divelab/Sys2Bench huggingface dataset:
Question: How many numbers between 0 and 1670 have a prime tens digit and a prime units digit?
Options:
A)268
B)272
C)202
D)112
E)262
Rationale: There are 4 single digit prime numbers: 2, 3, 5 and 7. Hence, last two digits (tens and units) can take 4*4=16 different values: 22, 23, ..., 77.
So, in each hundred there are 16 such numbers. In 17 hundreds there will be 17*16=272 such numbers, but 4 out of them will be more than 1670, namely: 1672, 1673, 1675 and 1677. Which means that there are 272-4=268 numbers between 0 and 1670 which have a prime tens digit and a prime units digit.
Answer: A.
Answer: A
Question: If 'b' is a positive integer exactly divisible by 5 or 7 but not divisible by 11.What could possibly be the value of 'b' ?
Options:
A)55
B)35
C)77
D)110
E)165
Rationale: 55 and 77 are both divisible by 5 and 7 but also by 11. so they are not the right answer.
110 and 165 are both clearly not divisible by 7(not correct)
35 is both divisible by 5 and 7 but not by 11.
answer : (B) 35
Answer: B
Question: If x and y are non-zero integers, and 16x^4 – 4y^4 = 4x^2 + 2y^2, which of the following could be the value of x2 in terms of y?
Options:
A)2y^2
B)2y^2+3/4
C)2y^2+1/4
D)2y^2+1/2
E)2y^2+1/6
Rationale: 16x^4 – 4y^4 = 4x^2 + 2y^2
(4x^2 + 2y^2) (4x^2 - 2y^2) = 4x^2 + 2y^2
4x^2 - 2y^2 = 1
4x^2 = 2y^2+1
x^2 = 2y^2+1/4
Answer : C
Answer: C
Question: What sum of money will produce Rs.70 as simple interest in 4 years at 3 1/2 percent?
Options:
A)339
B)500
C)277
D)266
E)2812
Rationale: 70 = (P*4*7/2)/100
P = 500
Answer:B
Answer: B
Question: The average of first five prime numbers greater than 20 is?
Options:
A)32.5
B)32.0
C)32.4
D)32.2
E)32.8
Rationale: 23 + 29 + 31 + 37 + 41 = 161/5
= 32.2
Answer: D
Answer: D
Question: How long does a train 130 m long running at the speed of 80 km/hr takes to cross a bridge 140 m length?
Options:
A)13.9 sec
B)12.3 sec
C)17.9 sec
D)61.9 sec
E)47.98 sec
Rationale: Speed = 80 * 5/18 = 22 m/sec
Total distance covered = 130 + 140 = 270 m.
Required time = 270/22 = 12.3 sec.
Answer:B
Answer: B
Question: A case of 12 rolls of paper towels sells for $9. The cost of one roll sold individually is $1.What is the percent E of savings per roll for the 12-roll package over the cost of 12 rolls purchased individually?
Options:
A)9%
B)11%
C)15%
D)25%
E)90%
Rationale: Cost of 12 paper towels individually = 1*12=12
Cost of a set of 12 paper towels = 9
Cost of one roll = 9/12 = 3/4 = 0.75
Savings per roll = 1-.75 = 0.25
% of savings is E= .25/ 1 *100 = 25% D is the answer.
Answer: D
Question: On a sum of money, the S.I. for 2 years is $600, while the C.I. is $609, the rate of interest being the same in both the cases. The rate of interest is?
Options:
A)2%
B)3%
C)4%
D)5%
E)6%
Rationale: Difference in C.I. and S.I for 2 years = $609 - $600 = $9
S.I for one year = $300
S.I. on $300 for 1 year = $9
Rate = (100 * 9)/(300) = 3%
The answer is B.
Answer: B
Question: Positive integers indicated by x and y satisfy 3 1/x * y 2/5 = 13 3/4, the fractions being in their lowest terms, then x = ? and y = ?
Options:
A)x = 4, y = 8
B)x = 4, y = 4
C)x = 2, y = 4
D)x = 8, y = 4
E)None of these
Rationale: 3 1/x * y 2/5 = 13¾
=> (3x + 1) / x + (5y + 1) / 2 += 55 / 4
only choice (4) i.e x = 8 and y = 4 satisfies the given equation.
3 (1/8) * 4 (2/5) = (25 / 8 ) * (22 / 5) = 55/4 = 13¾
ANSWER:D
Answer: D
Question: There is a train and car. The ratio btw the speed of a train & a car is 16:15 respectively. Also, a bus covered a distance of 480km in 8h. The speed of the bus is 3/4th of the speed of the train. How much distance will the car cover in 6h?
Options:
A)410 km
B)420 km
C)460 km
D)430 km
E)450 km
Rationale: Sol. Speed of bus = 480/8 = 60km/ h
Speed of train = (60*4)/3=80 km / h
Speed of train : Speed of car = 16 : 15
Speed of car =80/16 * 15 = 75 km/ h
Distance covered by car in 6 hr = 75 × 6 = 450 km
E
Answer: E
Question: Paul purchased a house for Rs.46000 and a site for Rs.14000 respectively, if he sold the house for Rs.44000 and the site for Rs.20000, then find the resultant percentage of gain?
Options:
A)3.33%
B)4.44%
C)5.55%
D)6.66%
E)7.77%
Rationale: Sol.
Total CP = 60000 & total SP =64000 ⇒ gain = SP/CP = 64000/60000 = 1.0666 = 6.66%.
Answer D
Answer: D
Question: In an examination series, which consists of 5 exams, Arvind scored an average of 60 marks in
the first 3 exams and an average of 70 in the last 4 exams, what is the average score of
Arvind for the first and last two exams if his average scores of all the five exams are 65?
Options:
A)63.33
B)6
C)64
D)12
E)67.33
Rationale: let a,b,c,d,e be the five exams
(a+b+c+d+e)/5=65
a+b+c+d+e=325
first 3 exams avg is (a+b+c)/3=60
a+b+c=180
d+e=325-180=145
avg of last 4 exams is (b+c+d+e)/4=70
b+c+d+e=280
a=325-280=45
avg of first and last two exams are(a+d+e)/3=(45+145)/3=(190)/3=63.33
ANSWER:A
Answer: A
Question: A reduction of 25% in the price of oil enables a house wife to obtain 5kgs more for Rs.800, what is the reduced price for kg?
Options:
A)33
B)77
C)40
D)88
E)112
Rationale: 800*(25/100) = 200 ---- 5
? ---- 1 => Rs.40
Answer: C
Answer: C
Question: In how many ways can a committee of 7 people comprising at least 3 boys be formed using a group of 5 boys and 6 girls?
Options:
A)69
B)64
C)65
D)66
E)None of these
Rationale: There are 2 options: the selected groups have no girls or one girls.
-First case: 1 girl + 3 boys: 6C1 * 5C3 = 6*10 = 60
-Second case: 4 boys: 5C4 = 5
So there are 60 + 5 = 69 ways in total.
A
Answer: A
Question: A man can row with a speed of 10 kmph in still water. If the stream flows at 25 kmph, then the speed in downstream is?
Options:
A)10 kmph
B)35 kmph
C)20 kmph
D)22 kmph
E)25 kmph
Rationale: M = 10
S = 25
DS = 10 + 25 = 35
ANSWER:B
Answer: B
Question: A total of 3000 chocolates were distributed among 120 boys and girls such that each boy received 2 chocolates and each girl received 3 chocolates. Find the respective number of boys and girls?
Options:
A)32
B)60
C)27
D)29
E)21
Rationale: Let the number of boys be x.
Number of girls is 120 - x.
Total number of chocolates received by boys and girls = 2x + 3(120 - x) = 300
=> 360 - x = 300 => x = 60.
So, the number of boys or girls is 60.
Answer: B
Answer: B
Question: The time it took car P to travel 750 miles was 2 hours less than the time it took car R to travel the same distance. If car P’s average speed was 10 miles per hour greater than that of car R, what was car R’s average speed, in miles per hour?
Options:
A)40
B)56
C)60
D)70
E)80
Rationale: Let speed of car R be=x
Then speed of car P= x+10
A/Q,
(750/x)-(750/(x+10))=2
Solving for x=56 miles\hr.
B
Answer: B
Question: How many 2's are there between the terms 112 to 375?
Options:
A)156
B)157
C)158
D)159
E)160
Rationale: Let us calculate total 2's in the units place. (122, 132, 142 ... 192), (201, 212, 222, ... 292), (302, 312, ... 372) = 8 + 10 + 8 = 26
Total 2's in tenth's place, (120, 121, 122, ..., 129) + (220, 221, ..., 229) + (320, 321, ..., 329) = 30
Total 2's in hundred's place = (200, 201, ... 299) = 100.
Total 2's between 112 and 375 = 26 + 30 + 100 = 156
Answer:A
Answer: A
Question: If 12 men and 16 boys can do a piece of work in 5 days; 13 men and 24 boys can do it in 4 days, then the ratio of the daily work done by a man to that of a boy is?
Options:
A)2:1
B)2:98
C)2:2
D)2:9
E)2:4
Rationale: Let 1 man's 1 day work = x and 1 boy's 1 day work = y.
Then, 12x + 16y = 1/5 and 13x + 24y = 1/4
Solving these two equations, we get:
x = 1/100 and y = 1/200
Required ratio = x:y = 1/100 : 1/200 = 2:1.
Answer: A
Answer: A
Question: Plane leaves from Chelsea every 50 minutes from West Ham airport. Air hostess told Frank Lampard that the plane had left 25 minutes ago and the next plane for Chelsea will leave at 7:00 p.m.
At what time air hostess convey this information to Frank Lampard?
Options:
A)5:35 p.m
B)6:35 p.m
C)7:35 p.m
D)8:35 p.m
E)9:35 p.m
Rationale: Solution:
6:35 pm
Explanation:
Time of Frank Lampard last missed plane = 7:00 p.m - 50 min = 6:10 p.m
As this information has been given to Frank Lampard 15 minutes after the plane has already left, the air hostess gave the information at 6:10 p.m + 25 min = 6:35 p.m
Answer B
Answer: B
Question: Circular gears P and Q start rotating at the same time at constant speeds. Gear P makes 10 revolutions per minute and Gear Q makes 40 revolutions per minute. How many seconds after the gears start rotating will gear Q have made exactly 15 more revolutions than gear P?
Options:
A)12
B)15
C)20
D)24
E)30
Rationale: Gear Q makes 30 more revolutions each 60 seconds.
The time to make 15 = 30/2 more revolutions is 60/2 = 30 seconds.
The answer is E.
Answer: E
Question: A certain population of bacteria doubles every 10 minutes. If the number of bacteria in the population initially was 10^5, then what was the number in the population 1 hour later?
Options:
A)2(10^5)
B)6(10^5)
C)(2^6)(10^5)
D)(10^6)(10^5)
E)(10^5)^6
Rationale: x bacteria would become 2x in 10 mins, which would become 4x in the next 10 (total 20 mins)...
So in 60 mins x becomes 2^6 times into x
Therefore Answer is C, (2^6)(10^5)
Answer: C
Question: How many paying stones, each measuring 2 1/2 m * 2 m are required to pave a rectangular court yard 30 m long and 16 1/2 m board?
Options:
A)99
B)88
C)77
D)65
E)44
Rationale: 30 * 33/2 = 5/2 * 2 * x => x = 99
Answer: A
Answer: A
Question: Anil spends 40% of his income on rent, 30% of the remaining on medicines and 20% of the remaining on education. If he saves Rs. 840 every month, then find his monthly salary?
Options:
A)Rs. 1800
B)Rs. 2000
C)Rs. 2200
D)Rs. 2500
E)None of these
Rationale: Let's Anil's salary be Rs. 100.
Money spent on Rent = 40% of 100 = Rs. 40.
Money spent on medical grounds = 30% of (100 - 40) = 3/10 * 60 = Rs. 18.
Money spent on education = 20% of (60 - 18) = 1/5 * 42 = Rs. 8.40
Anil saves 100 - (40 + 18 + 8.40) i.e., Rs. 33.60
for 33.6 ---> 100 ; 840 ---> ?
Required salary = 840/33.6 * 100 = Rs. 2500
ANSWER:D
Answer: D
Question: The banker's discount on Rs.1800 at 4% per annum is equal to the true discount on Rs.1872 for the same time at the same rate. Find the time?
Options:
A)3 months
B)4 months
C)5 months
D)6 months
E)12 months
Rationale: Solution
S.I on Rs.1800 = T.D on Rs.1872.
P.W on Rs.1872 is Rs.1800.
Rs.72 is S.I on Rs. 1800 at 4%.
Time	=(100x72 / 4x1800)
= 1 year
= 12 months.
Answer E
Answer: E
Question: The ratio of men to women in a class is 4 to 3. If 4 men drop out of the class and the ratio of men to women after the drop out is 10 to 9, then how many women are currently in the class?
Options:
A)14
B)16
C)18
D)20
E)22
Rationale: Equation on the basis of question
4x-4/3x=10/9
x=6
Original number of men = 4*6=24
Original Number of Women = 3*6=18 (Answer)
Current number of men = 24-4=20
Current number of women = 18
Ratio = 20/18= 10/9 ( Just to verify)
Ans C
Answer: C
Question: A can do a piece of work in 10 hours; B and C together can do it in 9 hours, while A and C together can do it in 18 hours. How long will B alone take to do it?
Options:
A)5 5/4 hours
B)6 5/8 hours
C)15 8/6 hours
D)6 8/9 hours
E)6 6/14 hours
Rationale: A's 1 hour's work = 1/10 ;
(B + C)'s 1 hour's work = 1/9 ;
(B + C)'s 1 hour's work = 1/18
(A + B + C)'s 1 hour's work = (1/10 + 1/9) = 19/90
B's 1 hour's work = (19/90 - 1/18) = 14/90
B alone will take 90/14 hours to do the work.
=6 6/14
Answer = E
Answer: E
Question: Working together, Tim and Tom can type 12 pages in one hour. If they would be able to type 14 pages in one hour if Tom increases his typing speed by 25%, what is the ratio of Tom's normal typing speed to that of Tim?
Options:
A)2/1
B)1/2
C)1/3
D)4/1
E)1/4
Rationale: Lets say Tim types x pages an hour and Tom types y pages an hour.
We know that x+y=12
Tom increase speed by 25% means he will type 1.25y pages an hour.
So we get x+1.25y=14
We need to know the ratio of Tom's speed to Tim's speed. This is going to be proportional to the number of pages each can type in an hour, hence (y/x).
Subtracting both : 0.25y=2 so y=8 ... so x=4
(y/x)=8/4 =2/1
Answer is (A)
Answer: A
Question: A person got Rs.52 more when he invested a certain sum at compound interest instead of simple interest for two years at 7% p.a. Find the sum?
Options:
A)10612
B)11234
C)10678
D)2667
E)2671
Rationale: P = (d * 1002) / R2
=> (52 * 100 * 100) / 7 * 7 = Rs.10612
Answer:A
Answer: A
Question: Find the average of first 4 multiples of 11?
Options:
A)10
B)12.6
C)27.5
D)31.3
E)40.8
Rationale: average = (11+22+33+44)/4 = 27.5
Answer is C
Answer: C
Question: Of the science books in a certain supply room, 30 are on botany, 37 are on zoology, 90 are on physics, 50 are on geology, and 110 are on chemistry. If science books are removed randomly from the supply room, how many must be removed to ensure that 80 of the books removed are on the same area science?
Options:
A)81
B)121
C)164
D)225
E)276
Rationale: The worst case scenario is to remove all the books on botany, zoology, and geology.
Also we can remove 79 books each from physics and chemistry.
The total is 30 + 37 + 50 + 79 + 79 = 275.
The next book removed must either be physics or chemistry, ensuring 80 books in that subject.
The answer is E.
Answer: E
Question: A box contains 4 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are picked at random, what is the probability that they are either blue or red?
Options:
A)8/10
B)5/10
C)9/10
D)6/10
E)7/10
Rationale: Given that there are 4 blue marbles, 3 red marbles, 6 green marbles and 2 yellow marbles. Probability that both marbles are blue = 4Câ‚‚/Â¹âµCâ‚‚ = (3 * 2)/(15 * 14) = 2/35
Probability that both are red = 3Câ‚‚/Â¹âµCâ‚‚ = (1)/(15 * 14) = 1/35
Probability that one blue and other is red = (4Câ‚ * 3Câ‚)/Â¹âµCâ‚‚ = (4*2)/(15 * 14) = 4/35
Required probability = 2/35 + 1/35+ 4/35
= 7/10
Answer:E
Answer: E
Question: From a square piece of a paper having each side equal to 10 cm, the largest possible circle is being cut out. The ratio of the area of the circle to the area of the original square is nearly :
Options:
A)4⁄5
B)3⁄5
C)5⁄6
D)6⁄7
E)None of these
Rationale: Area of the square = (10)2 = 100 cm2
Area of the circle = 22⁄7 × (5)2 = 22×25/7
Required ratio = 22×25/7×100=22/28=11/14
= 0.785 ≈ 0.8 = 4⁄5
Answer A
Answer: A
Question: A shop owner sells 50mtr of cloth and gains SP of 10 mtrs. Find the gain %?
Options:
A)25%
B)40%
C)50%
D)60%
E)70%
Rationale: Here, selling price of 10 m cloth is obtained as profit.
Profit of 10 m cloth = (S.P. of 50 m cloth) – (C.P. of 50 m cloth)
Selling price of 40 m cloth = Selling Price of 50 m of cloth
Let cost of each metre be Rs. 100.
Therefore, cost price of 40 m cloth = Rs. 4000 and S.P. of 40 m cloth = Rs. Rs. 5000
Profit% = 10/40 × 100 = 25%
Profit of 25% was made by the merchant.
A
Answer: A
Question: If |m+5|−5 = m, which of the following must be true?
Options:
A)m = 0
B)m = −10
C)m is a multiple of 5.
D)m ≥ −5
E)|m+5| > 0
Rationale: Case 1 : |m+5| = 0, then m= -5
|-5+5|−5 = -5 --> true
Case 2; |m+5| < 0, then m< -5
|m+5|−5 = -m - 5 -5 = m , then m = -5 --> false
Case 3: Case 2; |m+5| > 0, then m> -5
|m+5|−5 = m+5 -5 = m , then m = m --> always true
Only case 1 and 3 satisfy the equation, so D is the answer.
Answer: D
Question: Each digit 1 through 5 is used exactly once to create a 5-digit integer. If the 1 and the 5 cannot be adjacent digits in the integer, how many 5-digit integers are possible?
Options:
A) 48
B) 66
C) 76
D) 78
E) None of these
Rationale: Number of arrangements using 5 distinct digits = 5!
Number of arrangements in which 1 and 5 are adjacent - consider 1 and 5 together as one group. Now you have 4 numbers/groups to arrange which can be done in 4! ways. In each of these arrangements, 1 and 5 can be arranged as 15 or 51.
Number of arrangements in which 3 and 4 are not adjacent = 5! - 2*4! = 72
Answer : E
Answer: E
Question: If 0 < m < 1 < n< 7, which of the following must be less than 1? I.m/n II. mn III. n - m
Options:
A)II,III only
B)I,III only
C)I only
D)III only
E)II only
Rationale: n > 1. So, option II, III is not possible.
So, Option I is correct.
Answer : C
Answer: C
Question: there are 6 elements and few are a ,b,c,d.find permutation and combination?
Options:
A)350,15
B)360,15
C)370,15
D)380,15
E)360,10
Rationale: 6p4 =3*4*5*6=360
6c4=15
ANSWER:B
Answer: B
Question: For which of the following does f(p)−f(q)=f(p−q) for all values of p and q?
Options:
A)f(a)=a^2
B)f(a)=a/2
C)f(a)=a+5
D)f(a)=2a−1
E)f(a)=|a|
Rationale: To solve this easiest way is just put the value and see that if it equals or not.
with option 1. f(p) = p^2 and f(q) = q^2
so L.H.S = p^2 - q^2
and R.H.S = (p-q)^2 ==> p^2 + q^2 -2pq.
so L.H.S not equal to R.H.S
with option 2. f(p) = p/2 and f(q) = q/2
L.H.S = p/2 - q/2 ==> 1/2(p-q)
R.H.S = (p-q)/2
so L.H.S = R.H.S which is the correct answer.
B
Answer: B
Question: A cyclist covers a distance of 750 meter in 2 minutes 30 seconds. What is the speed in km/hr of cyclist
Options:
A)16 km/hr
B)17 km/hr
C)18 km/hr
D)19 km/hr
E)None of these
Rationale: ExplanaƟon:
Speed=DistanceTimeDistance=750meterTime=2 min 30
sec=150secSpeed=750150=5m/sec=>5
∗
185km/hr=18km/hr
Answer: C
Answer: C
Question: The sum of the first k positive integers is equal to k(k+1)/2. What is the sum of the integers from a to b, inclusive, where 0<a<b?
Options:
A)b(b+1)/2 - (a+1)(a+2)/2
B)b(b+1)/2 - a(a+1)/2
C)b(b+1)/2 - (a-1)a/2
D)(b-1)b/2 - (a+1)(a+2)/2
E)(b-1)b/2 - a(a+1)/2
Rationale: Or try plug-in method: let b=4 and a=3 --> then b+a=7. Let see which option yields 7.
A. b(b+1)/2 - (a+1)(a+2)/2 = 10-10=0;
B. b(b+1)/2 - a(a+1)/2 = 10-6=4;
C. b(b+1)/2 - (a-1)a/2 = 10-3=7 --> OK;
D. (b-1)b/2 - (a+1)(a+2)/2 = 6-10=-4;
E. (b-1)b/2 - a(a+1)/2 = 6-6=0.
Answer: C.
Answer: C
Question: TATA company has four empty trucks that will head out in the morning, all four to the same destination. The clerk has four different boxes to ship to that same destination. All four boxes could go on any one of the trucks, or the boxes could be split up into any groupings and given to the trucks in any combinations (ie. two to one truck, one to another, and one to another). In how many different ways could the boxes be put on the four trucks?
Options:
A) 16
B) 64
C) 256
D) 576
E) 4096
Rationale: MAGOOSHOFFICIAL SOLUTION:
TATA company has four empty trucks that will head out in the morning, all four to the same destination. Where we put one box has absolutely no bearing on where we put any of the other boxes. The placement of the four boxes is completely independent of one another. For each box, we have four choices.
N = 4*4*4*4 = 16*16 = 256
Answer = (C)
Answer: C
Question: The average monthly salary of 20 employees in an organisation is Rs. 1500. If the manager's salary is added, then the average salary increases by Rs. 1000. What is the manager's monthly salary ?
Options:
A)Rs.16003
B)Rs.16029
C)Rs.22500
D)Rs.16108
E)Rs.16011
Rationale: Explanation:
Manager's monthly salary Rs. (2500 * 21 - 1500 * 20) = Rs.22500.
Answer: C
Answer: C
Question: A can do a piece of work in 10 days and B can do it in 15 days and C can do it 20 days. They started the work together and A leaves after 2 days and B leaves after 4 days from the beginning. How long will work lost?
Options:
A)10 2/8
B)10 2/9
C)10 2/3
D)10 2/2
E)10 2/1
Rationale: 2/10 + 4/15 + x/20 = 1
x = 32/3 = 10 2/3
Answer: C
Answer: C
Question: 76^77 /7
remainder is ?
Options:
A)5
B)6
C)7
D)8
E)9
Rationale: as, 4^3/3=64/3 remainder=1 and also 4/3=1
and 5^3/3 remainder=2 and also 5/3=2
so it does not matter on the power value
so the answer will be 76/7 remainder=6
ANSWER:B
Answer: B
Question: In a simultaneous throw of a pair of dice, find the probability of getting a total more than 11
Options:
A)11/25
B)7/12
C)5/13
D)5/12
E)6/17
Rationale: Total number of cases = 10*10 = 100
Favourable cases = [(2,10),(3,9),(3,10),(4,8),(4,9),(4,10),(5,7),(5,8),(5,9),(5,10),(6,6),(6,7),(6,8),(6,9),(6,10),(7,5),(7,6),(7,7),(7,8),(7,9),(7,10),(8,4),(8,5),(8,6),(8,7),(8,8),(8,9),(8,10),(9,3),(9,4),(9,5),(9,6),(9,7),(9,8),(9,10),(10,2),(10,3),(10,4),(10,5),(10,6),(10,7),(10,8),(10,9),(10,10)] = 44
So Probability = 44/100 = 11/25
Answer is A
Answer: A
Question: The compound ratio of 2/5, 6/7, 1/3 and 1/8 is given by?
Options:
A)7/98
B)1/70
C)1/98
D)1/96
E)1/68
Rationale: 2/5 * 6/7 * 1/3 * 1/8 = 12/840 = 1/70
ANSWER:B
Answer: B
Question: On a certain number line, there are 10 marks evenly spaced. If the fifth mark has a value equal to 2.3 and the tenth mark's value is equal to 3.8, then what is the value of the second mark?
Options:
A)0.3
B)1.1
C)1.4
D)1.5
E)1.7
Rationale: 5th Mark = 2.3
10th Mark = 3.8
Evenly spaced means we have 5 gaps of equal length between 5th and 10th mark.
So, Each gap distance = 3.8 - 2.3 /10 = 0.3
So, 2nd mark will be 2.3 - 3*0.3 = 1.4
Answer C.
Answer: C
Question: AMOUNT OF BACTERIA PRESENT
Time Amount
1:00 P.M. 20.0 grams
4:00 P.M. x grams
7:00 P.M. 24.4 grams
Data for a certain biology experiment are given in the table above. If the amount of bacteria present increased by the same fraction during each of the two 3-hour periods shown, how many grams of bacteria were present at 4:00 P.M.?
Options:
A)22.0
B)12.1
C)12.2
D)22.3
E)12.4
Rationale: The question says that bacteria increased by same fraction, not by same amount in 2 intervals of 3 hours.
Let X represent the amount of bacteria present at 4:00 PM. Since the fractional increase must remain constant from 1 to 4pm as it is from 4pm to 7pm:
Fractional increase from 1 PM to 4 PM = X / 20.0
Fractional increase from 4 PM to 7 PM = 24.4 / X
X \ 20 = 24.4 \ X
X^2 = 24.4 * 20
X^2 = 444
X = 22
answer : A
Answer: A
Question: Tourist purchased a total of 30 travelers checks in $50 and $100 denominations. The total worth of the travelers checks is $1800. How many checks of $50 denominations can he spend so that average amount (arithmetic mean) of the remaining travelers checks is $62.5?
Options:
A)6
B)12
C)15
D)20
E)24
Rationale: you could set-up a quick table and brute force the answer.
A	6	*	50	300 1800	-300	1500 24 62.50
B	16	*	50	600 1800	-600	1200 18 66.67
C	15	*	50	750 1800	-750	1050 15 70.00
D	20	*	50	1000 1800	-1000 800 10 80.00
E	24	*	50	1200 1800	-1200 600 6 100.00
Answer is A
Answer: A
Question: There are 15 cans in the refrigerator. 7 of them are red and 8 of them are blue. In how many ways we can remove 8 cans so that at least one red and at least one blue cans to remain the refrigerator.
Options:
A)460
B)490
C)493
D)455
E)445
Rationale: Answer: B.
Answer: B
Question: A thief steals at a car at 4.30 p.m. and drives it at 60 km/hr. The theft is discovered at 3 p.m. and the owner sets off in another car at 75 km/hr. When will he overtake the thief?
Options:
A)1 p.m
B)3 p.m
C)4 p.m
D)5 p.m
E)7 p.m
Rationale: E
7 p.m
Suppose the thief is overtaken x hrs after 4.30 p.m.
Then, distance covered by the owner in (x - 1/2) hrs.
60x = 75(x - 1/2) => x = 5/2 hrs.
So, the thief is overtaken at 7 p.m.
Answer: E
Question: The C.P of 16 books is equal to the S.P of 18 books. Find his gain% or loss%?
Options:
A)11 1/9%
B)16 2/8%
C)16 2/5%
D)16 2/1%
E)16 1/3%
Rationale: 16 CP = 18 SP
18 --- 2 CP loss
100 --- ? => 11 1/9% loss.Answer: A
Answer: A
Question: A person buys an article at Rs.480. At what price should he sell the article so as to make a profit of 24%?
Options:
A)595
B)882
C)772
D)662
E)521
Rationale: Cost price = Rs.480
profit = 24% of 480 = Rs.115
Selling price = Cost price + Profit
= 480 + 115 = 595
Answer: A
Answer: A
Question: A bag contains 12 white and 18 black balls. 2balls are drawn in succession. What is the probability that 1st is white and second is black?
Options:
A)12/123
B)36/145
C)13/115
D)1/213
E)2/231
Rationale: The probability that first ball is white:
=12C130C1=12C130C1
=1230=1230
=25=25
Since, the ball is not replaced; hence the number of balls left in bag is 29.
Hence, the probability the second ball is black:
=18C129C1=18C129C1
=1829=1829
Required probability,
=(25)×(1829)=(25)×(1829)
=36/145
B
Answer: B