A={4,5,6,7,8,9,10,11,12,13,14,15}
B={6,7,8,9,10,11,12...20}
Thus we see that there are 10 distinct integers that are common to both. E is the correct answer.
Answer: (E) 10
Question: To save money, Arkadelphia ice cream will reduce each dimension of its rectangular box container (which is entirely full of ce cream) by 50%, and reduce the price it charges its consumers by 50% as well. By what percentage does this increase the price-per-cubic-inch that each consumer will pay for ce cream?
(A) 1. No change
(B) 2. 50%
(C) 3. 300%
(D) 4. 400%
(E) 5. 450%
Rationale: If the current volume is L * W * H, then the new volume is 12 (L) * 12 (W) * 12 (H), or 18 * LWH. So the new portion is 1/8 the size of the old portion. But the new cost is only ½ the cost, meaning that if the old price-per-unit was 1:1, now it’s 12 : 18, or 4:1. So the consumer is paying 400% of what it used to, or 300% more than it used to. The answer is therefore C.
Answer: (C) 3. 300%
Question: A is two years older than B who is twice as old as C.If the total ages of A,B and c be 27 . what is the age of B?
(A) 12 years
(B) 10 years
(C) 8 years
(D) 14 years
(E) 16 years
Rationale: c age x,
then b age is 2x
so a age is 2x+2.
(2x+2)+2x+x=27
5x=25
x=5
so b is 2x=2(5)
2x5= 10 ANSWER : B
Answer: (B) 10 years
Question: A trader mixes 26 kg of rice at Rs. 20 per kg with 30 kg of rice of other variety at Rs. 36 per kg and sells the mixture at Rs. 36 per kg. His profit percent is:
(A) No profit, no loss
(B) 26%
(C) 8%
(D) 10%
(E) None of these
Rationale: Explanation :
C.P. of 56 kg rice = (26 * 20 + 30 * 36) Rs. = (520 + 1080) Rs. = 1600 Rs.
S.P. of 56 kg rice = (56 * 36) Rs. = 2016 Rs.
Profit % = (2016−1600/1600∗100)% = 26%
Answer : B
Answer: (B) 26%
Question: If a person walks at 15 km/hr instead of 10 km/hr, he would have walked 15 km more. The actual distance traveled by him is?
(A) 30
(B) 50
(C) 15
(D) 12
(E) 20
Rationale: Let the actual distance traveled be x km. Then,
x/10 = (x + 15)/15
x - 30=>x = 30km.
Answer: A
Answer: (A) 30
Question: Let d > c >e > a. If c is twice as far from a as it is from d, and e is twice as far from c as it is from a, then (d - e)/(d - a) = ?
(A) 2/9
(B) 1/3
(C) 2/3
(D) 7/9
(E) 3/2
Rationale: Draw a number line and label with x and y. You would have:
Before calculating recognize it would be more effcient to express x or y in terms of the other. here 2x = 3y so x =3/2 y.
Now you can calculate d -e and d -a
d - e= x +2y = 7/2 y
d - a = x + 2x = 3x = 9/2y
Dividing both you get: 7/9
Answer D
Answer: (D) 7/9
Question: Rs. 1400 is divided into three parts A, B and C. How much A is more than C if their ratio is 1/3:1/3:1/6?
(A) 300
(B) 992
(C) 772
(D) 552
(E) 280
Rationale: 1/3:1/3:1/6 = 2:2:1
1/5*1400 = 280
560-280 = 280
Answer: E
Answer: (E) 280
Question: When a number is divided by 6 &then multiply by 12 the answer is 8 what is the no.?
(A) 4.5
(B) 5
(C) 5.5
(D) 5.8
(E) 4
Rationale: if $x$ is the number, x/6 * 12 = 8
=> 2x = 8
=> x = 4.0
E
Answer: (E) 4
Question: Amy has two decks of 55 cards each: Deck 1 and Deck 2. She takes 8 black cards from Deck 2 and adds them to Deck 1 and shuffles it thoroughly. She now picks a card from the newly formed pack of cards. If the probability of either picking a red ace or a king from the newly formed pack is greater than 1/8, what is the probability that Amy picks a black king or a red Jack from the new pack?
(A) 1/6
(B) 1/8
(C) 1/9
(D) 1/10
(E) 1/11
Rationale: Your solution is correct answer should be 1/11.
E
Answer: (E) 1/11
Question: 2 cow’s and 5 goats are brought for Rs.1050. If the average price of a goat be Rs.90. What is the average price of a cow.
(A) 300
(B) 320
(C) 330
(D) 350
(E) 375
Rationale: Explanation:
Average price of a goat = Rs.90
total price of 5 goats = 5*90 = Rs.450
But total price of 2 cows and 5 goats = Rs. 1050
Total price of 2 cows is = 1050 - 450
= 600
Average price of a cow = 600/2
= Rs. 300
Answer: A
Answer: (A) 300
Question: How many 13 digit numbers are possible by using the digits 1,2,3,4,5 which are divisible by 4 if repetition is allowed?
(A) 511
(B) 519
(C) 515
(D) 512
(E) 513
Rationale: By divisibility rule of 4(Click here to know about the rule of divisibility ) only 12,24,32,44,52 are the numbers from 1 to 5 are divisible by 4.
So the remaining 11 digits can be any number from 1 to 5. So 511
Since there are 5 set of numbers we will get 5* 511 = 512 numbers divisible by 4.
Answer D
Answer: (D) 512
Question: What is the maximum number W of 27 cubic centimetre cubes that can fit in a rectangular box measuring 8 centimetre x 9 centimetre x 12 centimetre ?
(A) 36
(B) 32
(C) 24
(D) 21
(E) 15
Rationale: 27 cubic centimetre cubes gives side = 3cm
so if:
L*W*H is 9*12*8, then max. cube we can have are 3*4*2 = 24
L*W*H is 9*8*12, then max. cube we can have are 3*2*4 = 24
L*W*H is 12*8*9, then max. cube we can have are 4*2*3 = 24
L*W*H is 12*9*8, then max. cube we can have are 4*3*2 = 24
L*W*H is 8*12*9, then max. cube we can have are 2*4*3 = 24
L*W*H is 8*9*12, then max. cube we can have are 2*3*4 = 24
In all cases we get W=24 cubes.
Ans. C
Answer: (C) 24
Question: A man swims downstream 54 km and upstream 18 km taking 3 hours each time, what is the speed of the man in still water?
(A) 2
(B) 8
(C) 9
(D) 10
(E) 12
Rationale: 54 --- 3 DS = 18
? ---- 1
18 ---- 3 US = 6
? ---- 1 M = ?
M = (18 + 6)/2 = 12
Answer: E
Answer: (E) 12
Question: In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 50, the dividend is?
(A) 6300
(B) 6325
(C) 6330
(D) 6334
(E) 6336
Rationale: Divisor = (5 * 50) = 250
= 10 * Quotient = Divisor
=> Quotient = 250/10 = 25
Dividend = (Divisor * Quotient) + Remainder
Dividend = (250 * 25) + 50= 6330
A
Answer: (A) 6300
Question: At Joes Steakhouse the hourly wage for a chef is 25% greater than that of a dishwasher, and the hourly wage of a dishwasher is half as much as the hourly wage of a manager. If a managers wage is $8.50 per hour, how much less than a manager does a chef earn each hour?
(A) $1.40
(B) $2.40
(C) $3.40
(D) $3.19
(E) $5.40
Rationale: Manager wages per hour = $8.50
Dishwasher wages per hour = half of manager's wages. = 1/2($8.50) ==> $4.25
Chef wages per hour = 25% greater than Dishwasher wages
--> 25% of $4.25 = (25*($4.25)) /100
--> ($106.25)/100
--> $1.06
Therefore,
Chef wages per hour = $4.25 + $1.06 ==> $5.31
Difference of wages between manager and chef = $8.50 - $5.31 ==> $3.19
ANSWER:D
Answer: (D) $3.19
Question: The dimensions of a field are 20 m by 10 m. A pit 8 m long, 5 m wide and 2 m deep is dug in one corner of the field and the earth removed has been evenly spread over the remaining area of the field. What will be the rise in the height of field as a result of this operation ?
(A) 1 m
(B) 2 m
(C) 0.5 m
(D) 0.75 m
(E) 1.5 m
Rationale: The volume of the earth removed is 8*5*2 = 80 m^3.
The remaining area of the field is 20*10 - 8*5 = 160 m^2.
80 m^3 of the earth evenly spread over the area of 160 m^2 will rise the height by (height) = (volume)/(area) = 80/160 = 0.5 m.
Answer: C
Answer: (C) 0.5 m
Question: A can do a work in 15 days and B in 20 days. If they work on it together for 4 days then the fraction of the work that is left is?
(A) 1/4
(B) 1/10
(C) 7/15
(D) 8/15
(E) 9/13
Rationale: Explanation:
A’s one day work = 1/15
B’s one day work = 1/20
(A+B )’s one day work is = 1/15 +1/20 = 7/60
their 4 days work = 4 x 7/60 = 7/15
Remaining work = 8/15
Answer: Option D
Answer: (D) 8/15
Question: The number 500 can be written as the sum of the squares of 2 different positive integers. What is the difference of these 2 integers?
(A)  17
(B)  16
(C)  15
(D)  18
(E)  13
Rationale: 22^2 + 4^2 = 500 --> 22 - 4 = 18.
D
Answer: (D)  18
Question: What is the difference between the local value of 3 and 9 in the number 23974?
(A) 430
(B) 377
(C) 288
(D) 277
(E) 210
Rationale: Explanation:
300 â€“ 90 = 210
Answer: E
Answer: (E) 210
Question: In one day, Juan sends Keith eight times as many messages as he sends Laurence, and Laurence sends Missy 4.5 times as many messages as he receives from Juan. If Missy received 18 messages from Laurence, how many messages does Keith receive from Juan?
(A) 13
(B) 26
(C) 32
(D) 48
(E) 56
Rationale: Juan --> Laurence = x messages;
Juan --> Keith = 8x messages (Juan sends Keith eight times as many messages as he sends Laurence);
Laurence --> Missy = 4.5x =18 (Laurence sends Missy 4.5 times as many messages as he receives from Juan).
4.5x =18 --> x = 4 --> 8x = 32.
Answer: C.
Answer: (C) 32
Question: Two trains leave the same train station at 6:00 am and 7:15 am and they travel at 100 kph and 125 kph respectively. How many kilometers from the train station will the two trains be together?
(A) 525
(B) 550
(C) 575
(D) 600
(E) 625
Rationale: At 7:15, the first train is 125 km ahead.
The second train gains 25 km each hour.
The time it takes the second train to catch the first train is 125 / 25 = 5 hours.
In this time, the second train travels 5*125=625 km.
The answer is E.
Answer: (E) 625
Question: David mixed 10 kg of ghee at Rs. 200 per kg with 30 kg ghee at the rate of Rs. 100 per kg. At what price per kg should he sell the mixture to make a profit of 10% in the transaction?
(A) Rs. 187.50
(B) Rs. 147.50
(C) Rs. 137.50
(D) Rs. 127.50
(E) Rs. 107.50
Rationale: Cost of Ghee = 10*200+ 30*100 /40 =5000/40 = 125
10% of 125 = 12.50
S.P. should be = 125+12.5= Rs. 137.50/ kg
Answer : C
Answer: (C) Rs. 137.50
Question: An athlete runs 200 metres race in 24 seconds. His speed is :
(A) 20 km/hr
(B) 24 km/hr
(C) 28.5 km/hr
(D) 30 km/hr
(E) None of these
Rationale: Speed = 200/24 m/sec=25/3 m/sec=(25/3*18/5)km/hr=30 km/hr.
Correct Option: D
Answer: (D) 30 km/hr
Question: On a sum of money, simple interest for 2 years is Rs 660 and compound interest is Rs 696.30, the
rate of interest being the same in both cases.
(A) 8%
(B) 9%
(C) 10%
(D) 11%
(E) None of these
Rationale: Explanation:
Difference between C.I and S.I for 2 years = 36.30
S.I. for one year = 330.
S.I. on Rs 330 for one year = 36.30
So R% = \frac{100*36.30}{330*1} = 11%
Answer: D
Answer: (D) 11%
Question: Three pipes of same capacity can fill a tank in 8 hours. If there are only two pipes of same capacity, the tank can be filled in.
(A) 16
(B) 12
(C) 18
(D) 15
(E) 19
Rationale: Explanation:
The part of the tank filled by three pipes in one hour = 1/8
=> The part of the tank filled by two pipes in 1 hour = 2/3 * 1/8 = 1/12.
The tank can be filled in 12 hours.
Answer:B
Answer: (B) 12
Question: What is the place value of 4 in the numeral 4259
(A) 4000
(B) 3000
(C) 2000
(D) 1000
(E) 5000
Rationale: 4* 1000 = 4000
ANSWER A
Answer: (A) 4000
Question: The equation of line q is y = 4/3*x - 100. What is the smallest possible distance in the xy-plane from the point with coordinates (0, 0) to any point on line q?
(A) 48
(B) 50
(C) 60
(D) 75
(E) 100
Rationale: This can be solve in two steps and without any complex calculation.
Given : equation of line q as y=(4/3)x -100. So the line intercept the axes at (0,-100) and (75,0).
This can be considered a right angle triangle with right angle at (0,0) . So Base=100 , Height=75 and Hypotenuse =125 (By Pythagoras triplet)
So a perpendicular from the (0,0) to hypotenuse will be the answer.
Area of triangle= 0.5*100*75=0.5*125* x
=> x=60;
SO answer is 60=C
Answer: (C) 60
Question: A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is:
(A) 500
(B) 698
(C) 780
(D) 910
(E) None
Rationale: Sol.
S.I. for 1 year = Rs. (854 - 815) = Rs. 39.
S.I. for 3 years = Rs. (39 * 3) = Rs. 117.
∴ Principal = Rs. (815 - 117) = Rs. 698
Answer B
Answer: (B) 698
Question: What is the next number in 0, 1, 1, 3, 1, 3, 1, 3, 5?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: C
1
As the series is 0, 1, 1, 3, 1, 3, 1, 3, 5....
It can clearly be observed that the sequence given is about the no of composite numbers between any two consecutive prime number.
That means all the no excluding the primes.
The series continues as 0, 1, 1, 3, 1, 3, 1, 3, 5,1,5,3,1,5,5,5,1,5.....
The answer to this question is 1
Answer: (A) 1
Question: A candidate got 35% of the votes polled and he lost to his rival by 2250 votes. How many votes were cast?
(A) 7500
(B) 2776
(C) 8767
(D) 1997
(E) 6991
Rationale: 35%-----------L
65%-----------W
------------------
30%----------2250
100%---------? => 7500
Answer: A
Answer: (A) 7500
Question: A man buys 1kg of sandalwood and 1kg of teakwood. He sells one for 10% profit and other for 10% loss. What is total profit/loss percentage?
(A) 1% loss
(B) 2% loss
(C) 3% loss
(D) 4% loss
(E) 5% loss
Rationale: if x is both the profit and loss % then it must be loss of x^2/100;
so 10*10/100=1;
1% loss
ANSWER:A
Answer: (A) 1% loss
Question: A number has exactly 32 factors out of which 4 are not composite. Product of these 4 factors (which are not composite) is 30. How many such numbers W are possible?
(A) 2
(B) 4
(C) 6
(D) 3
(E) Not possible
Rationale: Firstly , we should note that 1 is NEITHER a prime nor a composite number.The first composite number is 4.Thus, when the problem states that there are 4 factors that are not composite, these nos are 1,2,3,5. Thus, the given number = 2^a*3^b*5^c. Also, (a+1)*(b+1)*(c+1) = 32. We can break down 32 into 3 integers as : 2*2*8 or 4*4*2
Also, the only possible combinations for a,b,c are : 3,3,1 OR 1,1,7. Thus, each combination has 3 possible orders and we have a total W of 6 possibilities.
C.
Answer: (C) 6
Question: The average age of 39 students in a group is 14 years. When teacher's age is included to it, the average increases by one. What is the teacher's age in years ?
(A) 35 years
(B) 45 years
(C) 51 years
(D) 54 years
(E) None of these
Rationale: Explanation:
Age of the teacher = (40 * 15 - 39 * 14) years = 54 years. Answer: D
Answer: (D) 54 years