divelab/Sys2Bench huggingface dataset:
Question: A cistern 6m long and 4 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is:
Options:
A)49 m2
B)50 m2
C)53.5 m2
D)55 m2
E)58 m2
Rationale: Area of the wet surface	= [2(lb + bh + lh) - lb]
= 2(bh + lh) + lb
= [2 (4 x 1.25 + 6 x 1.25) + 6 x 4] m2
= 49 m2. Answer: Option A
Answer: A
Question: HCF of two numbers is 11 and the product of these numbers is 363, what is the the greater number?
Options:
A)28
B)31
C)33
D)35
E)38
Rationale: The numbers be 11a and 11b
11a × 11b = 363
ab = 3
co-primes with product 3 are (1, 3)
Hence the numbers with HCF 11 and product 363
= (11 × 1, 11 × 3)
= (11, 33)
Numbers are 11 and 33
The greater number = 33
Answer: C
Question: Sony and Johnny caught 25 fishes. Sony caught four times as many as Johnny. How many fishes did Johnny catch?
Options:
A)5
B)16
C)34
D)38
E)42
Rationale: s+j=25
s=4*j
j=5
ANSWER:A
Answer: A
Question: Which of the following is closer to (21!+20!)/(21!-20!)?
Options:
A)49
B)36
C)25
D)16
E)1
Rationale: Notice that 21! = (21)(20!), so we can factor out 20! from top and bottom.
(21!+20!)/(21!-20!)=[20!(21+1)]/[20!(21-1)]
= (21+1)/(20-1)
= 22/19
≈ 1
Answer: E
Answer: E
Question: if a@b = a * b^(1/2) then 2@16 = ?
self made
Options:
A)2
B)6
C)3
D)8
E)4
Rationale: 2* (16)^1/2= 2*4= 8
D is the answer
Answer: D
Question: If integers ending in zero are excluded, what is the unit digit of the product of the even integers from 802 to 898, inclusive?
Options:
A)14
B)12
C)10
D)6
E)8
Rationale: 802 x 804 x 806 x 808 => unit digit 4
812 x 814 x 816 x 818 => unit digit 4
892 x 894 x 896 x 898 => unit digit 4
So we have 10 numbers ending by 4 to multiply.
Given that 4 x 4 = 16, we have 5 numbers ending by 6 to multiply
Given that 6 x 6 = 36, we have 3 numbers ending by 6 to multiply
So the unit digit is 6
Answer : D
Answer: D
Question: Three 6 faced dice are thrown together. The probability that no two dice show the same number on them is ?
Options:
A)5/8
B)5/9
C)5/2
D)5/1
E)5/6
Rationale: No two dice show same number would mean all the three faces should show different numbers. The first can fall in any one of the six ways. The second die can show a different number in five ways. The third should show a number that is different from the first and second. This can happen in four ways.
Thus 6 * 5 * 4 = 120 favourable cases.
The total cases are 6 * 6 * 6 = 216.
The probability = 120/216 = 5/9.
Answer: B
Answer: B
Question: It is given that 2^32 + 1 is exactly divisible by a certain number. Which one of the following is also divisible by the same number W?
Options:
A)a. 2^96 + 1
B)b. 2^16 - 1
C)c. 2^16 + 1
D)d. 7 * 2^33
E)e. 2^64 + 1
Rationale: a³ + b³ =(a+b)(a² -ab +b²)
Now, let (2^32 + 1) be (a+b)
a³ + b³ = (2^96 + 1)
Now, as mentioned in formula above,
a³ + b³ is always divisible by (a+b)
So any factor of W (a+b) is a factor of (a³ + b³)
Henca A
Answer: A
Question: There are 20 students with an average height of 105 cms in a class. Then 10 students with an average height of 120 cms join the class. What will be the average height of the class now?
Options:
A)110 cms
B)120 cms
C)100 cms
D)115 cms
E)130 cms
Rationale: 20 students average height is 105cms
sum of heights/ 20 =105cms
sum of heights of 20 students= 105*20= 2100
10 students of average height 120 added
so their, sum of 10 students height / 10 = 120
sum of heights of 10 students = 1200cms
By adding heights of 20 and 10 students , 1200+2100 = 3300
average of 30 students = 3300/30 = 110 cms
ANSWER:A
Answer: A
Question: In how many ways 7 boys and 7 girls can be seated in a row so that boys and girls are alternate?
Options:
A)50803200
B)50328000
C)50003280
D)50703200
E)50603200
Rationale: number of ways = 2*7!*7! = 50803200
Answer is A
Answer: A
Question: √{(1.5)(10^9)} is closest to which of the following?
Options:
A)5,000
B)20,000
C)40,000
D)100,000
E)200,000
Rationale: √{(1.5)(10^9)} = √{(15)(10^8)} = √(15)√(10^8) = (√15) * 10,000 which is almost 40,000.
The answer is C.
Answer: C
Question: The football association pays $2000 out of $8000 it owes to refrees. Then it pays $6000 out of the $12000 owes for the year to players.
How much did the ratio of payments made to monies owed increase?
Options:
A)A) 75%
B)B)100 %
C)C)1%
D)D) 50%
E)E) 25%
Rationale: Ratio in 1st case 2000:8000(1/4)
Ratio in second case 6000/12000 (2/4)
percentage increase is (difference/initial quantity)*100
(1/4)/(2/4 )* 100= 100%
Correct option is B
Answer: B
Question: 8 boys complete a work in 14 days . In how many days will 14 boys complete that work?
Options:
A)14 days
B)7 days
C)8 days
D)6 days
E)5 days
Rationale: Explanation:
1 boy 1 day work = 14 × 8,
14 boys complete the work in 14 × 8/14= 8 days
Answer: Option C
Answer: C
Question: The side of a square is increased by 20% then how much % does its area increases?
Options:
A)44.00 %
B)45.25 %
C)48.75 %
D)50.00 %
E)40.00 %
Rationale: a = 100 a2 = 10000
a = 120 a2 = 14400
----------------
10000 --------- 4400
100 -------? => 44.00 %
Answer:A
Answer: A
Question: A room of 5m 44cm long and 3m 74cm broad is to be paved with squre tiles. Find the least number of squre tiles required to cover the floor.
Options:
A)233
B)877
C)279
D)176
E)291
Rationale: Explanation:
area of the room = 544 * 374 sq cm
size of largest square tile = H.C.F of 544cm and 374cm= 34cm
area of 1 tile = 34*34 sq cm
no. of tiles required = (544*374) / (34 * 34) = 176
Answer: D) 176
Answer: D
Question: If the price of a commodity is decreased by 20% and its consumption is increased by 20%, what will be the increase or decrease in expenditure on the commodity?
Options:
A)4% increase
B)4% decrease
C)8% increase
D)8% decrease
E)None
Rationale: Solution: Let the initial expenditure on the commodity be Rs. 100.
Now, the price decreases by 20%,
Current Price = (100 - 20% of 100) = Rs. 80.
Same time due to decrement in price 20% consumption has been increased. So,
Current expenses on commodity = (80 + 20% of 80)= Rs. 96.
Here, the initial expenditure was Rs. 100 which became 96 at the end, it means there is 4% decrement in the expenditure of the commodity.
Mind Calculation Method:
100===20%↓(Decrement in Price)===>80===20%↑(Increment in Consumption)===>96.
Thus, there is a decrement of 4%.
Answer: Option B
Answer: B
Question: What is the present worth of Rs. 122 due in 2 years at 5% simple interest per annum?
Options:
A)Rs.154.32
B)Rs.121.42
C)Rs. 112
D)Rs.110.99
E)Rs.120.99
Rationale: Let the present worth be Rs. x. Then,
S.I. = (122 - x)
(x * 5 * 2) / 100 = (122 - x)
10x = 12200 - 100x
110x = 12200 => x = 110.99
ANSWER:D
Answer: D
Question: For any positive integer p, the sum of the first p positive integers equals p(p+1)/2 . If q and p are positive integers and q > p, what is the sum of all the integers between q and p, inclusive?
Options:
A) q(q+1)/2 + p(p+1)/2
B) q(q+1)/2 - p(p-1)/2
C) q(q+1)/2 - p(p+1)/2
D) q(q+1)/2 + p(p-1)/2
E) q(p+1)/2 - p(q-1)/2
Rationale: The sum of all the integers between q and p,inclusiveis the sum of the first q positive integersminusthe sum of the first p-1 positive integers.
The sum of the first q positive integers is q(q+1)/2;
The sum of the first p-1 positive integers is (p-1)p/2;
Therefore the answer is q(q+1)/2 - (p-1)p/2.
Answer: B.
Answer: B
Question: The average age of applicants for a new job is 31, with a standard deviation of 5. The hiring manager is only willing to accept applications whose age is within one standard deviation of the average age. What is the maximum number of different ages of the applicants?
Options:
A)11
B)14
C)15
D)18
E)30
Rationale: within one standard deviation of the average age means 31 +/- 7
26--31--36
number of dif.ages -26 27 28 29 30 31 32 33 34 35 36
total=11
A
Answer: A
Question: In how many different E ways can 4 ladies and 4 gentlemen be seated at a round table so that all ladies sit together?
Options:
A)70
B)288
C)576
D)10,080
E)20,160
Rationale: Treat the 4 ladies as one object, now you have 5 objects to arrange around a table (m1,m2,m3,m4,women). This can be done in (5-1)! ways
And there are 4! ways to arrange ladies among themselves
Answer E= (4!)^2 = 576 or C
Answer: C
Question: 0.999991+0.111119=?
Options:
A)1
B)1.0001
C)1.0021
D)1.11111
E)1.1111
Rationale: 0.999991 + 0.111119
= 0.999991 + 0.11111 + 0.00009
= (0.999991 + 0.00009) + 0.11111
= 1 + 0.11111
= 1.11111
D
Answer: D
Question: If c persons take y days to complete z similar jobs, how long does it take y persons to complete 1 such job?
Options:
A)z
B)x
C)x/y
D)z/x
E)y/z
Rationale: the Q doesn't seem to be having the any correct answer as a choice..
since we are looking for days, lets keep days in end and work out a solution..
c person can do z jobs in y days..
so c person can do 1 job in y/z days..
and 1 person can do 1 job in y^2/z days..
so y person can complete 1 job in y^2/zy=y/z..
so the answer should be y/z=E
Answer: E
Question: Which of the following inequalities is equivalent to –2 < y< 4 ?
Options:
A) | y– 2 | < 4
B) | y– 1 | < 3
C) | y+ 1 | < 3
D) | y+ 2 | < 4
E) None of the above
Rationale: First remove the mod
then set the expression to 0
then get a value of y
then add and subtract the value from the given number on the RHS
Lets try with an example (B) --------------> | y– 1 | < 3
First remove the mod -------------------> y-1
then set the expression to 0--------------> y-1=0
then get a value of y---------------------> y=1
then add and subtract the value from the given number on the RHS 1+3=4 and 1-3= -2
the range become -2 to 4 correct answer
Now try its with an incorrect option (C) | ----------> |y+ 1 | < 3
First remove the mod --------------------------> y+1
then set the expression to 0----------------------> y+1=0
then get a value of y------------------------------> y=-1
then add and subtract the value from the given number on the RHS -1+3=2 and -1-3= -4
the range become -4 to 2 Incorrect
THE CORRECT ANSWER IS B
Answer: B
Question: If Suresh distributes his pens in the ratio of 1/2 : 1/4 : 1/5 : 1/7 between his four friends A, B, C and D, then find the total number of pens Suresh should have?
Options:
A)153
B)150
C)100
D)125
E)135
Rationale: EXPLANATION:
Here, A : B : C : D = 1 / 2 : 1 / 4 : 1 / 5 : 1 / 7
1) L.C.M of 2, 4, 5, 7 is 140
2) Find the number of pens each friend received --------- (To find no. of pens each friend has, multiply the ratio with the L.C.M. calculated)
A = (1/2) x 140 = 70
B = (1/4) x 140 = 35
C = (1/5) x 140 = 28
D = (1/7) x 140 = 20
3) Total number of pens = (70 x + 35 x + 28 x + 20 x) = 153 x
Minimum number of pens (x) = 1
Therefore, total number of pens = 153 pens.
ANSWER IS A
Answer: A
Question: A tin of oil was 4/5 full. When 6 bottles of oil were taken out and four bottles of oil were poured into it, it was 3/4 full. how many bottles of oil can the tin contain?
Options:
A)10
B)40
C)46
D)36
E)25
Rationale: Suppose X bottles can fill the tin completely
Then Present oil = 4/5 X
after 6 bottles taken out it is 4/5 X - 6
after four bottles poured in it is 4/5 X - 6 + 4
now the oil level is 3/4X
so 4/5 X - 6+4 = 3/4X ===> 4/5 X - 3/4 X = 6-4
X/20=2
X=40
Therefore required no of bottles = 40
so 40 bottles of oil can fill the tin.
the answer is option B) 40.
Answer: B
Question: The total number of problems in the mathematics and algebra books is 28 more than the total number of problems in the algebra and geometry books. How much lesser is the number of problems in the geometry book as compared to the mathematics book?
Options:
A)30
B)18
C)28
D)25
E)32
Rationale: (Mathematics + Algebra) - (Algebra + Geometry) = 28
Mathematics - Geometry = 28
Answer: C
Answer: C
Question: With both inlets open, a water tank will be filled with water in 20 minutes. The first inlet alone would fill the tank in 2 hours. If in every minutes the second inlet admits 50 cubic meters of water than the first, what is the capacity of the tank ?
Options:
A)9,000
B)1,500
C)1,750
D)1,200
E)1,300
Rationale: The work Done by Inlet A and B together in 1 min = 1/20
The work Done by Inlet A (First Inlet) in 1 min = 1/120
The work Done by Inlet B (Second Inlet) in 1 min = (1/20)- (1/120) =1/24
DIfference of Work done by B and A = B - A = 50 Cubic meter
i.e. (1/24)- (1/120) = 50 Cubic meter
i.e. 1500 Cubic Meter
Answer: option B
Answer: B
Question: Amar takes as much time in running 18 meters as a car takes in covering 48 meters. What will be the distance covered by Amar during the time the car covers 1.3 km?
Options:
A)600 m
B)325 m
C)300 m
D)400 m
E)100 m
Rationale: B
325 m
Distance covered by Amar = 18/4.8 (1.3km) = 3/8(1300) = 325 m
Answer is B
Answer: B
Question: Two taps A and B can fill a tank in 5 hours and 20 hours respectively. If both the taps are open then due to a leakage, it took 30 minutes more to fill the tank. If the tank is full, how long will it take for the leakage alone to empty the tank ?
Options:
A)8 hrs
B)9 hrs
C)18 hrs
D)36 hrs
E)33 hrs
Rationale: 2 taps can fill in 4 hrs
With leak it will take 4 1/2 hrs
now leak can empty in 1/4-1/(4 (1/2))
1/4-8/9=1/36. so it an empty tank in 36 hrs
ANSWER:D
Answer: D
Question: A merchandise feedback online portal accords ‘ratings’ to a product by recording the percentage of customers who have reported their views as either ‘satisfied’ or ‘unsatisfied’ only. The portal rounds off the exact percentage value calculated to the closest integral value. If the percentage of unsatisfied customers as recorded by the portal is 57%, what is the LEAST possible number of people that could have reported their views as ‘satisfied’ ?
Options:
A)2
B)3
C)12
D)43
E)57
Rationale: 57% unsatisfied . So ~43% satisfied
But 100% should be an integer only and since the above percentages are approximations 100% should be as close as possible to an integer.
Now substitute value
[1] If 43% is 2 what is 100% -> 200/43 is not giving a number which is closest to an integer.
[2] If 43% is 3 what is 100% -> 300/43 [43*7=301] ...therefore closest possible to an integer. [It also satisfies the least possible and hence we need not check for other choices which are greater than 3]
Therefore Ans is B.
Answer: B
Question: There are 780 male and female participants in a meeting. Half the female participants and one-quarter of the male participants are Democrats. One-third of all the participants are Democrats. How many of the Democrats are female?
Options:
A)75
B)100
C)125
D)130
E)225
Rationale: female = x
Male = 780-x
x/2 + 780-x/4 = 1/3* (780)= 260
x= 260
x/2 = 130 is supposed to be the answer
M is missing something
Correct Option D
Answer: D
Question: Find the odd man out. 742, 743, 633, 581, 871, 990, 532
Options:
A)532
B)990
C)581
D)743
E)None of these
Rationale: Explanation :
In all numbers except 581, the difference of third and first digit is the middle digit. Answer : Option C
Answer: C
Question: A bullet train leaves Kyoto for Tokyo traveling 240 miles per hour at 12 noon. Ten minutes later, a train leaves Tokyo for Kyoto traveling 160 miles per hour. If Tokyo and Kyoto are 400 miles apart, at what time will the trains pass each other?
Options:
A)12:40pm
B)12:49pm
C)12:55pm
D)1:00pm
E)1:04pm
Rationale: Train A: going from K to T
Train B: going from T to K
First I calculated how far Train A will have travelled by the time Train B starts at 12:10:
10 minutes at 240 mph
1/6*240=40miles
They have 400-40=360 miles to travel to meet each other.
I found the combined rate of the two trains
Rate(A) + Rate(B) = 400mph
Divide Distance/Rate to find total time each will travel:
360/400>>> 54 Minutes to meet
12:10+54 minutes = 01:04 or Answer E
Answer: E
Question: In a bag of small balls 1/4 are green, 1/8 are blue, 1/12 are yellow and the remaining 26 white. How many balls are blue?
Options:
A)8 balls.
B)4 balls.
C)7 balls.
D)5 balls.
E)6 balls.
Rationale: Let us first find the fraction of green, blue and yellow balls
1/4 + 1/8 + 1/12 = 6 / 24 + 3 / 24 + 2 / 24 , common denominator
= 11 / 24 , add numerators
The fraction of white balls is given by
24 / 24 - 11 / 24 = 13 / 24
So the fraction 13 / 24 corresponds to 26 balls. If x is the total number of balls then
(13 / 24) of x = 26 balls
or (13 / 24) * x = 26
x = 26 * (24 / 13) = 48 , total number of balls
The fraction of blue balls is 1 / 8 of x. The number of blue balls is given by
(1 / 8) of 48 = 6 balls. correct answer E
Answer: E
Question: Each employee of Company X is a member of precisely 1 of 3 shifts of employees. Among the 60 members of the first shift, 20 percent participate in the pension program; among the 50 members of the second shift, 40 percent participate in the pension program; and among the 40 members of the third shift, 10 percent participate in the pension program. What percent of the workers at Company X participate in the pension program?
Options:
A)20%
B)24%
C)36%
D)37.5%
E)70%
Rationale: 60 members & 20 percent = 12
50 members & 40 percent = 20
40 members & 10 percent = 4
=> 36/150∗100 = 24%
Answer B
Answer: B
Question: Every student in a room is either a junior or a senior. There is at least one junior and at least one senior in the room. If 2/5 of the juniors is equal to 1/3 of the seniors, what fraction of the students in the room are juniors?
Options:
A)3/20
B)1/3
C)5/12
D)12/17
E)5/11
Rationale: Let total number of juniors= J
total number of seniors =S
(2/5) J = (1/3) S
=> S = 6/5 J
Total number of students = J+S = (11/5) J
Fraction of the students in the room are juniors = J/(J+S) = J/[(11/5) J]
=5/11
Answer E
Answer: E
Question: A is half good a work man as B and together they finish a job in 14 days. In how many days working alone B finish the job?
Options:
A)76 days
B)21 days
C)97 days
D)45 days
E)97 days
Rationale: WC = 1:2
2x + x = 1/14 => x = 1/42
2x = 1/21 => 21 days
Answer:B
Answer: B
Question: The total of the ages of Jayant,Prem and Saransh is 93 years.Ten years ago,the ratio of their ages was 2:3:4.What is the present age of Saransh ?
Options:
A)24 years
B)32 years
C)34 years
D)38 years
E)None of these
Rationale: Solution
Let the ages of Jayant,Prem and Saransh 10 years ago be 2x,3x and 4x years respectively.
Then,(2x +10)+ (3x +10) +(4x +10)= 93 ⇔ 9x = 63 ⇔ x =7.
∴ Saransh's present age = (4x +10)=38 years. Answer D
Answer: D
Question: A copy machine, working at a constant rate, makes 25 copies per minute. A second copy machine, working at a constant rate, makes 55 copies per minute. Working together at their respective rates, how many copies do the two machines make in half an hour ?
Options:
A)90
B)2,400
C)4,500
D)5,400
E)324,000
Rationale: Together the two machines make 25+55=80 copies per minute. So, in half an hour they will make 80*30=2,400 copies.
Answer: B.
Answer: B
Question: 3,7,12,18,25,33,..............7th terms
Options:
A)43
B)42
C)63
D)65
E)78
Rationale: 3+4=7
7+5=12
12+6=18
18+7=25
25+8=33
33+9=42
ANSWER:B
Answer: B
Question: Cubes with each side one inch long are glued together to form a larger cube. The larger cube's face is painted with red color and the entire assembly is taken apart. 24 small cubes are found with no paints on them . How many of unit cubes have at least one face that is painted red?
Options:
A)64
B)72
C)86
D)98
E)101
Rationale: Use the options.
The options which after getting added to 24 shows a cube of a number could be right.
Here
64+24 = 88
72+24 = 96
86+24 = 110
98+24 = 122
101+24=125 ---(5*5*5)
So we have 101 as the answer!
E
Answer: E
Question: If a function f is defined by f(x)= (2x-1)/3 for all non zero numbers x. If f(a) = 1 and f(ab) = 1/9 then b= ?
Options:
A)3
B)1/3
C)-1/3
D)-3
E)-12
Rationale: Given that f(x)= (2x-1)/3 and f(a) = 1, then f(a) =(2a-1)/3=1 ===> a=2, then backsolve using the answer choices:
f(ab) = f(2b) = 1/6
A) 3 ===> f(2*3) = f(6) = (12-1)/3 = 11/3
B) 1/3 ===> f((2*1/3) = f(2/3) = (4/3-1)/3 = 1/9 WINS
C) -1/3 ===> f(2*-1/3) = f(-2/3) = (-4/3-1)/3 = -7/9
D) -3 ===> f(2*-3) = f(-6) = (-12-1)/3 = -13/3
E) -12 ===> f(2*-12) = f(-24) = (-24-1)/3 = -25/3
Answer: B
Answer: B
Question: A small company reduced its faculty by approximately 13 percent to 263 employees. What was the original number of employees?
Options:
A)A)182
B)B)208
C)C)220
D)D)224
E)E)302
Rationale: If x is the original number of employees, then after 13% reduction in employees number is .87x
but we are given .87x = 263
x = 302
So the original number of employees is 302
Correct Answer - E
Answer: E
Question: In a race of 1000 m, A can beat by 100 m, in a race of 800m, B can beat C by 100m. By how many meters will A beat C in a race of 600 m?
Options:
A)221.8
B)127.5
C)881.2
D)223.1
E)122.5
Rationale: When A runs 1000 m, B runs 900 m and when B runs 800 m, C runs 700 m.
When B runs 900 m, distance that C runs = (900 * 700)/800 = 6300/8 = 787.5 m.
In a race of 1000 m, A beats C by (1000 - 787.5) = 212.5 m to C.
In a race of 600 m, the number of meters by which A beats C = (600 * 212.5)/1000 = 127.5 m.Answer:B
Answer: B
Question: A number a is squared and then multiplied by negative 3. The result of this operation is equal to three times the sum of three times a and 1. What is one possible value of a ?
Options:
A)25
B)3
C)4
D)1
E)8
Rationale: -3*a^2=3(3a+1)
a= -1 or -1
a=-1=B
ANSWER:D
Answer: D
Question: A coin has two sides. One side has the number 1 on it and the other side has the number 2 on it. If the coin is flipped four times what is the probability that the sum of the numbers on the landing side of the coin will be greater than 7?
Options:
A)3/8
B)1/16
C)1/8
D)1/2
E)1/4
Rationale: There are 16 possible outcomes but only one outcome (2222) has a sum greater than 7.
P(the sum is greater than 7) = 1/16
The answer is B.
Answer: B
Question: A mixture of 150 liters of wine and water contains 20% water. How much more water should be added so that water becomes 25% of the new mixture?
Options:
A)7 liters
B)15 liters
C)10 liters
D)9 liters
E)19 liters
Rationale: Number of liters of water in150 liters of the mixture = 20% of 150 = 20/100 * 150 = 30 liters.
P liters of water added to the mixture to make water 25% of the new mixture.
Total amount of water becomes (30 + P) and total volume of mixture is (150 + P).
(30 + P) = 25/100 * (150 + P)
120 + 4P = 150 + P => P = 10 liters.
ANSWER:C
Answer: C
Question: Find the remainder R when 12^190 is divided by 1729 ?
Options:
A)12
B)1
C)1728
D)1717
E)4
Rationale: 12^(190) can be written as. ((12^3)^63)* 12. 12^3 when divided by 1729 gives a remainder R -1. so in the numerator we have -12. Now acccording to remainder theorm the answer will be 1729-12=1717.D
Answer: D
Question: The compound interest on Rs.30,000 at 7% per annum is Rs. 4347. The period (in years) is:
Options:
A)2
B)2 ½
C)3
D)4
E)3 ½
Rationale: Amount = Rs. (30000 + 4347) = Rs. 34347.
Let the time be n years.
Then, 30000 (1 + 7/100)^n = 34347
(107/100)^ n = 34347/30000 = 11449/10000 = (107/100)^2
So the period is 2 years.
ANSWER:A
Answer: A
Question: Last year a certain bond yielded 5 percent of its face value in interest. If that interest was approximately 4 percent of the bonds selling price of $9,000, what is the bonds face value?
Options:
A) $6,000
B) $6,750
C) $7,425
D) $7,200
E) $9,375
Rationale: Interest = 0.05*face value = 0.04*9,000 --> face value = 0.04*9,000/0.05 = 7,200.
Answer: D.
Answer: D
Question: A work which could be finished in 7 days was finished 3 days earlier after 10 more men joined. The number of men employed was?
Options:
A)22
B)20
C)60
D)71
E)11
Rationale: x ------- 7
(x + 10) ---- 6
x * 7 = (x + 10)6
x = 60
\Answer: C
Answer: C
Question: A basket contains 6 apples, of which 1 is spoiled and the rest are good. If we select 2 apples from the basket simultaneously and at random, what is the probability that the 2 apples selected will include the spoiled apple?
Options:
A)1/2
B)1/3
C)1/4
D)1/5
E)1/6
Rationale: The total number of ways to choose 2 apples is 6C2 = 15
The number of ways that include the spoiled apple is 5C1 = 5
P(the spoiled apple is included) = 5/15 = 1/3
The answer is A.
Answer: A
Question: The number of all possible selections of one or more questions from 10 given questions, each question having one alternative is
Options:
A)3 10
B)2 10 – 1
C)3 10 – 1
D)2 10
E)None of these
Rationale: Since each question can be selected in 3 ways, by selecting it or by selecting its alternative or by rejecting it. Thus, the total number of ways of dealing with 10 given questions is 310 including a way in which we reject all the questions.
Hence, the number of all possible selections is 3 10 – 1.
Answer C
Answer: C