divelab/Sys2Bench huggingface dataset:
Question: Three pieces of timber 36 m, 42 m and 54 m long have to be divided into planks of the same length, What is the greatest possible length of each plank ?
Options:
A)7 m
B)1 m
C)2 m
D)6 m
E)None of these
Rationale: Answer
Greatest possible length of each plank = H.C.F of 36, 42, 54 = 6 m
Correct Option: D
Answer: D
Question: A polygon has 54 diagonals. How many sides does it have?
Self made
Options:
A) 12
B) 13
C) 14
D) 15
E) 16
Rationale: The best way to solve this problem is to use the formula: An n sided polygon can have n*(n - 3)/2 diagonals
n*(n - 3)/2 = 54
n*(n - 3) = 108
Substitute n from the answer choices. n = 12
Answer: A
Answer: A
Question: A person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 30%?
Options:
A)650
B)882
C)772
D)652
E)271
Rationale: Cost price = Rs.500
profit = 30% of 500 = Rs.150
Selling price = Cost price + Profit
= 500 + 150 = 650
Answer:A
Answer: A
Question: Nitin’s salary is reduced by 10% and then reduced salary is increased by 10%. Find ,how many percentage his present salary is less as compared to his previous salary?
Options:
A)6%
B)8%
C)1%
D)2%
E)9%
Rationale: 10*10
-------- = 1%
100
Answer: C
Answer: C
Question: Jill, who lives in City C, plans to visit 5 different cities, M, L, S,N,and O. She plans to visit each city exactly once and return to City C after the 5 visits. She can visit the cities in any order. In how many different orders can she visit the 5 cities?
Options:
A) 3
B) 120
C) 8
D) 9
E) 12
Rationale: 5! = 120 =B
Answer: B
Question: A pair of articles was bought for $900 at a discount of 10%. What must be the marked price of each of the article?
Options:
A)$300
B)$500
C)$350
D)$400
E)$600
Rationale: S.P. of each of the article = 900/2 = $450
Let M.P = $x
90% of x = 450
x = 450*100/90 =$500
Answer is B
Answer: B
Question: Out of first 20 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is
Options:
A)17/29
B)17/25
C)17/21
D)17/20
E)17/23
Rationale: n(S) = 20
n(Even no) = 10 = n(E)
n(Prime no) = 8 = n(P)
P(EᴜP) = 10/20 + 8/20 - 1/20 = 17/20
Answer:D
Answer: D
Question: Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. If the faster train passes the slower train in 36 seconds,what is the length of each train?
Options:
A)88
B)70
C)62
D)50
E)54
Rationale: Explanation:
Assume the length of each train = x
Total distance covered for overtaking the slower train = x+x = 2x
Relative speed = 46-36 = 10km/hr = (10×10)/36 = 100/36 m/s
Time = 36 seconds
2x/ (100/36) = 36
=> (2x × 36 )/100 = 36
=> x = 50 meter
Answer: Option D
Answer: D
Question: What is the 4 digit number in which the 1st digit is 1/3 of the second, the 3rd is the sum of the 1st and 2nd, and the last is three times the second?
Options:
A)1243
B)1345
C)1349
D)1467
E)1500
Rationale: First digit is 1/3 second digit => The numbers can be 1 & 3, 2& 6, 3 & 9.
First + second = third => we can eliminate 3 & 9 since 3 + 9 = 12.
Last is 3 times the second => we can eliminate option 2 & 6 since 3 * 6 = 18.
Hence the number is 1349
C
Answer: C
Question: A man sells two articles for Rs.3640 each and he gains 25% on the first and loses 25% on the next. Find his total gain or loss?
Options:
A)9%loss
B)2%loss
C)6%loss
D)8%loss
E)1%loss
Rationale: Explanation:
(25*25)/100
= 6%loss
Answer:C
Answer: C
Question: A merchant marks his goods up by 40% and then offers a discount of 20% on the marked price. What % profit does the merchant make after the discount?
Options:
A)21%
B)25%
C)69%
D)31%
E)12%
Rationale: Let the price be 100.
The price becomes 140 after a 40% markup.
Now a discount of 20% on 140.
Profit=112-100
12%
answer E
Answer: E
Question: An athlete runs 200 metres race in 40 seconds. What is his speed?
Options:
A)23
B)38
C)18
D)30
E)28
Rationale: Speed=Distance/Time = 200/40 = 5 m/s = 5 * 18/5 = 3618 km/hr
Answer :C
Answer: C
Question: The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle?
Options:
A)10 cm
B)16 cm
C)18 cm
D)20 cm
E)22 cm
Rationale: 2(l + b)	=	5
b	1
2l + 2b = 5b
3b = 2l
b =	2	l
3
Then, Area = 216 cm2
l x b = 216
l x	2	l	= 216
3
l2 = 324
l = 18 cm.
C)
Answer: C
Question: How many seconds will a 500 meter long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
Options:
A)300
B)400
C)500
D)600
E)700
Rationale: Let length of tunnel is x meter
Distance = 800+x meter
Time = 1 minute = 60 seconds
Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s
Distance = Speed*Time
800+x = (65/3) * 60
800+x = 20 * 65 = 1300
x = 1300 - 800 = 500 meters
Answer: Option C
Answer: C
Question: Two pipes can fill a tank in 18 minutes and 15 minutes. An outlet pipe can empty the tank in 45 minutes. If all the pipes are opened when the tank is empty, then how many minutes will it take to fill the tank?
Options:
A)22
B)77
C)18
D)10
E)81
Rationale: Part of the filled by all the three pipes in one minute
= 1/18 + 1/15 - 1/45 = (5 + 6 - 2)/90 = 9/90 = 1/10
So, the tank becomes full in 10 minutes.
Answer:D
Answer: D
Question: Eric, Nick and Archi make contributions to the Society Of Nature Protection in the ratio of 5:3:2.5. If altogether they contribute 5145 Nis, how much more money does Nick contribute than Archi?
Options:
A)128 Nis
B)212 Nis
C)234 Nis
D)245 Nis
E)288 Nis
Rationale: Normalising the fraction from 5:3:2.5 to 10:6:5 (Eric: Nick:Archi)
Given Nick contributes one unit more than Archi and one unit of 5145/(10+6+5) = 245
Answer is D: 245 Nis
Answer: D
Question: Two trains of equal are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 sec. The length of each train is?
Options:
A)40
B)50
C)60
D)70
E)80
Rationale: Let the length of each train be x m.
Then, distance covered = 2x m.
Relative speed = 46 - 36 = 10 km/hr.
= 10 * 5/18 = 25/9 m/sec.
2x/36 = 25/9 => x = 50.
Answer: Option A
Answer: A
Question: At a certain diner, Joe ordered 3 doughnuts and a cup of coffee and was charged $ 2.25. Stella ordered 2 doughnuts and a cup of coffee and was charged $ 1.35. What is the price of 2 doughnuts?
Options:
A)$ 0.55
B)$ 1.00
C)$ 1.10
D)$ 1.30
E)$ 1.80
Rationale: 3D + C = 2.25......(1)
2D + C = 1.35........(2)
(1) - (2) --> D = 0.9 --> 2D = 1.8
Answer: E
Answer: E
Question: Jane makes toy bears. When she works with an assistant, she makes 80 percent more bears per week and works 10 percent fewer hours each week. Having an assistant increases Jane’s output of toy bears per hour by what percent T?
Options:
A)20%
B)80%
C)100%
D)180%
E)200%
Rationale: C.
Let's assume just Jane 40 bears per 40/hrs a week, so that is 1 bear/hr. With an assistant she makes 72 bears per 36 hours a week or 2 bears/hr ([40 bears * 1.8] / [40 hrs * .90]).
T=[(2 - 1)/1] * 100% = 100%.C
Answer: C
Question: O(x) represents the least odd integer greater than x, whereas o(x) represents the greatest odd integer less than x. Likewise, E(x) represents the least even integer greater than x, whereas e(x) represents the greatest even integer less than x. According to these definitions, the value of O(5.3) + E(–6.7) + o(–7.3) + e(6.6) is:
Options:
A)-4
B)-2
C)0
D)2
E)4
Rationale: O(5.3) + E(–6.7) + o(–7.3) + e(6.6) = 7 + (-6) + (-9) + 6 = -2
The answer is B.
Answer: B
Question: A and B started business in partnership investing Rs. 20,000 and Rs. 15,000 respectively. After six months, C joined them with Rs. 20,000. What will be B's share in the total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business?
Options:
A)7500
B)4366
C)2877
D)2768
E)26871
Rationale: A:B:C = (20000 * 24) : (15000 * 24) : (20000 * 18) = 4:3:3
B's share = 25000 * 3/10
= Rs. 7500.
Answer: A
Answer: A
Question: The area of a square field is 28808 sq m. How long will a lady take to cross the field diagonally at the rate of 7.2 km/hr?
Options:
A)2.5 min
B)3 min
C)2 min
D)4 min
E)4.5 min
Rationale: Area of a square field = 28808 sq m
Let the side of square = a
a^2 = 28808
=> a = 169.73
Diagonal = (2)^(1/2) * a
= 1.414 * 169.73
=240
Speed of lady = 7.2 km / hour
= 7200 m / hour
= 120 m / min
Time taken by lady to cross the field diagonally = 240/120 = 2 min
Answer C
Answer: C
Question: A rectangular table seats 7 people on each of two sides, with every person directly facing another person across the table. If 14 people choose their seats at random, what is probability that person P directly faces person Q?
Options:
A)1/10
B)1/11
C)1/12
D)1/13
E)1/14
Rationale: Person P will be seated somewhere at the table.
Each of the other 13 people has an equal chance of sitting opposite person P.
The probability that person Q sits across is 1/13.
The answer is D.
Answer: D
Question: A man & his wife appear in an interview for 2vacancies in the same post. The probability of husband's selection is 1/7 & the probability of wife's selection is 1/5. What is the probability that only 1 of them is selected ?
Options:
A)1/3
B)2/3
C)2/7
D)3/11
E)4/5
Rationale: Let A = Event that the husband is selected and
B = Event that the wife is selected.
Then, P (A) = 1/7
and P(B) = 1/5
∴P(A¯) = (1 - 17/5) = 6/7
and
= (1 - 1/5) = 4/5
Required probability = P [(A and not B) or (B and not A)]
= P[(A and B¯) or (B and A¯)]
= P(A and B¯) + P(B and A¯)
= P(A).P(B¯) + P(B).P(A¯)
= (1/7* 4/5) + (1/5* 6/7)
= 10/35
= 2/7
C
Answer: C
Question: If a, t, and c are consecutive even integers and a < t < c, all of the following must be divisible by 4 EXCEPT
Options:
A)a + c
B)t + c
C)ac
D)(bc)/2
E)(abc)/4
Rationale: I did get the correct answer within 80 seconds and it was not by luck either. I did not pick numbers but just used the concept stated by Ian.
The 3 numbers can be written as
a, (a + 2)(a + 4).
If 'a' is divisible by 4, then even 'c' or 'a + 4' is divisible by 4. However, is 'b' is divisible by 4, then both 'a' and 'a + 4' are still divisible by 2.
A - (a + c) = a + (a + 4) = 2a + 4 = 2(a + 2) = 2b. 2b will always be divisible by 4 even if 'b' is not divisible by 4. Reason: 'b' already has a prime factorization of at least a '2'. Hence '2b' has two 2s.
C - ac = a(a+4). If, as stated above, one of them is divisible by 4, then the product is divisible. If both of them are not divisible by 4, then the product is still divisible by 4 because of the presence of two 2s again in the prime factorization.
D - bc/2 = (a + 2)(a + 4)/2. Either b or c is divisible by 2. Hence, if we assume that b is divisible by 2 and not divisible by 4, then it leaves us just one possibility. Is c divisible by 4? It has to be because c is the next consecutive even integer.
E - atc/4 = a(a + 2)(a + 4)/4. One of these integers is divisible by 4 already. If we again assume 'b' to be that integer divisible by 4, then we are left with the question - Is a(a + 4) divisible by 4? This is the same as option C.
B - b + c = (a + 2) + (a + 4) = 2a + 6 = 2(a + 3). (a + 3) will never be divisible by 2 because it is an odd integer. Hence, 2(a + 3), although divisible by 2, will not be divisible by 4 because it has just one 2 in its prime factorization.
As a whole, whether you choose numbers (2, 46 being the easiest) or solve conceptually, the answer is still easily obtainable within 2 minutes.B
Answer: B
Question: The difference between a two digit number and the number obtained by interchanging the positions of its digit is 36. What is the difference between the two digits of that number?
Options:
A)3
B)4
C)9
D)8
E)7
Rationale: Let the ten’s digit be x
Unit’s digit be y
Then (10x+y)-(10y+x)=36
9(x-y)=36
x-y=4
Option B
Answer: B
Question: How many positive numbers not greater than 4300 can be formed using the digits 0,1,2,3,4 where repeatation is allowed?
Options:
A)576 numbers
B)575
C)620
D)640
E)660
Rationale: 1 digit = 5
2 digits = 4* 5 = 20
3 digits = 4*5*5= 100
Now,4 digit number till 4000 can have digits 1,2,3 in thousands place ( total choices = 3 )
0,1,2,3,4 in hundreds ,tens and ones place
I.e 3*5*5*5 = 375
Now From 4000 to 4299 = 1*3*5*5 =75
Total = 5+20+100+375+75+1 =576 (1 for 4300)
ANSWER:A
Answer: A
Question: A train crosses a platform of 200 m in 20 sec, same train crosses another platform of length 350 m in 25 sec. then find the length of the train?
Options:
A)150m
B)180m
C)400m
D)250m
E)155m
Rationale: Length of the train be ‘X’
X + 200/20 = X + 350/25
5X + 1000 = 4X + 1400
X = 400m
Answer:C
Answer: C
Question: The ratio of three numbers is 5:3:4 and their sum is 108. The second number of the three numbers is?
Options:
A)13
B)16
C)27
D)29
E)30
Rationale: 5:3:4
Total parts = 12
12 parts --> 108
1 part ---->9
The second number of the three numbers is = 3
3 parts ----> 27
C)
Answer: C
Question: A and B starts a business with Rs.8000 each, and after 4 months, B withdraws half of his capital . How should they share the profits at the end of the 16 months?
Options:
A)18:11
B)16:11
C)18:19
D)18:121
E)18:112
Rationale: A invests Rs.8000 for 16 months, but B invests Rs.8000 for the first 4 months and then withdraws Rs.4000. So, the investment of B for remaining 14 months is Rs.4000 only.
A : B
8000*16 : (8000*4) + (4000*14)
128000 : 88000
A:B = 16:11.Answer:B
Answer: B
Question: Worker A takes 10 hours to do a job. Worker B takes 12 hours to do the same job. How long it take both A & B, working together but independently, to do the same job?
Options:
A)40 days
B)40/9 days
C)60/11 days
D)30/9 days
E)60/9 days
Rationale: A's one hour work = 1/10.
B's one hour work = 1/12.
(A+B)'s one hour work = 1/10+1/12 = 11/60.
Both A & B can finish the work in 60/11 days
C
Answer: C
Question: The simple form of the ratio 4/2:2/5 is?
Options:
A)10:6
B)5:1
C)15:3
D)25:3
E)30:3
Rationale: 4/2 : 2/5 = 20:4 = 5:1
ANSWER:B
Answer: B
Question: What is the smallest no. which must be added to 8261955 so as to obtain a sum which is divisible by 11?
Options:
A)1
B)2
C)4
D)6
E)8
Rationale: For divisibility by 11, the difference of sums of digits at even and odd places must be either zero or divisible by 11.
For 8261955, Difference =(8+6+9+5) -(2+1+5)=28-8=20.
The units digit is at odd place. So we add 2 to the number
=> 8261955 +2 = 8261957
Now , (8+6+9+7) -(2+1+5)=30-8=22 => 22 is a multiple of 11 and hence 8261957 is also divisible by 11
B
Answer: B
Question: A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 700 m long?
Options:
A)94sec
B)90sec
C)85sec
D)80sec
E)76sec
Rationale: Speed = 240/24 = 10 m/sec.
Required time = (240 + 700)/10 = 94 sec.
Answer:A
Answer: A
Question: There are 5 cars to be displayed in 5 parking spaces with all the cars facing the same direction. Of the 5 cars, 3 are red, 1 is blue and 1 is yellow. If the cars are identical except for color, how many different display arrangements of the 5 cars are possible?
Options:
A)20
B)25
C)40
D)60
E)125
Rationale: I think the above logic is correct except one thing:
# of arrangements is 5!3!=205!3!=20.
But a car can be arranged facing TWO directions (within one particular parking space), so we should multiply 20 by 2, 20∗2=4020∗2=40
Answer: C.
Answer: C
Question: If w is 40 percent less than e, e is 40 percent less than y, and z is 46 percent less than y, then z is greater than w by what percent of w?
Options:
A)4%
B)18%
C)36%
D)40%
E)50%
Rationale: GIven w= 0.6e, e=0.6y, z=0.54y, substituting, w=2/3 Z----> z= 1.5w and thus z is 50% greater than w. E is the correct answer.
Answer: E
Question: Which of the following is NOT the sum of the squares of two integers?
Options:
A)36
B)37
C)65
D)146
E)147
Rationale: List the numbers that are smaller than the given options - 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144.
(A) 36 - 9+25. NO.
(B) 37 - 1+36. NO.
(C) 65 - 1+64. NO.
(D) 146 - 25+121. NO.
(E) - must be the answer.
ANSWER:E
Answer: E
Question: Which of the following cannot be the square of an integer
Options:
A)275625
B)385641
C)227529
D)261121
E)426408
Rationale: The square of an integer (n^2) can have only the following units digit:
0, if the units digit of n is 0;
1, if the units digit of n is 1 or 9;
4, if the units digit of n is 2 or 8.
5, if the units digit of n is 5;
6, if the units digit of n is 6 or 4;
9, if the units digit of n is 3 or 7.
As, you can see the square of an integer cannot have the units digit of 2, 3, 7, or 8.
Answer: E.
Answer: E
Question: Two cubes of their volumes in the ratio 64 : 125. The ratio of their surface area is:
Options:
A)1.5:5
B)2:5
C)3:5
D)1:5
E)4:5
Rationale: The ratio of their surface area is
64 : 125
4 : 5
Answer is E.
Answer: E
Question: Out of first 20 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is ?
Options:
A)17/26
B)17/29
C)17/24
D)17/20
E)17/21
Rationale: n(S) = 20
n(Even no) = 10 = n(E)
n(Prime no) = 8 = n(P)
P(EᴜP) = 10/20 + 8/20 - 1/20 = 17/20
Answer: D
Answer: D
Question: What is the banker's discount if the true discount on a bill of Rs.540 is Rs.90 ?
Options:
A)Rs. 108
B)Rs. 120
C)Rs. 102
D)Rs. 106
E)None of these
Rationale: Explanation :
Present Worth, PW = F - TD = 540 - 90 = Rs. 450
Simple Interest on the Present Worth = True Discount
Hence Simple Interest on 450 = 90 ------(Equation 1)
Simple Interest on the face value = Bankers Discount
=> Simple Interest on 540 = Bankers Discount
From Equation 1, Simple Interest on 450 = 90
Hence, Simple Interest on 540 = 90/450×540=540/5 = Rs. 108
=> Bankers Discount = Rs. 108 Answer : Option A
Answer: A
Question: In one year, the population, of a village increased by 10% and in the next year, it decreased by 10%. If at the end of 2nd year, the population was 7920, what was it in the beginning?
Options:
A)3337
B)8000
C)2788
D)2999
E)1121
Rationale: x*110/100 * 90/100 = 7920
X*0.99=7920
X=7920/0.99
=> 8000
Answer: B
Answer: B
Question: During a trip, Francine traveled x percent of the total distance at an average speed of 40 miles per hour and the rest of the distance at an average speed of 80 miles per hour. In terms of x, what was Francine's average speed for the entire trip?
Options:
A)(180-x)/2
B)4800/x+60
C)(300-x)/5
D)600/(115-x)
E)12,000/(x+200)
Rationale: total distance =100 ;total time = T
t1 = x/40 t2 = 100-x /80
T =t1+t2 = x/30 + 100-x/80 = (80x + 3000- 30x)/2400
= (50x+3000)/2400
= x +60 / 48
av speed = 100*48/x+60 = 4800/x+60
B
Answer: B
Question: The ratio between the present ages of P and Q is 6:7. If Q is 4 years old than P, what will be the ratio of the ages of P and Q after 4 years
Options:
A)7:8
B)7:9
C)3:8
D)5:8
E)6:8
Rationale: Explanation:
Let P age and Q age is 6x years and 7x years.
Then 7x - 6x = 4 <=> x = 4
So required ratio will be (6x+4): (7x+4) => 28:32 => 7:8
Answer: Option A
Answer: A
Question: Pipes A and B can fill a tank in 5 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in:
Options:
A)3 9 /17 hours
B)1 13 /17 hours
C)2 8 /11 hours
D)4 1 /2 hours
E)None of these
Rationale: Explanation:
Solution 1
Pipes A and B can fill the tank in 5 and 6 hours respectively. Therefore,
part filled by pipe A in 1 hour =1/5
part filled by pipe B in 1 hour =1/6
Pipe C can empty the tank in 12 hours. Therefore,
part emptied by pipe C in 1 hour =1/12
Net part filled by Pipes A,B,C together in 1 hour =1/5 +1/6+1/12 =17/60
i.e., the tank can be filled in 60/17=3 9/17 hours.
ANSWER IS A
Answer: A
Question: Simple interest on a certain sum is 9.8 over 20 of the sum. Find the rate per cent and time, if both are equal.
Options:
A)7% and 7 years
B)6% and 6 years
C)10% and 10 years
D)12 % and 12 years
E)None of these
Rationale: 9.8â„20 P = PÃ—RÃ—R/100
â‡’ R2 = 980â„20=49 â‡’ R = 7%
Also, time = 7 years
Answer A
Answer: A
Question: An businessman earns an income of Re 2 on the first day of his business. On every subsequent day, he earns an income which is just double of that made on the previous day. On the 20th day of business, he earns an income of:
Options:
A)21
B)22
C)36
D)20
E)30
Rationale: 2nd day he earns = 2(2 – 2)
3rd day he earns = 2(3 – 2)
On 20th day he earns 2(20 -2) = 36 rupees
ANSWER:C
Answer: C
Question: Walking 6/7th of his usual speed, a man is 12 minutes too late. The usual time taken by him to cover that distance is :
Options:
A)1 hr 20 min
B)1 hr 10 min
C)1 hr 11 min
D)1 hr 12 min
E)None
Rationale: Sol.
New speed = 6/7 of usual speed.
New time = 7/6 of usual time
∴ [7/6 of usual time] - (usual time) = 1/5 hr.
⇒ 1/6 of usual time = 1/5 hr ⇒ usual time = 6/5 hr = 1 hr 12 min.
Answer D
Answer: D
Question: Raju age after 25 years will be 5 times his age 5 years back, What is the present age of Raju
Options:
A)28
B)17
C)10.21
D)77
E)12.5
Rationale: Clearly,
x+25 = 5(x-5)
<=> 4x = 50 => x = 12.5
Answer:E
Answer: E
Question: What is the least integer that is a sum of four different prime numbers each greater than 10?
Options:
A)60
B)62
C)64
D)66
E)68
Rationale: The sum of the four smallest primes greater than 10 is 11+13+17+19=60.
The answer is A.
Answer: A
Question: At Company K, 15 percent of the employees are secretaries and 60 percent are salespeople. If there are 55 other employees of Company K, how many employees does Company K have?
Options:
A) 160
B) 180
C) 190
D) 200
E) 220
Rationale: Let the total number of employees in the company be x
% of secretaries = 15%
% of salespeople = 60%
% of of employees other than secretaries and salespeople = 100 - 75 = 25%
But this number is given as 55
so 25% of x = 55
x = 220
Therefore there a total of 220 employees in the company K
Correct answer - E
Answer: E
Question: If you divide 7^93 by 5, which remainder do you get?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: The units digit of 7^1 is 7.
The units digit of 7^2 is 9.
The units digit of 7^3 is 3.
The units digit of 7^4 is 1.
The units digit of 7^5 is 7.
etc...
The units digit of 7^n repeats in blocks of 4: {7, 9, 3, 1}
The remainder of 93/4 is 1.
So the units digit of 7^93 is 7.
The remainder of 7^93 / 5 is 2.
The answer is C.
Answer: C
Question: An athlete runs 200 meters race in 18sec. His speed is?
Options:
A)20km/hr
B)15km/hr
C)30km/hr
D)25km/hr
E)40km/hr
Rationale: speed = 200/18 = 100/9 m/sec
= 100/9 * 18/5 km/hr = 40km/hr
Answer is E
Answer: E
Question: The number of roots common between the two equations x3+3x2+4x+5=0x3+3x2+4x+5=0 and x3+2x2+7x+3=0x3+2x2+7x+3=0 is
Options:
A)22
B)27
C)13
D)88
E)21
Rationale: Here f(x) = x3+3x2+4x+5=0x3+3x2+4x+5=0 and g(x) = x3+2x2+7x+3=0x3+2x2+7x+3=0
To find the common roots we have to solve the equation f(x) - g(x) = 0
i.e. (x3+3x2+4x+5)(x3+3x2+4x+5) - (x3+2x2+7x+3)=0(x3+2x2+7x+3)=0
x2−3x+2=0x2−3x+2=0
x = 2, x = 1
These are the points of intersection f(x) and g(x). Whether these points are also the common root will have to be checked by putting these vales in f(x) = 0 and g(x) = 0.
For x = 2;
f(2) = g(2) = 43 ≠≠ 0. Hence 2 is not a common root but only a point of intersection.
For x = 1;
f(1) = g(1) = 13 ≠≠ 0. Again 1 is not a common root but a point of intersection. Hence, we find that the two equations do not have any common root between them.
Answer:C
Answer: C
Question: If a quality control check is made inspecting a sample of 2 light bulbs from a box of 8 lighbulbs, how many different samples can be chosen?
Options:
A)6
B)28
C)36
D)66
E)72
Rationale: Try using the formula for combinations:
n!/r!(n-r)!
8!/2!(8-2)!
8!/2!*6!
8*7/2*1
=28
B
Answer: B
Question: A boy want to make a cuboid of dimension 5m, 6m, 7m from small cubes of .04 m3. Later he realized he can make same cuboid by making it hollow. Then it takes some cubes less. What is the no. of these cubes?
Options:
A)2150
B)2250
C)2350
D)2850
E)3250
Rationale: volume of cuboid=5*6*7=210m3
volume of inner cuboid=(5-1)*(6-1)*(7-1)=120m3
therefore,volume of hollow cuboid=210-120=90 m3
no of cubes required=90/.04=2250 cubes
ANSWER:B
Answer: B
Question: If X,Y is 20%,25% greater than Z then how much percentage is X smaller than Y?
Options:
A)2
B)4
C)6
D)7
E)1
Rationale: X=120%
Y=125%
Z=100%
X-Y/Y*100 = 5/125*100
==>4%
ANSWER B
Answer: B