mathewhe/aqua_rat huggingface dataset:
Question: Two trains running in opposite directions cross a man standing on the platform in 35 seconds and 28 seconds respectively and they cross each other in 32 seconds. The ratio of their speeds is:
(A) 3 : 1
(B) 4: 3
(C) 3 : 8
(D) 3 : 25
(E) 3 : 4
Rationale: Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 35 x meters, and length of the second train = 28 y meters. (35 x + 28 y) / (x + y) = 32
==> 35 x + 28 y = 32 x + 32 y ==> 3 x = 4 y ==> x/y = 4/3
Answer: Option B
Answer: (B) 4: 3
Question: If $ 500 amounts to $ 583.20 in two years compounded annually, find the rate of interest per annum.
(A) 6
(B) 7
(C) 8
(D) 5
(E) 4
Rationale: Principal = Rs. 500; Amount = Rs. 583.20; Time = 2 years.
Let the rate be R% per annum. Then,
[ 500 (1+(R/100)^2 ] = 583.20 or [ 1+ (R/100)]^2 =
5832/5000 = 11664/10000
[ 1+ (R/100)]^2 = (108/100)^2 or 1 + (R/100) = 108/100 or R = 8
Answer C.
So, rate = 8% p.a.
Answer: (C) 8
Question: If selling price is doubled, the profit triples. Find the profit percent.
(A) 20%
(B) 25%
(C) 30%
(D) 60%
(E) 100%
Rationale: Let C.P. be Rs. x and S.P. be Rs. y.
Then, 3(y - x) = (2y - x) y = 2x.
Profit = Rs. (y - x) = Rs. (2x - x) = Rs. x.
Profit % = x	x 100	% = 100%
x
E)
Answer: (E) 100%
Question: If the true discount on s sum due 2 years hence at 14% per annum be Rs. 154, the sum due is:
(A) s. 704
(B) s. 968
(C) s. 1960
(D) s. 2400
(E) s. 2800
Rationale: td=pw*r*t/100 so 154=pw*14*2/100 so pw=550
sum=pw+td..
sum=550+154=704
ANSWER:A
Answer: (A) s. 704
Question: Two cards are drawn at random from a pack of 52 cards.what is the probability that either both are black or both are queen?
(A) 32/200
(B) 55/221
(C) 55/200
(D) 12/130
(E) 45/200
Rationale: n(S)=52C2=52*51/2*1
=1326
A = event of getting black cards
B- queen black cards
n(A)=2C2=26*25/2*1
4C2=4*3/2*1
==325/1326==>55/221
ANSWER B
Answer: (B) 55/221
Question: If 2^x + 2^y = 10^0 + 90^0, where x and y are non negative integers, what is the greatest possible value of |x â€“ y|?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: |x â€“ y| for x and y 2^x + 2^y = 10^0 + 90^0
A. x= y x=y=0 1 + 1 = 1 + 1 right
B. 1 x=2, y=1 4 + 2 = 1 + 1 wrong
C. 2 x=3, y=1 8 + 2 = 1 + 1 wrong
D. 3 x=4, y =1 16 + 2 = 1 + 1 wrong
E. 4 x=5, y =1 32 + 2 = 1 + 1 wrong
My answer is A.
Answer: (A) 0
Question: A man buys a cycle for Rs. 1400 and sells it at a loss of 10%. What is the selling price of the cycle?
(A) s. 1090
(B) s. 1160
(C) s. 1190
(D) s. 1260
(E) s. 1204
Rationale: since,c.p=1400
loss%=(c.p-s.p)/c.p*100
10=(1400-s.p)/1400*100
so,after solving answer=1260.
ANSWER:D
Answer: (D) s. 1260
Question: A train running at the speed of 30 km/hr crosses a pole in 9 seconds. Find the length of the train?
(A) 75
(B) 65
(C) 25
(D) 288
(E) 212
Rationale: Speed = 30*(5/18) m/sec = 25/3 m/sec
Length of Train (Distance) = Speed * Time
(25/3) * 9 = 75 meter
Answer:A
Answer: (A) 75
Question: What will come in place of the x in the following Number series? 5,28,57,88,125
(A) 140
(B) 150
(C) 166
(D) 170
(E) 180
Rationale: 28=23+5
57=29+28
88=31+57
125=37+88
166=41+125
=166
C
Answer: (C) 166
Question: Train A leaves New York at 7:00 am traveling to Boston at 80mph. Train B leaves Boston at 7:45 am traveling to New York at 70 mph on a parallel track. If the distance between New York and Boston is 210 miles, at what time will the two trains pass each other?
(A) 8:15 am
(B) 8:45 am
(C) 9:00 am
(D) 9:30 am
(E) Cannot be determined from the information given
Rationale: train A will cover 60 kms in 45 min at 7:45, the time when train B starts...
distance left to cover is 210-60=150..
combined speed=80+70=150..
so the trains meet in 1 hour i.e. 7:45 + 1 hr=8:45
ANSWER:B
Answer: (B) 8:45 am
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
(A) 816 m
(B) 167 m
(C) 156 m
(D) 150 m
(E) 178 m
Rationale: Speed=(60 * 5/18) m/sec
= (50/3) m/sec Length of the train
= (Speed x Time) = (50/3 * 9) m
= 150 m.
Answer: D
Answer: (D) 150 m
Question: Ajay sells goods to a customer at a profit of K % over the marked price, besides it he cheats his customer by giving 880g only instead of 1kg. Thus his overall profit percentage is 25%. Find the value of K.
(A) 8.33%
(B) 8.25%
(C) 10%
(D) 12.5%
(E) None of these
Rationale: Let C.P. of 1000g = Rs. 1000
Profit % = K %
Profit = K/100 x 1000 = Rs.10 K
He then cheats his customer by giving 880g only instead of 1kg,
So, C.P of 880g = Rs. 880
S.P. of 880g = 1000 + 10K
Profit % = [ ( 1000 + 10K - 880 ) / 880 ] x 100 = 25
K = 10%
ANSWER:C
Answer: (C) 10%
Question: Johnny travels a total of one hour to and from school. On the way there he jogs at 5 miles per hour and on the return trip he gets picked up by the bus and returns home at 25 miles per hour. How far is it to the school?
(A) 2 miles
(B) 4 miles
(C) 6.6 miles
(D) 8 miles
(E) 10 miles
Rationale: Answer: C) 6.6 miles.
Average speed for round trip = 2*a*b/(a+b), where a,b are speeds
so, average speed was = 2*5*25/(5+25) = 6.6m/hr
the distance between schoolhome should be half of that. ie. 6.6 miles
Answer C
Answer: (C) 6.6 miles
Question: Two successive discounts of 20% and 20% are equivalent to a single discount of
(A) 42%
(B) 40%
(C) 36%
(D) 34%
(E) None
Rationale: Answer
Given, r1 = 20% and r2 = 20%
∴ Single discount equal to r1 and r2
= (r1 + r2 - r1 x r2) / 100 %
= (20 + 20 - 20 x 20) / 100
= 40 - 4 = 36%
Correct Option: C
Answer: (C) 36%
Question: For each of her sales, a saleswoman receives a commission equal to 20 percent of the first $500 of the total amount of the sale, plus 30 percent of the total amount in excess of $500. If the total amount of one of her sales was $800, the saleswoman’s commission was approximately what percent of the total amount of the sale?
(A) 22%
(B) 24%
(C) 25%
(D) 28%
(E) 27%
Rationale: Total sales =800
Commission = (20/100)*500+ (30/100)*300
=100 + 90
=190
%Commission =(190/800)*100=23.7~ 24%
Answer is B
Answer: (B) 24%
Question: Jaylen was planning to save all summer for a pair of Jordan 12s. They cost $250. Jaylen figured that he could cut grass to help with the cost of the sneakers. How many yards would Jaylen have to cut if he charges $2.15 per yard?
(A) 116 yards
(B) 226 yards
(C) 97 yards
(D) 115.74 yards
(E) 1 yard
Rationale: D
Answer: (D) 115.74 yards
Question: A series of five integers have the following criteria:
I. The median of the integers is 6
II. The only mode is 2
III. The mean is 5
Which of the following is true?
(A) The sum of the five integers is 30.
(B) The sum of the five integers is 10
(C) The median of the three largest integers is 6.
(D) The largest integer is 9.
(E) The largest integer is 8.
Rationale: As per the given statements, we can infer (2+2+6+x+y)/5=5 ; x+y = 15
Since 6 is the median, x and y will have to be greater than 6. Only 7+8 can satisfy this condition.
Hence, E is the correct answer.
Answer: (E) The largest integer is 8.
Question: If the price has fallen by 10% what percent of its consumption be: increased so that the expenditure may be the same as before?
(A) 11%
(B) 10%
(C) 11 1/9 %
(D) 9 1/11 %
(E) 20 %
Rationale: 100 – 10 = 90
90------10
100------? => 11 1/9%
ANSWER:C
Answer: (C) 11 1/9 %
Question: A train sets off at 9:00 am at the speed of 70 km/h. Another train starts at 10:30 am in the same direction at the rate of 80 km/h. At what time will the second train catch the first train?
(A) 7:00
(B) 8:00
(C) 9:00
(D) 10:00
(E) 11:00
Rationale: In one hour and thirty minutes the first train travels 105 km.
The second train catches the first train at a rate of 80 km/h - 70 km/h = 10 km/h.
The second train will catch the first train in 105/10 = 10.5 hours, so at 9:00 pm.
The answer is C.
Answer: (C) 9:00
Question: Let f(x,y) be defined as the remainder when (x–y)! is divided by x. If x=45, what is the maximum value of y for which f(x,y)=0?
(A) 32
(B) 35
(C) 39
(D) 40
(E) 42
Rationale: The question is finding y such that (45-y)! is a multiple of 45. That means we need to have 5*3^2 in (45-y)!
6! is the smallest factorial number with 5*3^2 as a factor.
45-y = 6
y = 39
The answer is C.
Answer: (C) 39
Question: Find the invalid no.from the following series 2,3,12,37,86,166,288
(A) 2
(B) 3
(C) 166
(D) 86
(E) 288
Rationale: 3-2=1
12-3=9
37-12=25
86-37=49
166-86=80(this must be 81=167-86=81)
so wrong number in the sequence is 166
difference between two sucessive numbers sequence would be
1,9,25,49,81,121(square of 1,3,5,7,9,11)
C
Answer: (C) 166
Question: A letter lock consists of three rings each marked with six different letters. The number of distinct unsuccessful attempts to open the lock is at the most
(A) 272
(B) 277
(C) 215
(D) 187
(E) 165
Rationale: Since each ring consists of six different letters, the total number of attempts possible with the three rings is = 6 * 6 * 6 = 216. Of these attempts, one of them is a successful attempt.
Maximum number of unsuccessful attempts = 216 - 1
= 215
Answer:C
Answer: (C) 215
Question: If Rs.10 be allowed as true discount on a bill of Rs.110 at the end of a certain time , then the discount allowed on the same sum due at the end of double the time is?
(A) 68.33
(B) 18.33
(C) 28.33
(D) 48.33
(E) 98.33
Rationale: Explanation:
Present worth = Amount - TrueDiscount
= 110 -10 = Rs.100
SI on Rs.100 for a certain time = Rs.10
SI on Rs.100 for doube the time = Rs.20
TrueDiscount on Rs.120 = 120 - 100 = Rs.20
TrueDiscount on Rs.110 = = Rs.18.33
Answer: B
Answer: (B) 18.33
Question: A 64 gallon solution of salt and water is 10% salt. How many gallons of water must be added to the solution in order to decrease the salt to 8% of the volume?
(A) 8
(B) 12
(C) 13
(D) 14
(E) 16
Rationale: Amount of salt = 6.4
Assume x gallons of water are added.
6.4 / 64 + x = 8/100
640 = 8x + 512
8x = 128
x = 16
Correct Option: E
Answer: (E) 16
Question: Two pipes A and B can separately fill a tank 12 minutes and 15 minutes respectively. Both the pipes are opened together but 4 minutes after the start the pipe A is turned off. How much time will it take to fill the tank?
(A) 5min
(B) 6min
(C) 10min
(D) 8min
(E) 9min
Rationale: 4/12 + x/15 = 1
x = 10
ANSWER:C
Answer: (C) 10min
Question: A bag holds 4 red marbles and 3 green marbles. If you removed two randomly selected marbles from the bag, without replacement, what is the probability that both would be red?
(A) 1/10
(B) 1/5
(C) 3/10
(D) 2/7
(E) 1/2
Rationale: probability of selecting first red marble = 4/7
probability of selecting second red marble without replacement = 3/6
final probability = 4/7 * 3/6 = 2/7
The correct answer is D.
Answer: (D) 2/7
Question: A, B and C shared profits in ratio of 5 : 7 : 8. Theypartnered for 14months, 8months and 7months respectively. What was he ratio of their investments ?
(A) 10 : 49 : 45
(B) 20 : 49 : 64
(C) 10 : 19 : 64
(D) 20 : 29 : 64
(E) 30 : 29 : 63
Rationale: Simply multiply profit sharing ratio with investment ratio to get investment amount ratio.
Let X is the total investment
⇒14 x = 5
⇒ 8 x = 7
⇒ 7x = 8
⇒ Final investment ratio = 20 : 49 : 64
B
Answer: (B) 20 : 49 : 64
Question: If 2x-1 + 2x+1 = 1280, then find the value of x.
(A) 0
(B) 2
(C) 4
(D) 9
(E) 6
Rationale: Sol.
2x-1 + 2x+1 = 1280 ⇔ 2x-1 (1+22) = 1280
⇔ 2x-1 = 1280 / 5 = 256 = 28
⇔ x - 1 = 8 ⇔ x = 9.
Hence, x = 9.
Answer D
Answer: (D) 9
Question: What should come in the place of the question mark(?) in the following equation?
21⁄25 ÷ 9⁄20 × 5⁄12 ÷ 10⁄17
(A) 7 77⁄125
(B) 11 9⁄10
(C) 119⁄450
(D) 1 29⁄90
(E) None of these
Rationale: ? = 21⁄25 × 20⁄9 × 5⁄12 ÷ 17⁄10 = 119⁄90 = 129⁄90
Answer D
Answer: (D) 1 29⁄90
Question: A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.12100 after a year?
(A) 3630
(B) 2277
(C) 2668
(D) 1286
(E) 19881
Rationale: 6300:4200:10500
3:2:5
3/10 * 12100 = 3630
Answer:A
Answer: (A) 3630
Question: A woman started a business investing Rs. 70,000. Roja joined him after six months with an amount of Rs. 1,05,000 and Sachin joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Akash, Roja and Sachin respectively, 3 years after Aman started the business ?
(A) 7:6:10
(B) 12:15:16
(C) 42:45:56
(D) None of these
(E) Cannot be determined
Rationale: Explanation :
Akash : Roja : Sachin = (70,000 x 36) : (1,05,000 x 30) : (1,40,000 x 24)
= 12 : 15 : 16.
Answer : B
Answer: (B) 12:15:16
Question: A meeting has to be conducted with 5 managers.Find the number of ways in which the managers may be selected from among 9 managers,if 3 managers will not attend the meeting together.
(A) 1.24
(B) 2.91
(C) 3.12
(D) 4.126
(E) 5.15
Rationale: 9 managers, but 3 of them cannot attend the meeting together.
We can split it into two cases.
1. Meeting without these 3 managers in it. That would mean selecting 5, from the remaining 6 which is 6C5 = 6
2. Meeting with one of the 3 managers. select 1 manager from 3, and then select 4 from the remaining 6, which is 3C1 + 6C4 = 18 + 6 = 24.
Answer : A
Answer: (A) 1.24
Question: Nicole cycles at a constant rate of 15 kilometers per hour, and is passed by Jessica, who cycles at a constant rate of 30 kilometers per hour. If Jessica cycles at her constant rate for x minutes after passing Nicole, then stops to wait for her, how many minutes will Jessica have to wait for Nicole to catch up to her?
(A) a) x minutes
(B) b) x/2 minutes
(C) c) 2x/3 minutes
(D) d) 3x/2 minutes
(E) e) 2x minutes
Rationale: Speed of nicole = 20km/h or 20/60 km/min = 1/3 km/min.
Once jessica passed the nicole, the distance between the nicole and jessica will increase at the rate of (30-20) = 10km/h or 1/6 km/min
now jessica is cycling for x minutes after passing the nicole, so in those x minutes distance between jessica and nicole would be (1/6)*x = x/6 km.
So, the time taken by nicole to travel x/6 km = (x/6)/(1/3) = 2x. hence answer should be E.
Answer: (E) e) 2x minutes
Question: If the average marks of three batches of 58, 60 and 45 students respectively is 50, 55, 60, then the
average marks of all the students is
(A) 54.48
(B) 54.68
(C) 54.6
(D) 54.58
(E) None of these
Rationale: Explanation:
(58Ã—50)+(60Ã—55)+(45Ã—60)/(55+60+45)=54.60
Answer: Option C
Answer: (C) 54.6
Question: The sequence of numbers a1, a2, a3, ..., an is defined by an = 1/n - 1/(n+2) for each integer n >= 1. What is the sum of the first 60 terms of this sequence?
(A) (1+1/2)/ (1/51 +1/ 52)
(B) (1+1/2) – (1/61 +1/ 62)
(C) (1+1/2)* (1/51 +1/ 52)
(D) (1+1/2) + (1/51 +1/ 52)
(E) (1/51 +1/ 52)
Rationale: The answer would most certainly be[B]. But the question needs a slight modification.n>=1, since the answer does consider a1 under the sum.
The sequence is :
a1 = 1-1/3
a2 = 1/2 - 1/4
a3 = 1/3 - 1/5....
We can observe that the third term in the sequence cancels the negative term in the first. A similar approach can be seen on all the terms and we would be left with 1 + 1/2 from a1 and a2 along with -1/62 and -1/61 from a60 and a59 term which could not be cancelled.
Hence the sum = (1+1/2) – (1/61 +1/ 62)
Answer : B
Answer: (B) (1+1/2) – (1/61 +1/ 62)
Question: 5.511/10.02 =
(A)  0.35
(B)  0.55
(C)  0.3509
(D)  0.351
(E)  0.3527
Rationale: 5.511 / 10.02
5511 / 1002 = 5.5
move the comma two places to the left as we have 2 decimal places from the divisor: 0.55. Answer: B
Answer: (B)  0.55
Question: The radius of a semi circle is 6.3 cm then its perimeter is?
(A) 32.7
(B) 32.4
(C) 22.4
(D) 32.8
(E) 32.1
Rationale: 36/7 r = 6.3 = 32.4
Answer:B
Answer: (B) 32.4
Question: A certain elevator has a safe weight limit of 2,000 pounds. What is the greatest possible number of people who can safely ride on the elevator at one time with the average (arithmetic mean) weight of half the riders being 200 pounds and the average weight of the others being 230 pounds?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
Rationale: Lets assume there are 2X people.
Half of them have average weight of 200 and other half has 230.
Maximum Weight is = 2000
So 200*X + 230*X = 2000
=> 430X = 2000
=> X is approximately equal to 5.
So total people is 2*5 = 10
We are not taking 10 as answer because say 10th person has minimum of 200 weight then
200*5 + 230*5 = 2150 (Which is more than 2000)
Answer C.
Answer: (C) 9
Question: A manufacturer of chocolates makes 6 different flavors of chocolates. The chocolates are sold in boxes of 10. How many “different” boxes of chocolates can be made?
(A) 22
(B) 27
(C) 99
(D) 2712
(E) 211
Rationale: Answer:C
Answer: (C) 99
Question: A train 360 m long runs with a speed of 45 km/hr. What time will it take to pass a platform of 240 m long?
(A) 38 sec
(B) 35 sec
(C) 44 sec
(D) 48 sec
(E) 50 sec
Rationale: Explanation:
Speed = 45 km/hr = 45×(10/36) m/s
= 150/12 = 50/4 = 25/2 m/s
Total distance = length of the train + length of the platform
= 360 + 240 = 600 meter
Time taken to cross the platform = 600/(25/2) = 600×2/25 = 48 seconds
Answer: Option D
Answer: (D) 48 sec
Question: A man sells two articles for Rs.3600 each and he gains 30% on the first and loses 30% on the next. Find his total gain or loss?
(A) 9 % loss
(B) 10% gain
(C) 450
(D) 12% loss
(E) 12% gain
Rationale: (30*30)/100 = 9%loss
ANSWER A
Answer: (A) 9 % loss
Question: A fires 5 shots to B's 3 but A kills only once in 3 shots while B kills once in 2 shots. When B has missed 27 times, A has killed:
(A) 30
(B) 50
(C) 5
(D) 40
(E) 20
Rationale: Let the total number of shots be x. Then,
Shots fired by A = 5/8x
Shots fired by B = 3/8x
Killing shots by A = 1/3 of 5/8x = 5/24x
Shots missed by B = 1/2 of 3/8x = 3/16x
Therefore, 3x/16 = 27 or x = (27 x 16/3)= 144.
Birds killed by A = 5x/24 = (5/24 x 144)= 30.
Answer is A.
Answer: (A) 30
Question: Akshay buys a motorcycle for Rs.25000. If he decides to sell the motorcycle for a profit of 7%, find the selling price.
(A) 27000
(B) 26750
(C) 26000
(D) 25750
(E) None of these
Rationale: Explanation:
Profit = %profit/100 * cost price
P = 7/100 * 25000 = 1750.
Selling price = cost price + profit
= 25000 + 1750
= Rs.26750
ANSWER B
Answer: (B) 26750
Question: Which number replace question mark in the series?
16 8 40 20 100 50 250 ? 625
(A) 254
(B) 125
(C) 354
(D) 199
(E) 540
Rationale: Explanation: (alternate series of /2 and &5)
16/2 = 8
8 * 5 = 40
40/2 = 20
20 * 5 = 100
100/2 = 50
50 * 5 = 250
250/2 = 125
125 * 5 = 625
correct answer is B)125
Answer: (B) 125
Question: 2 is what percent of 50
(A) 2%
(B) 4%
(C) 6%
(D) 8%
(E) 10%
Rationale: Explanation:
2/50 * 100 = 1/25 * 100 = 4 %
Answer: Option B
Answer: (B) 4%
Question: Charges made by two companies for the same A/C
Company XCompany Y
Price$575$530
Surcharge as a Percent of Price4%3%
Installation Charge$82.50$93.00
The table above shows the various charges made by two companies for the same air conditioner. What is the total amount that can be saved on the purchase and installation of the air conditioner by dealing with the company that offers the lower total charge?
(A) $41.60
(B) $45.00
(C) $50.75
(D) $55.75
(E) $61.25
Rationale: Looking at the values / percentage, its clear that Company X costlier than Company Y
Just observed the OA; they have 4 distinct numbers after decimal point
Total calculation of company x gives.00 + .00 + .50 = .50at the decimal
Total calculation of company y gives.00 + .90 + .00 = .90at the decimal
There difference provides .60 at the decimal; only 41.60 fits in
Answer = A
Answer: (A) $41.60
Question: A work which could be finished in 9 days was finished 3 days earlier after 10 more men joined. The number of men employed was?
(A) 86
(B) 20
(C) 78
(D) 27
(E) 28
Rationale: x ------- 9
(x + 10) ---- 6
x * 9 = (x + 10)6
x = 20
Answer:B
Answer: (B) 20
Question: In an election only two candidates contested. A candidate secured 70% of the valid votes and won by a majority of 188 votes. Find the total number of valid votes?
(A) 430
(B) 438
(C) 436
(D) 470
(E) 422
Rationale: Let the total number of valid votes be x.
70% of x = 70/100 * x = 7x/10
Number of votes secured by the other candidate = x - 7x/100 = 3x/10
Given, 7x/10 - 3x/10 = 188 => 4x/10 = 188
=> 4x = 1880 => x = 470.
Answer:D
Answer: (D) 470
Question: Joe had $525,420 in his bank account but he donated 7% of it to charity. How much does Joe have in his bank account now?
(A) $588,660.60
(B) $488,640.60
(C) $488,600.60
(D) $478,640.60
(E) $348,660.60
Rationale: Multiplier representing 7% = 7/100
= 7/100
= 0.07
Percentage of money donated = 525,420 x 0.07
= 525,420 x 0.07
= 36,779.40
Now, we need to calculate how much is 36,779.40 subtracted from 525,420.
=> 525,420-36,779.40 = 488,640.60
B
Answer: (B) $488,640.60
Question: If n > 2, then the sum, S, of the integers from 1 through n can be calculated by the following formula: S = n(n + 1)/2. Which one of the following statements about S must be true?
(A) S is always odd.
(B) S is always even.
(C) S must be a prime number
(D) S must not be a prime number
(E) S must be a perfect square
Rationale: If n > 2, then the sum, S, of the integers from 1 through n can be calculated by the following formula: S = n(n + 1)/2. Which one of the following statements about S must be true?
A. S is always odd.
B. S is always even.
C. S must be a prime number
D. S must not be a prime number
E. S must be a perfect square
Notice that we are askedwhich of the following MUST be true, not COULD be true. For such kind of questionsif you can prove that a statement is NOT truefor one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer.
A. S is always odd --> not necessarily true if n=3 then 1+2+3=6=even.
B. S is always even --> not necessarily true if n=5 then 1+2+3+4+5=15=odd.
C. S must be a prime number --> not true if n=3 then 1+2+3=6=not prime.
E. S must be a perfect square --> not necessarily true if n=3 then 1+2+3=6=not a perfect square.
Only choice D is left.
Answer: D.
Answer: (D) S must not be a prime number
Question: If 4x+y+z=80, 2x-y-z=400,3x+y-z = 20 for integers of x,y and z, find x =?
(A) 10
(B) 20
(C) 15
(D) 26
(E) 18
Rationale: 4x+y+z = 80----------1)
2x-y-z = 40-------------2)
3x+y-z = 20 ------------3)
from 1) and 2)
6x = 120
x = 20
Answer is B
Answer: (B) 20
Question: A man has Rs. 480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has?
(A) 90
(B) 70
(C) 50
(D) 80
(E) 60
Rationale: Let number of notes of each denomination be x.
Then x + 5x + 10x = 480
16x = 480
x = 30.
Hence, total number of notes = 3x = 90.
Answer is A.
Answer: (A) 90
Question: A reading list for a certain course consists of 10 books, of which 6 are poems and the rest are novels. Each student is required to read a selection of 4 books from the list, including at most 2 novels. How many selections of 4 books satisfy the requirements?
(A) 90
(B) 125
(C) 130
(D) 144
(E) 195
Rationale: Ans: B
Solution: Selection requires at most 2 novels, means=
0N4P + 1N3P + 2N2P
4c0*6c4+ 4c1*6c3 + 4c2*6c2
= 15+ 20 + 90
= 125
Ans: B
Answer: (B) 125
Question: A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec. What is the length of the platform?
(A) 288
(B) 350
(C) 277
(D) 2651
(E) 212
Rationale: Speed = 300/18 = 50/3 m/sec.
Let the length of the platform be x meters.
Then, (x + 300)/39 = 50/3
3x + 900 = 1950 => x = 350 m.
Answer: B
Answer: (B) 350
Question: Tough and Tricky questions: Functions. Let a be a positive integer. Let n#a equal n^(2a) if a is odd and n^(a) if a is even. Then (2#3) + (3#2) – (3#3) is equal to
(A) 64
(B) -656
(C) 128
(D) 512
(E) 1522
Rationale: Answer:
2^6 + 3^2 - 3^6 = 2^6 = -656
ANs B
Answer: (B) -656
Question: Priya covers journey from kavali to nellore by car at average speed of 70 Km/hr. She returns back by scooty with an average speed of 20 Km/hr. Find her average speed during the whole journey?
(A) 30Km/hr
(B) 31.11Km/hr
(C) 35Km/hr
(D) 40Km/hr
(E) 45km/hr
Rationale: Explanation:
Average speed = 2 xy/x+y
= 2*70*20/110
= 31.11 Km/hr
Answer: Option B
Answer: (B) 31.11Km/hr