divelab/Sys2Bench huggingface dataset:
Question: If 5 people undertook a piece of construction work and finished half the job in 15 days. If two people drop out, then the job will be completed in?
Options:
A)8 days
B)10 days
C)18 days
D)20 days
E)25 days
Rationale: That is, half the work done = 5 × 15 × ½
Then, 5 × 15 × ½ = 3 × ? ×1/2
i.e. 5 × 15 = 3 × ?
therefore, ? (No. days required) = 5 × 15/3 = 25 days.
E)
Answer: E
Question: A firm is comprised of partners and associates in a ratio of 2:63. If 50 more associates were hired, the ratio of partners to associates would be 1:34. How many partners are currently in the firm?
Options:
A)5
B)10
C)12
D)20
E)25
Rationale: The ratio 1:34 = 2:68 so the ratio changed from 2:63 to 2:68.
68-63 = 5 which is 1/10 of the increase in 50 associates.
The ratio changed from 20:630 to 20:680.
Thus the number of partners is 20.
The answer is D.
Answer: D
Question: Simple interest on a certain sum is 16.2 over 20 of the sum. Find the rate per cent and time, if both are equal.
Options:
A)8% and 8 years
B)6% and 6 years
C)9% and 9 years
D)12 % and 12 years
E)None of these
Rationale: 16.2â„20 P = PÃ—RÃ—R/100
â‡’ R2 = 1620â„20 â‡’81=> R = 9%
Also, time = 9 years
Answer C
Answer: C
Question: A certain Social Security recipient will receive an annual benefit of $12,000 provided he has annual earnings of $9,360 or less, but the benefit will be reduced by $1 for every $3 of annual earnings over $9,360. What amount of total annual earnings would result in a 55 percent reduction in the recipient's annual Social Security benefit? (Assume Social Security benefits are not counted as part of annual earnings.)
Options:
A)$15,360
B)$17,360
C)$25,560
D)$21,360
E)$27,360
Rationale: For every $3 earn above $9360, the recipient loses $1 of benefit.
OR
For every $1 loss in the benefit, the recipient earns $3 above $9360
If earning is; 9360+3x
Benefit = 12000-x
Or the vice versa
If benefit is 12000-x, the earning becomes 9360+3x
He lost 50% of the benefit;
Benefit Received= 12000-0.55*12000 = 12000-6600
x=5400
Earning becomes 9360+3x=9360+3*5400=25560
Ans:C
Answer: C
Question: x and y are positive integers of T. If 1/x + 1/y < 2, which of the following must be true?
Options:
A) x + y > 4
B) xy>1
C) x/y + y/x < 1
D) (x - y)^2 > 0
E) None of the above
Rationale: Answer is B:
1/X + 1/Y < 2
The maximum value of 1/X is 1 because if X equals any other number greater than one it will be a fraction. The same is true with 1/Y.
So 1/X and 1/Y will always be less than 2 as long as both X and Y are not both equal to one at the same time.
Another way of putting it is:
X*Y>1.B
Answer: B
Question: If MANGO is written as 41576 and APPLE is written as 17735, then GRAPES would be written as:
Options:
A)7999340
B)7835610
C)7226710
D)7913350
E)7917510
Rationale: E
7917510
All letters whose position in the alphabet is below 10, are being represented by their position number.
All letters whose position is 10 or more, are being represented by their position number minus ten.
Therefore:
G is 7
R is 18-9=9
A is 1
P is 16-9=7
E is 5
S is 19-9=10
Answer: E
Question: A, B and C work on a task. To complete the task alone, B takes twice the time that A would take to complete the task alone and 1/4rd the time that C would take to complete the task alone. If B actually worked for half the number of days that A worked and 3/2 times the number of days that C worked, what proportion of the total work was completed by B?
Options:
A)1/3
B)2/9
C)9/49
D)16/81
E)1/6
Rationale: The first thing to notice is that A is faster than B and B is faster than C.
Since work is proportional to time, in 1 day lets say if A does 2 works, B does 1 work and C does 2/3rd of a work.
If A works for 2 days, B works for 1 day and C works for only 2/3 of the day.
Therefore total work done = (2*2) + (1*1) + (1/4*1/4) = 81/16
Proportion of work done by B = (1*1) / (81/16) = 16/81
Hence Answer D.
Answer: D
Question: If the positive integer N is a perfect square, which of the following must be true?
I. The number of distinct factors of N is odd.
II. The sum of the factors of N is odd.
III. The number of distinct prime factors of N is even.
Options:
A)I only
B)II only
C)I and II
D)I and III
E)I, II and III
Rationale: SOLN:
1. The number of distinct factors of a perfect square is ALWAYS ODD.
2. The sum of distinct factors of a perfect square is ALWAYS ODD.
3. A perfect square ALWAYS has an ODD number of Odd-factors, and EVEN number of Even-factors.
4. Perfect square always has even powers of its prime factors.
So I and II must be true.
ANSWER:C
Answer: C
Question: Two vessels P and Q contain 62.5% and 87.5% of alcohol respectively. If 2 litres from vessel P is mixed with 4 litres from vessel Q, the ratio of alcohol and water in the resulting mixture is?
Options:
A)19:2
B)18:3
C)19:1
D)19:5
E)19:4
Rationale: Quantity of alcohol in vessel P = 62.5/100 * 2 = 5/4 litres
Quantity of alcohol in vessel Q = 87.5/100 * 4 = 7/2 litres
Quantity of alcohol in the mixture formed = 5/4 + 7/2 = 19/4 = 4.75 litres
As 6 litres of mixture is formed, ratio of alcohol and water in the mixture formed = 4.75 : 1.25 = 19 : 5.
Answer:D
Answer: D
Question: Ram sold two bicycles, each for Rs.990. If he made 10% profit on the first and 10% loss on the second, what is the total cost of both bicycles?
Options:
A)Rs.2000
B)Rs.2029
C)Rs.2297
D)Rs.2020
E)Rs.2293
Rationale: (10*10)/100 = 1%loss
100 --- 99
? --- 1980 => Rs.2000
Answer: A
Answer: A
Question: A person borrowed Rs.500 at the rate of 5% per annum S.I what amount will he pays to clear the debts after 4 years?
Options:
A)300
B)700
C)500
D)800
E)600
Rationale: Explanation:500------>5*4=20%(500)=100500+100=600Answer: Option E
Answer: E
Question: Find the smallest number which should be multiplied with 1152 to make it a perfect square.
Options:
A)2
B)1
C)3
D)5
E)6
Rationale: 1152 = 2*2*2*2*2*2*2*3*3
Required smallest number = 2
2 is the smallest number which should be multiplied with 1152 to make it a perfect square.
ANSWER:A
Answer: A
Question: Two trains 140 m and 210 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?
Options:
A)12.6 sec
B)11.8 sec
C)27.7 sec
D)10.8 sec
E)17.8 sec
Rationale: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other = 140 + 210 = 350 m.
Required time = 350 * 9/250 =12.6 sec.
Answer: A
Answer: A
Question: How many integers are between 5 and 96/7, inclusive?
Options:
A)7
B)9
C)10
D)12
E)15
Rationale: 96/7 = 13.xx
We are not concerned about the exact value of 96/7 as we just need the integers.
Since the values are small, we can write down the integers.
The different integers between 5 and 96/7 would be 5, 6, 7, 8, 9, 10, 11, 12,13
Total number of integers = 9
Option B
Answer: B
Question: How many zeroes are there at the end of the number N, if N = 60! + 120! ?
Options:
A)12
B)14
C)16
D)18
E)20
Rationale: The number of zeroes at the end of 60! will be less than the number of zeroes at the end of 120!
Hence it is sufficient to calculate the number of zeroes at the end of 60!
The number of zeroes = [60/5] + [60/25] + [60/125] = 12 + 2 + 0 = 14
The answer is B.
Answer: B
Question: A pupil's marks were wrongly entered as 67 instead of 45. Due to that the average marks for the class got increased by half. The number of pupils in the class is :
Options:
A)30
B)80
C)44
D)25
E)26
Rationale: Let there be x pupils in the class.
Total increase in marks = (X*1/2) = X/2.
X/2 = (67 - 45)
=> X/2 = 22
=> X = 44.
ANSWER:C
Answer: C
Question: The distance between two cities A and B is 330 km. A train starts from A at 8 a.m. and travels towards B at 60 km/hr. Another train starts from B at 9 a.m. and travels towards A at
75 km/hr. At what time will they meet?
Options:
A)11 am.
B)12 a.m
C)10 a.m
D)9 a.m
E)8 a.m
Rationale: x hrs after 8 am
train 1 starting from A travel x hours till the trains meet
dist travelled by train 1 in x hrs = 60x km
train 2 starting from B, travels (x-1) hrs
distance travelled by train 2 in(x-1) hrs = 75(x-1) km
total dist travelled = dist travelled by train 1 + dist travelled by train 2
=>330 = 60x+75(x-1)
12x+15(x-1) = 66
12x+15x-15 =66
27x=66+15=81
3x=9=>x=3
hence 3 hrs after 8 am =>11 am
ANSWER A
Answer: A
Question: The average of 13 numbers is 60. Average of the first 6 of them is 57 and that of the last 8 is 61. Find the 8th number?
Options:
A)46
B)48
C)50
D)52
E)54
Rationale: Sum of all the 13 numbers = 13 * 60 = 780
Sum of the first 6 of them = 6 * 57 = 342
Sum of the last 8 of them = 8 * 61 = 488
So, the 8th number = 342 + 488 - 780 = 50.
ANSWER:C
Answer: C
Question: A bag marked at Rs. 80 is sold for Rs. 68. The rate of discount is :
Options:
A)12 %
B)13 %
C)15 %
D)18 %
E)19 %
Rationale: Sol.
Rate of discount = [12/80 * 100] % = 15%.
Answer C
Answer: C
Question: A corporation triples its annual bonus to 50 of its employees. What percent Q of the employees’ new bonus is the increase?
Options:
A)50%
B)662⁄3%
C)100%
D)200%
E)300%
Rationale: Q of the employees’ new bonus is the increase Hence B.
Answer: B
Question: One-sixth of the attendees at a certain convention are female students, two-thirds of the attendees are female, and one-third of the attendees are students. If 200 of the attendees are neither female nor students, what is the total number of attendees at the convention?
Options:
A)600
B)300
C)1200
D)900
E)1000
Rationale: Let no. of Attendee are A.
Now As per the condition of the problem stated above .
We have following population in the convention as Attendee.
Total no. of females = [2/3]*A
Total no. of females as student : [1/6]*A
Total no. of students = [1/3]*A
Total no. of male as student = [1/6]*A
Total no. of males = A - [2/3]*A = [1/3]A
No. of males which are not student = [1/3]A - [1/6]*A = 200
Hence A = 1200
Total no of males who are not student will be the answer as it states it should be neither female nor student
So Answer is C
Answer: C
Question: if price of t.v set is reduced by 22%, then its sale increases by 86%, find net effect on sale value
Options:
A)44
B)45
C)46
D)47
E)48
Rationale: - a + b + ((-a)(b)/100)
= -22+86+(-22*86)/100
= -22+86-19
=45
ANSWER:B
Answer: B
Question: A person can row at 9 kmph and still water. He takes 4 1/2 hours to row from A to B and back. What is the distance between A and B if the speed of the stream is 1 kmph?
Options:
A)55 km
B)20 km
C)77 km
D)34 km
E)22 km
Rationale: Let the distance between A and B be x km.
Total time = x/(9 + 1) + x/(9 - 1) = 4.5
=> x/10 + x/8 = 9/2 => (4x + 5x)/40 = 9/2 => x = 20 km.
Answer: B
Answer: B
Question: How many three letter words are formed using the letters of the word TIME?
Options:
A)16
B)86
C)12
D)24
E)27
Rationale: The number of letters in the given word is four.
The number of three letter words that can be formed using these four letters is 4P3
= 4 * 3 * 2 = 24.
Answer:D
Answer: D
Question: The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, then the weight of B is:
Options:
A)17
B)20
C)26
D)31
E)NONE OF THESE
Rationale: Explanation:
Let A, B, C represent their respective weights. Then, we have:
A + B + C = (45 x 3) = 135 .... (i)
A + B = (40 x 2) = 80 .... (ii)
B + C = (43 x 2) = 86 ....(iii)
Adding (ii) and (iii), we get: A + 2B + C = 166 .... (iv)
Subtracting (i) from (iv), we get : B = 31.
B's weight = 31 kg.
ANSWER: D
Answer: D
Question: The dimensions of a rectangular solid are 6 inches, 5 inches, and 8 inches. If a cube, a side of which is equal to one of the dimensions of the rectangular solid, is placed entirely within thespherejust large enough to hold the cube, what the ratio of the volume of the cube to the volume within thespherethat is not occupied by the cube?
Options:
A) 10:17
B) 2:5
C) 5:16
D) 10:19
E) 32:25
Rationale: Answer: D.
Answer: D
Question: The average of 6 no.'s is 3.95. The average of 2of them is 4.2, while the average of theother 2 is 3.85. What is the average of the remaining 2 no's?
Options:
A)4.2
B)4.4
C)4.6
D)3.8
E)5.7
Rationale: Sum of the remaining two numbers = (3.95 * 6) - [(4.2 * 2) + (3.85 * 2)]
=7.60.
Required average = (7.6 / 2) = 3.8.
D
Answer: D
Question: A charitable association sold an average of 66 raffle tickets per member. Among the female members, the average was 70 raffle tickets. The male to female ratio of the association is 1:2. What was the average number W of tickets sold by the male members of the association
Options:
A)50
B)56
C)58
D)62
E)66
Rationale: Given that, Total average W sold is 66, Male/Female = 1/2 and Female average is 70. Average of Male members isX.
(70*F+X*M)/(M+F) = 66 -> Solving this equation after substituting 2M=F, X = 58. ANS C.
Answer: C
Question: A metallic sphere of radius 12 cm is melted and drawn into a wire, whose radius of cross section is 16 cm. What is the length of the wire?
Options:
A)8 cm
B)5 cm
C)4 cm
D)2 cm
E)9 cm
Rationale: Volume of the wire (in Cylindrical shape) is equal to the volume of the sphere.
π(16)2 * h
= (4/3)π (12)3
=> h = 9 cm
Answer:E
Answer: E
Question: In a village there are 150 men and 90 women in present time.if in next year population will be P=(a^2 +b^2)^1/2 , and in every year men are reduces 6%.what is population of after 2 year.
Options:
A)140
B)141
C)142
D)143
E)145
Rationale: next year total population=[150^2+90^2]^.5=174.92=175
man decreased by 6% so total man =150*.94=141
women will be= 175-141=34
so population after two years= [135^2+34^2]^.5=145.04=145
so population after two year= 145
ANSWER:E
Answer: E
Question: If the price of 23 toys is 276, then what will the price of 12 toys ?
Options:
A)144
B)361
C)117
D)287
E)112
Rationale: Explanation:
Less toys, Less Price (Direct Proportion)
So, let the price be Rs. x
then,
23:12::276:x => x=(276*12)/23
=> x=144
So price of 12 toys will be Rs. 144
Answer: A
Answer: A
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%?
Options:
A)228
B)144
C)268
D)277
E)299
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
Question: A can do a piece of work in 80 days. He works at it for 10 days & then B alone finishes the remaining work in 42 days. In how much time will A and B, working together, finish the work?
Options:
A)20 days
B)10 days
C)30 days
D)60 days
E)50 days
Rationale: Work done by A in 10 days=10/80=1/8
Remaining work=(1-(1/8))=7/8
Now, work will be done by B in 42 days.
Whole work will be done by B in (42*8/7)=48 days
Therefore, A's one day's work=1/80
B’s one day's work=1/48
(A+B)'s one day's work=1/80+1/48=8/240=1/30
Hence, both will finish the work in 30 days.
Answer : C.
Answer: C
Question: In a car wheel, twenty spokes cover 120 degrees. Then for the entire car,how many spokes are there?
Options:
A)240
B)340
C)440
D)540
E)640
Rationale: given, 20 spokes cover 120degrees,
so for 360 degrees.---->360*20/120=60..
so, for entire car, 4*60=240
ANSWER:A
Answer: A
Question: What is the sum of the greatest common factor and the lowest common multiple of 24 and 36?
Options:
A)92
B)84
C)24
D)60
E)184
Rationale: Prime factorization of 24 = 2 x 2 x 2 x 3
Prime factorization of 36 = 2 x 2 x 3 x 3
GCF = 12
LCM = 72
Sum = 84
Answer B.
Answer: B
Question: A question paper has two parts X and Y, each containing 10 questions. If a student wants to choose 8 from part X and 4 from part Y, in how many ways can he do that?
Options:
A)9450
B)1200
C)1500
D)8500
E)9500
Rationale: No of ways => 8 ques from X = 10C8
No of ways => 4 ques from part Y = 10C4
Total no of ways => 10c8*10c4==> 45 * 210
= 9450
ANSWER A
Answer: A
Question: If a radio is purchased for Rs 490 and sold for Rs 465.50 Find the loss%?
Options:
A)3%
B)4%
C)5 percent
D)6%
E)None of these
Rationale: Explanation :
Loss = 490 – 465.5 = 24.5 loss in % = 24.5/ 490 x 100 = 5%.
Answer : C
Answer: C
Question: Analyze the number square carefully and find out what number fits in place of question mark.
2	4	6
3	6	9
4	8	?
Options:
A)2
B)8
C)4
D)14
E)20
Rationale: 20 fits in place of question mark.
This is because (number in first column) / (number in second column) * 8 = number in third column.
Here (left number / middle number) * 8 = right number
(4 / 8) * 8 = (1 / 2) * 8 = 1 x 4= 4
C
Answer: C
Question: The cost to rent a small bus for a trip is x dollars, which is to be shared equally among the people taking the trip. If 10 people take the trip rather than 18, how many more dollars, in terms of x, will it cost per person?
Options:
A) x/6
B) x/16
C) x/40
D) 3x/40
E) 3x/80
Rationale: Choose x as a multiple of 16, I chose 64:
So for 10 people, that's 6.4 each and for 18 people it's 4 USD each... Pick one of the options that gives you 6.4 - 4 = 2.4... The answer is B.
Answer: B
Question: Expenditures of a Company (in Lakh Rupees) per Annum Over the given Years.
Year	Item of Expenditure
Salary	Fuel and Transport	Bonus	Interest on Loans	Taxes
1998	288	98	3.00	23.4	83
1999	342	112	2.52	32.5	108
2000	324	101	3.84	41.6	74
2001	336	133	3.68	36.4	88
2002	420	142	3.96	49.4	98
What is the average amount of interest per year which the company had to pay during this period?
Options:
A)Rs. 35 lakhs
B)Rs. 36.66 lakhs
C)Rs. 45.66 lakhs
D)Rs. 47 lakhs
E)Rs. 47.45 lakhs
Rationale: Average amount of interest paid by the Company during the given period
= Rs.	[	23.4 + 32.5 + 41.6 + 36.4 + 49.4	]	lakhs
5
= Rs.	[	183.3	]	lakhs
5
= Rs. 36.66 lakhs.
B)
Answer: B
Question: 8.008/2.002
Options:
A)0.004
B)0.04
C)4
D)40
E)400
Rationale: Answer is 4, move the decimal forward three places for both numerator and denominator or just multiply both by a thousand. The result is 8008/2002= 4
Answer C
Answer: C
Question: A man goes downstream at 10 kmph, and upstream8 kmph. The speed of the stream is
Options:
A)0kmph
B)4kmph
C)1kmph
D)2.5kmph
E)26kmph
Rationale: Speed of the stream = 1/2(10-8)kmph
=1kmph.
correct option :C
Answer: C
Question: The average marks of a class of 35 students is 40 and that of another class of 45 students is 60. Find the average marks of all the students?
Options:
A)52.6
B)52.4
C)52.1
D)51.2
E)52.9
Rationale: Sum of the marks for the class of 35 students = 35 * 40 = 1400
Sum of the marks for the class of 45 students = 45 * 60 = 2700
Sum of the marks for the class of 80 students =
1400 + 2700 = 4100
Average marks of all the students = 4100/80 = 51.2.Answer: D
Answer: D
Question: A sum of money is to be distributed among A, B, C, D in the proportion of
5 : 2 : 4 : 3. If C gets Rs. 2000 more than D, what is B's share?
Options:
A)Rs. 500
B)Rs. 1000
C)Rs. 4000
D)Rs. 2000
E)NOne
Rationale: Sol.
Let the shares of A, B, C and D be Rs. 5x, Rs. 2x, Rs. 4x and Rs. 3x respectively.
Then, 4x - 3x = 2000 ⇔ x = 2000.
∴ B's share = Rs. 2x= Rs. (2x2000) = Rs. 4000.
Answer C
Answer: C
Question: 375 metres long yard, 26 trees are palnted at equal distances, one tree being at each end of the yard. What is the distance between 2consecutive trees
Options:
A)10
B)12
C)14
D)16
E)15
Rationale: 26 trees have 25 gaps between them,
Required distance (375/25) = 15
E
Answer: E
Question: If a(a - 8) = 9 and b(b -8) = 9, where a ≠ b, then a + b =
Options:
A)−48
B)−2
C)8
D)9
E)48
Rationale: i.e. if a = -1 then b = 9
or if a =9 then b = -1
But in each case a+b = -1+9= 8
Answer: option C
Answer: C
Question: Mary decided to save a certain amount of her monthly salary each month and her salary was unchanged from month to month. If Mary's savings by the end of the year from these monthly savings were FOUR times the amount she spent per month, what should be the fraction of her salary that she spent each month?
Options:
A)1/4
B)3/4
C)1/2
D)1
E)5/4
Rationale: Saving = S, Expenditure = E, Income = I
At the end of 12months; 12S=4E=4(I-S)
=> 16S = 4I => Savings = 1/4 I
Hence Expenditure = 1-(1/4) = 3/4 I
Answer (B)
Answer: B
Question: A tourist purchased a total of $2,000 worth of traveler’s checks in $10 and $50 denominations, During the trip the tourist cashed 7 checks and then lost all of the rest. If the number of $10 checks cashed was one more or one less than the number of $50 checks cashed, what is the minimum possible value of the checks that were lost?
Options:
A)$1,430
B)$1,310
C)$1,290
D)$1,770
E)$1,150
Rationale: Let the number of $10 checks cashed beT
Let the number of $50 checks cashed beF
7 checks cashed;
T+F=7
Now; T can be F+1 OR T can be F-1
Let's check both conditions;
T=F+1
T+F=7
F+1+F=7
2F=6
F=3
T=4
Value cashed = 3*50+4*10=150+40=$190
Let's check the other condition as well;
T=F-1
T+F=7
F-1+F=7
2F=8
F=4
T=3
Value cashed = 4*50+3*10=200+30=$230
The more money he cashes, the less loss he incurs. Thus, we must consider the latter case.
Value cashed = $230
Value lost = 2000-230 = $1770
Ans:D
Answer: D
Question: If x, y, and z are three different prime numbers, which of the following is the smallest possible value of x + y + z?
Options:
A)10
B)12
C)14
D)16
E)18
Rationale: The sum of the three small smallest primes numbers is 2+3+5=10.
The answer is A.
Answer: A
Question: In the city of San Durango, 60 people own cats, dogs, or rabbits. If 30 people owned cats, 40 owned dogs, 10 owned rabbits, and 8 owned exactly two of the three types of pet, how many people owned all three?
Options:
A)2
B)4
C)6
D)12
E)32
Rationale: You are considering a case when cat dogs and rabbit are not exactly equal to 12 .
The solution shall be 60=30+40+10-8-2x
and hence x shall be 6
Answer C
Answer: C
Question: A man travels 100km by train at 60km/hr, 200km by ship at 20km/hr, 300km by aeroplane at 100km/hr and 100km by car at 50km/hr. What is the average speed for the entire distance?
Options:
A)35.3km/hr
B)42km/hr
C)48.9km/hr
D)52.6km/hr
E)27.6km/hr
Rationale: Total distance traveled = 100+200+300+100 = 700km
Total time taken = 100/60 + 200/20 + 300/100 + 100/50 = 16.67 hrs
Average speed = 700/16.67 = 42km/hr approximately ;
Answer is B
Answer: B
Question: It is being given that (5^32+1) is completely divisible by a whole number. Which of the following numbers is completely divisible by this number?
Options:
A)5^16+1
B)5^16-1
C)7*5^33
D)5^96+1
E)None
Rationale: Solution: Let 5^32=x.
Then (5^32+1)=(x+1). Let (x+1) be completely divisible by the whole number Y.
then (5^96+1)=[(5^32)^3+1]=>(x^3+1)=(x+1)(x^2-x+1) which is completely divisible by Y.
since (x+1) is divisible by Y.
Answer D
Answer: D
Question: For any positive integer n, the sum of the first n positive integers equals n(n+1)/2. What is the sum of all the even integers between 99 and 301?
Options:
A)10,100
B)20,200
C)22,650
D)40,200
E)45,150
Rationale: Firstly calculate the number of even integers between 99 and 301:
No of even integers = (300 - 100)/2 + 1 = 101
Avg of the even integers is (100+300)/2 = 200.
The sum would be = no of even integers * Avg.
==> 101*202 = 20,200
Answer B.
Answer: B
Question: A man cheats while buying as well as while selling. While buying he takes 10% more than what he pays for and while selling he gives 20% less than what he claims to. Find the profit percent, if he sells at 13% below the cost price of the claimed weight.
Options:
A)19.63%
B)20%
C)37.5%
D)25%
E)37.5%
Rationale: There is a one step calculation method too. It requires more thought but is faster.
The man takes 10% more than what he pays for. So if he claims to take 100 pounds, he pays $100 but he actually takes 110 pounds for which he will take from the customer $110. Hence, in effect, there is a 10% mark up.
While selling, he sells 20% less. This means, he claims to sell 100 pounds and gets $100 but actually sells only 80 pounds and should have got only $80 for it. So this is again a mark up of $20 on $80 which is 25%.
But he also sells at 13% less
(1 + m1%)(1 + m2%)(1 - d%) = (1 + p%)
11/10 * 5/4 * 87/100 = (1 + p%)
profit % = 19.63%
A
Answer: A
Question: How many numbers from 32 to 97 are exactly divisible by 9?
Options:
A)5
B)7
C)9
D)11
E)12
Rationale: Option 'B'
32/9 = 3 and 97/9 = 10 ==> 10 - 3 = 7 Numbers
Answer: B
Question: On dividing a number by 5, we get 3 as remainder. What will be the remainder when the square of this number is divided by 5 ?
Options:
A)0
B)1
C)3
D)4
E)2
Rationale: Let the number be x and on dividing x by 5, we get k as quotient and 3 as remainder.
x=5k+3
x^2=(5k+3)^2=(25k^2+30k+9)
=5(5k^2+6k+1)+4
on dividing x^2 by 5,we get 4 as remainder.
Answer is D
Answer: D