divelab/Sys2Bench huggingface dataset:
Question: What is the sum of the prime factors of 3 and the prime factors of 1656?
Options:
A)35
B)45
C)55
D)25
E)65
Rationale: The prime factors of 3 are 3*1
The prime factors of 1656 are 2x2x2x3x3x23
2+2+2+3+3+23 = 35. A is the correct answer
Answer: A
Question: For any positive x, y and z if x is n% of y and z is m% of y then what percentage E must x be of z?
Options:
A)(n/m)%
B)(m × n)%
C)(100 / [m × n]) %
D)(100 × m/n)%
E)(100 × n/m)%
Rationale: x is n% of y MEANS x= (n/100 )* y------------------------eq1
z is m% of y MEANS z= (m/100 )* y------------------------eq2
Find equation of xz
substitute value of y from 2nd equation into Ist equation
so x= (n/100)*(100z/m)
so x= (n/m)z
or x= (100n/m)z/100
so answer E is 100n/m %.E
Answer: E
Question: If 105 divides into n with no remainder, which of the following must be a factor of n?
Options:
A)2
B)4
C)6
D)7
E)11
Rationale: 105 / n = k (with k an integer)
(7)(5)(3) / n = k
n must have a 7 in his prime factorization to divide 105 without remainder.
answer D
Answer: D
Question: Two numbers are in the ratio of 5:9. If 25 be subtracted from each, they are in the ratio of 35:59. Find the numbers?
Options:
A)150,170
B)150,270
C)50,270
D)180,270
E)150,290
Rationale: (5x-25):(9x-25) = 35:59
x = 30 => 150,270
ANSWER:B
Answer: B
Question: On Monday morning, Chris receives tickets to a baseball game that will be played at 7pm on the next evening that it does not rain. However, Chris is only in town until Wednesday morning, at which point he must fly to another city. If there is a 70% chance of rain each of the next two evenings, what is the probability that Chris will be able to attend the game?
Options:
A) 36%
B) 51%
C) 66%
D) 80%
E) 84%
Rationale: Chris won't be able to attend the game if it be raining on Monday eveningandTuesday evening. The probability of that is 0.7*0.7 = 0.49. So, the probability that he will be able to attend is 1 - 0.49 = 0.51.
Answer: B.
Answer: B
Question: How many 2 3/4 foot pieces of cable can be cut out of a piece that is 30 feet long?
Options:
A)a.10
B)b.16
C)c.17
D)d.18
E)e. 20
Rationale: Pretty Simple..the answer is choice (A) 10.
All that one has to do is :
1: Convert 2 3/4 into an improper fraction (11/4) or a decimal (2.75)
2: Divide 30 by 11/4 (or 2.75)
Answer =10 (A)
Answer: A
Question: The perimeter of one square is 44 cm and that of another is 20 cm. Find the perimeter and the diagonal of a square which is equal in area to these two combined?
Options:
A)13√4
B)12.1√2
C)23√2
D)12√4
E)13√9
Rationale: 4a = 44 4a = 20
a = 11 a = 5
a2 = 121 a2 = 25
Combined area = a2 = 146 => a = 12.1
d = 12.1√2
Answer: B
Answer: B
Question: Three pipes A, B and C can fill a tank in 6 hours. After working at it together for 2 hours, C is closed and A and B can fill the remaining part in 9 hours. How many hours will take C alone to fill the tank?
Options:
A)23/2
B)41/3
C)49/4
D)54/5
E)63/6
Rationale: The rate of A+B+C is 1/6 of the tank per hour.
After 2 hours, the tank is 1/3 full.
The rate of A+B is 2/3 * 1/9 = 2/27 of a tank per hour.
The rate of C is 1/6 - 2/27 = 5/54
C can fill the tank in 54/5 hours.
The answer is D.
Answer: D
Question: The difference between a number and its three-fifths is 50.What is the number?
Options:
A)75
B)100
C)125
D)Cannot be determined
E)None of these
Rationale: Suppose the number is N.
Then N - 3⁄5N = 50
⇒ 2N⁄5 = 50
∴ N=50×52=125
Answer.C
Answer: C
Question: Number N is randomly selected from a set of all primes between 10 and 40, inclusive. Number Z is selected from a set of all multiples of 5 between 10 and 40 inclusive. What is the probability that N+Z is odd?
Options:
A) 1/2
B) 2/3
C) 3/4
D) 4/7
E) 5/8
Rationale: All primes except 2 are odd, thus N must be odd. For N + Z = odd + Z to be odd, Z must be even.
There are 7 multiples of 5 between 10 and 40, inclusive: 10, 15, 20, 25, 30, 35, and 40. Out of them 3 (15, 25, and 35) are odd.
Therefore the probability that N + Z is odd is 4/7.
Answer: D.
Answer: D
Question: A rectangular field has area equal to 150 sq m and perimeter 50 m. Its length and breadth must be?
Options:
A)5,2
B)6,9
C)2,1
D)5,8
E)15,10
Rationale: Explanation:
lb = 150
2(l + b) = 50 => l + b = 25
l – b = 5
l = 15 b = 10
Answer: E
Answer: E
Question: If the reciprocals of two consecutive positive integers are added together, what is the sum in terms of the greater integer x?
Options:
A)x/3
B)x^2 - x
C)2x - 1
D)(2x - 1)/(x^2 + x)
E)(2x - 1)/(x^2 - x)
Rationale: Let two consecutive positive integers be x and x-1 (Greater integer is x)
So,
(1/x) + [1/(x-1)]
= (2x-1)/x(x-1)
=(2x-1)/(x^2- x)
Answer E
Answer: E
Question: A person starting with Rs.64 & making 6 bets, wins three times and loses 3times, the wins and loses occurring in random order. The chance for a win is equal to the chance for a loss. If eachwager is for half the money remaining at thetime of the bet, then the final result is?
Options:
A)Rs.37
B)Rs.57
C)Rs.60
D)Rs.64
E)Rs.68
Rationale: As the win leads to multiplying the amount by 1.5 and loss leads to multiplying the amount by 0.5, we will multiply initial amount by 1.5 thrice and by 0.5 thrice (in any order).
The overall resultant will remain same.
So final amount with the person will be (in all cases):
=64(1.5)(1.5)(1.5)(0.5)(0.5)(0.5)==64(1.5)(1.5)(1.5)(0.5)(0.5)(0.5)= Rs 2727
Hence the final result is:
64−27=3764−27=37:
A loss of Rs.37
A
Answer: A
Question: The 19th of September 1987 was a Saturday. If 1988 was a leap-year, what day of the week was the 22nd of September 1990?
Options:
A)Monday
B)Tuesday
C)Wednesday
D)Friday
E)Saturday
Rationale: 19th September
1987: Saturday
1988: Monday (due to leap year)
1989: Tuesday
1990: Wednesday
Hence 22nd September was a Saturday.
The answer is E.
Answer: E
Question: When 100 is divided by positive integer x, the remainder is 4. What is the remainder when 196 is divided by x?
Options:
A)2
B)3
C)4
D)6
E)8
Rationale: f100/x leaves a reminder 4 then (100-4) i.e. 96 is divisible by x
So (100+96)/x leaves a reminder rem(100/x)+rem(96/x)=> 4+0=4
Answer :C
Answer: C
Question: An order was placed for the supply of a carpet whose breadth was 6 m and length was 1.44 times the breadth. What be the cost of a carpet whose length and breadth are 40% more and 25% more respectively than the first carpet. Given that the ratio of carpet is Rs. 45 per sq. m ?
Options:
A)Rs. 4082.40
B)Rs. 1024.21
C)Rs. 2810.6
D)Rs. 3214
E)Rs. 2140
Rationale: Explanation:
Length of the first carpet = (1.44)(6) = 8.64 cm
Area of the second carpet = 8.64(1 + 40/100) 6 (1 + 25/100)
= 51.84(1.4)(5/4) sq m = (12.96)(7) sq m
Cost of the second carpet = (45)(12.96 x 7) = 315 (13 - 0.04) = 4095 - 12.6 = Rs. 4082.40
ANSWER IS A
Answer: A
Question: If 3 persons can do 3 times of a particular work in 3 days, then, 7 persons can do 7 times of that work in?
Options:
A)2 days
B)3 days
C)5 days
D)7 days
E)9 days
Rationale: That is, 1 person can do one time of the work in 3 days.
Therefore, 7 persons can do 7 times work in the same 3 days itself.
B)
Answer: B
Question: Nicky and Cristina are running a race. Since Cristina is faster than Nicky, she gives him a 48 meter head start. If Cristina runs at a pace of 5 meters per second and Nicky runs at a pace of only 3 meters per second, how many seconds will Nicky have run before Cristina catches up to him?
Options:
A) 15 seconds
B) 18 seconds
C) 24 seconds
D) 30 seconds
E) 45 seconds
Rationale: used pluging in method
say t is the time for cristina to catch up with Nicky, the equation will be as under:
for Nicky=N=3*t+48
for Cristina=C=5*t
@t=24, N=120 C=120 right answer
ans:C
Answer: C
Question: Submarine P and Submarine Q are equipped with sonar devices that can operate within a 2,000 yard range. Submarine P remains in place while Submarine Q moves 1,700 yards south from Submarine P. Submarine Q then changes course and moves due east, stopping at the maximum range of the sonar devices. In which of the following directions can Submarine Q continue to move and still be within the sonar range of Submarine P? I. North II. South III. West
Options:
A)III only
B)I,II only
C)II only
D)I only
E)I and III only
Rationale: It's evident if we make a diagram for the Movement of Q respect to P.
From its South position to the east position, it has covered the maximum radius for the south direction. Similarly, it's east movement further will also make it out of range.
Thus it can only move north or west or anything in that curve.
Answer : E
Answer: E
Question: Number of divisors of 22050 except 1 and itself is.
Options:
A)22
B)52
C)87
D)26
E)19
Rationale: Explanation: 2 22050 3 11025 3 3675 5 1225 5 245 7 49 7 ⇒ 22050 = 21 × 32 × 52 × 72 Using the formula discussed earlier, ∴ Number of divisors = (1+1) (2+1) (2+1) (2+1) = 54 ∴ Number of divisors except 1 and itself = 54 –2 = 52
Answer:B
Answer: B
Question: Paul completes a piece of work in 80 days, Rose completes the same work in 120 days. If both of them work together, then the number of days required to complete the work is?
Options:
A)42
B)44
C)46
D)48
E)50
Rationale: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days.
That is, the required No. of days = 80 × 120/200 = 48 days
Answer is D
Answer: D
Question: If log303 = a, log305 = b, then log308 =?
Options:
A)3(1 - a - b)
B)(a - b + 1)
C)(1 - a - b)
D)(a - b + 1)
E)none of these
Rationale: a + b = log3015 = log30(30/2) = 1- log302
=> log302 = (1 - a - b)
Therefore, log308 = 3(1 - a - b).
ANSWER:A
Answer: A
Question: If the height of an equilateral triangle QBC is equal in length to the hypotenuse of an isosceles right triangle DEF, a side of ΔQBC is how many times as long as a leg of the right triangle DEF?
Options:
A)(√2)/(√3)
B)(√3)/(√2)
C)√2
D)(2√2)/(√3)
E)2/(√3)
Rationale: Side of the equilateral triangle QBC = 2m ----> height = m * sqtr(2)
Hipotenuse of the right triangle QBC = m * sqrt(3) ----> side = m * sqtr(3) / sqtr(2)
Question is 2m/m * sqtr(3) / sqtr(2) = 2*sqrt(2)/sqrt(3)=D
Answer: D
Question: If a-b= 6 and a^2+b^2=100, find the value of ab
Options:
A)10
B)32
C)15
D)18
E)19
Rationale: 2ab = (a^2 + b^2) - (a - b)^2
= 100 - 36 = 64
=> ab = 32
ANSWER:B
Answer: B
Question: Find the area of a parallelogram with base 24 cm and height 16 cm.
Options:
A)384 cm^2
B)200 cm^2
C)250 cm^2
D)350 cm^2
E)400 cm^2
Rationale: Area of a parallelogram = base * height = 24 * 16 = 384 cm2
ANSWER A
Answer: A
Question: If Q is an odd number and the median of Q consecutive integers is 110, what is the largest of these integers?
Options:
A)(Q - 1)/2 + 110
B)Q/2 + 109
C)Q/2 + 110
D)(Q + 109)/2
E)(Q + 110)/2
Rationale: Consider the easiest case, say Q=3, then;
Set = {109, 110, 111};
The largest integer = 111.
Now, plug Q=3 into the answers to see which yields 111.
Answer: A.
Answer: A
Question: The area of one square is x^2 + 10x + 25 and the area of another square is x^2 − 6x + 9. If the sum of the perimeters of both squares is 32, what is the value of x?
Options:
A)3
B)2
C)2.5
D)4.67
E)10
Rationale: spotting the pattern of equations both are in form of (X+C)^2 so
A1= (x+5)^2A2= (x-3)^2
L1= x+5L2= -3
P1 = 4( x+5)P2=4(x-3)
P1+P2=32
4( x+5) +4(x-3)=32.....3
Ans :A
Answer: A
Question: What is the value of 3x^2 − 2x + 0.3 for x = 0.5?
Options:
A)−0.3
B)0
C)0.05
D)1.08
E)2.46
Rationale: 3x^2-2x+0.3 for x=0.6
=3(0.5*0.5)-4*0.5*(0.5)+0.3
=-0.5*0.5+0.3
=-0.25+0.3
=0.05
Correct Option : C
Answer: C
Question: A certain manufacturer of cake, muffin, and bread mixes has 90 buyers, of whom 50 purchases cake mix, 40 purchase muffin mix, and 20 purchase both cake mix and muffin mix. If a buyer is to be selected at random from the 100 buyers, what is the probability that the buyer selected will be one who purchases neither cake mix nor muffin mix?
Options:
A)a. 1/10
B)b. 3/10
C)c. 1/3
D)d. 7/10
E)e. 9/10
Rationale: C+M+B-CM-MB-CB-2CMB = 90
C - cake buyers, M - muffin and B - Bread buyers. CM,MB,CB and CMB are intersecting regions.
the question asks for people who have bought only bread mixes = B-CB-MB-2CMB has to be found out.
50 + 40 + B-CB-MB-20-2CMB = 90
B-CB-MB-2CMB = 30
hence the probability = 30/90 = 30/90=1/3.
C
Answer: C
Question: The avg. age of a group of 32 students is 20 years.If 4 more students join the group,the avg age increases by 1 year.The avg age of the new student is?
Options:
A)22 years
B)23 years
C)24 years
D)25 years
E)29 years
Rationale: Total age of 32 students=32*20=640
If total age of 4 students=x
Then, (640+x)/(32+4) =(20+1), x=116
So average age of new students=116/4= 29 years
ANSWER:E
Answer: E
Question: Find the C.I. on Rs. 15,625 for 9 months at 16% per annum compounded quarterly?
Options:
A)2776
B)2777
C)1951
D)2966
E)1971
Rationale: Explanation:
P = Rs. 15625, n = 9 months = 3 quarters, R = 16% p.a. per quarter.
Amount = [15625 * (1 + 4/100)3]
= (15625 * 26/25 * 26/25 * 26/25) = Rs. 17576 C.I. = 17576 - 15625 = Rs. 1951.
Answer: C
Answer: C
Question: In my core I have 5 But 500 stand in the beginning and the end of mine. I also include the first letter and the first number to make me complete. I am the name of a King.
Who am I?
Options:
A)Johny
B)Jacky
C)Ricky
D)David
E)Alex
Rationale: D
I am DAVID.
At the core I have 5
If we talk in roman numeric system, 5 = V
Similarly, 500 stands in the beginning and end
500 = D
I also include the first letter i.e. A and the first number i.e. I (in roman numeric system)
All of them combine to form DAVID.
Answer: D
Question: A train 120 m long passed a pole in 20 sec. How long will it take to pass a platform 780 m long?
Options:
A)150
B)170
C)160
D)100
E)120
Rationale: Speed = 120/20 = 6 m/sec.
Required time = (120 + 780)/6 = 150 sec.
Answer: Option A
Answer: A
Question: Raju age after 9 years will be 5 times his age 3 years back, What is the present age of Raju
Options:
A)8 years
B)7 years
C)6 years
D)5 years
E)4 years
Rationale: Explanation:
Clearly,
x+9 = 5(x-3)
<=> 4x = 24 => x = 6
Option C
Answer: C
Question: The perimeter of a rhombus is 120 feet and one of its diagonal has a length of 40 feet. Find the area of the rhombus.
Options:
A)100 sqrt(5) ft.sq
B)400 sqrt(5) ft.sq
C)500 sqrt(5) ft.sq
D)200 sqrt(5) ft.sq
E)150 sqrt(5) ft.sq
Rationale: A perimeter of 120 when divided by 4 gives the side of the rhombus 30 feet. The length of the side OC of the right triangle is equal to half the diagonal: 20 feet. Let us now consider the right triangle BOC and apply Pythagora's theorem to find the length of side BO.
30^2 = BO^2 + 20^2
BO = 10 sqrt(5) feet
We now calculate the area of the right triangle BOC and multiply it by 4 to obtain the area of the rhombus.
area = 4 ( 1/2) BO * OC = 4 (1/2)10 sqrt (5) * 20
= 400 sqrt(5) ft.sq
Answer is B
Answer: B
Question: How many positive integers less than 24 are prime numbers, odd multiples of 5, or the sum of a positive multiple of 2 and a positive multiple of 4?
Options:
A)19
B)25
C)24
D)22
E)20
Rationale: 9 prime numbers less than 28: {2, 3, 5, 7, 11, 13, 17, 19, 23}
2 odd multiples of 5: {5, 15}
9 numbers which are the sum of a positive multiple of 2 and a positive multiple of 4: {6, 8, 10, 12, 14, 16, 18, 20, 22}
Notice, that 5 is in two sets, thus total # of integers satisfying the given conditions is 9+2+9-1=19.
Answer: A.
Answer: A
Question: A newly-wed couple is using a website to design an eBook Wedding Album to distribute to their friends and families. The template they have chosen has places for 3 large photos and 19 smaller photos. The couple has 6 large photos they could use for those three slots, and 21 smaller photos they could use for those 19 slots. Given these choices, how many different possible albums could they create?
Options:
A)3,150
B)4,200
C)5,040
D)20,520
E)84,000
Rationale: For the big album they have to choose 3 out of their 6 photos, and leave out 3:
6! / 3!3! = 20
For the small album they have to choose 19 out of their 21 photos and leave out 2:
21! / 19!2! = 210
All combinations together: 210*20 = 4200, ANS B
Answer: B
Question: Find the average of the series : 235,222,125,135,123
Options:
A)168
B)308
C)267
D)207
E)174
Rationale: Average = (235+222+125+135+123)/5
= 840/5
= 168
Answer: A
Answer: A
Question: (0.5)(power 3) - (0.1)(power 3)/ (0.5)(power 2) + 0.05 + (0.1)(power 2) is:
Options:
A)0.8
B)0.4
C)0.96
D)0.69
E)0.76
Rationale: Given expression
= (0.5) (power 3) - (0.1)(power 3) / (0.5)(power 2) + (0.5 x 0.1) + (0.1)(power 2)
= a (power 3) - b(power 3) / a(power 2) + ab + b(power 2)
= (a - b)
= (0.5 - 0.1)
= 0.4
Answer is B
Answer: B
Question: At a certain ice cream parlor, customers can choose among five different ice cream flavors and can choose either a sugar cone or a waffle cone. Considering both ice cream flavor and cone type, how many distinct triple-scoop cones with three different ice cream flavors are available?
Options:
A)12
B)16
C)20
D)24
E)30
Rationale: Customer can choose 3 out of 5 flavors 5C3=10;
Customer can choose 1 out of 2 cone type 2C1=2;
Total # of combinations possible 10*2=20.
ANS:C
Answer: C
Question: Set K contains every multiple of 6 from 18 to 306 inclusive. If w is the median of set K, and x is the average (arithmetic mean) of set K, what is the value of w-x?
Options:
A)-6
B)-3
C)0
D)3
E)6
Rationale: Set K ={18,24,30,....306}
Let the no. of terms be n.
so we know the AP formulae to calculate the the tn term:
tn= a+(n-1)*d where d = common difference of the terms.
306= 18 +(n-1)*6
n=49.
So the set K consist of n terms.
The median of the set having odd nos of elements is (n+1)/2., which in this case is 25.
Let's find the 25th term using the same formulae again:
t25= 18+(25-1)*6
t25= 162
So , the median of the set K is 162 i.e. w=162.
Now. lets find the average (arithmetic mean) of the set. For that we need to find the sum of all the elements first, lets call it S.
Since, set k is nothing but a Arithmetic Progression series having first element(a) as 18, common difference (d) as 6 and no. of terms(n) as 49.
Using the formulae to calculate sum of an AP series, which is
S= n/2[2a + (n-1)*d], we will calculate the sum.
so, S= 49/2 [2*18 + (49-1)*6]
This gives us S= 7938.
Now Arithmetic mean of Set K = 7938/no. of terms= 7938/49= 162.
So x= 162.
Now, (w-x) = (162-162)= 0.
Therefore Correct Answer = C
Answer: C
Question: In a 300 member association consisting of men and women, exactly 20% of men and exactly 25 % women are homeowners. What is the least number of members who are homeowners?
Options:
A)79
B)77
C)85
D)83
E)61
Rationale: Solution simple
Out of 300 20% are male i.e 60 and 25% are female i.e 75 , so total homeowner is 135.
Now min number homeowner is 60 and max is 135 so question ask us to find least and 61 has least value among all option.
So ans is 61.
Answer : E
Answer: E
Question: If 3 persons can do 3 times of a particular work in 3 days, then, 7 persons can do 7 times of that work in?
Options:
A)days
B)days
C)days
D)days
E)days
Rationale: That is, 1 person can do one time of the work in 3 days.
Therefore, 7 persons can do 7 times work in the same 3 days itself.
B)
Answer: B
Question: The labeled price of a table is Rs. 7,500. The shopkeeper sold it by giving 5% discount on the labeled price and earned a profit of 15%. What approximately is the cost price of the table?
Options:
A)Rs. 6195
B)Rs. 6199
C)Rs. 6192
D)Rs. 6191
E)Rs. 6194
Rationale: Explanation:
Labeled price = Rs. 7,500
By giving 5% discount on labeled price, the selling price is
= 95 / 100 * 7500 = Rs. 7125
By earning 15% profit on the selling of price Rs. 7125 the cost price is
= 100 / 115 * 7125 = Rs. 6195.65
Therefore, approximate cost is 6195.65
ANSWER: A
Answer: A
Question: From the set of numbers {t, u, v, w, x, y, z}, how many different combinations can we have without the t in them? Ex:. (x,y), (x), (w,z,y,x), etc... and note that (x,y)=(y,x)
Options:
A)16
B)31
C)32
D)63
E)64
Rationale: Any letter (u, v, w, x, y, z) can be included or not.
Thus there are 2^6 combinations - 1 empty combination = 63 combinations
The answer is D.
Answer: D
Question: Find out the C.I on Rs.3000 at 4% p.a. compound half-yearly for 1 1/2 years.
Options:
A)A)Rs.181.62
B)B)Rs.182.62
C)C)Rs.183.62
D)D)Rs.184.62
E)E)Rs.185.62
Rationale: A = 3000(51/50)3
= 3183.62
3000
-----------
183.62
ANSWER:C
Answer: C
Question: If a man can cover 20 metres in one second, how many kilometres can he cover in 3 hours 45 minutes?
Options:
A)288
B)162
C)220
D)270
E)122
Rationale: 20 m/s = 20 * 18/5 kmph
3 hours 45 minutes = 3 3/4 hours = 15/4 hours
Distance = speed * time = 20 * 18/5 * 15/4 km = 270 km.
Answer: D
Answer: D
Question: The area of a square field is 7201 sq m. How long will a lady take to cross the field diagonally at the rate of 2.4 km/hr?
Options:
A)1 min 15 sec
B)1.5 min
C)1 min
D)2.5 min
E)2 min
Rationale: Area of a square field = 7201 sq m
Let the side of square = a
a^2 = 7201
=> a = 84.86
Diagonal = (2)^(1/2) * a
= 1.414 * 84.86
=120
Speed of lady = 2.4 km / hour
= 2400 m / hour
= 60 m / min
Time taken by lady to cross the field diagonally = 120/60 = 2 min
Answer E
Answer: E
Question: What is the rate percent when the simple interest on Rs.5000 amount to Rs.2500 in 5 Years?
Options:
A)9%
B)8%
C)10%
D)10.5%
E)7.5%
Rationale: Interest for 1 year = 2500/5 = 500
Interest on Rs 5000 p/a = 500
interest rate = 500/5000*100 = 10%
Answer : C
Answer: C
Question: The speed of light is approximately 1,86 * 10^6 miles per second. This approximate speed is how many miles per hour?
Options:
A) 1,11 * 10^7
B) 6,70 * 10^7
C) 1,11 * 10^8
D) 6,,70 * 10^9
E) 6,70 * 10^8
Rationale: The easiest way to answer this question is by POE, it does not require any calculation (answered in 30seconds). In one hour there are 3600 seconds, therefore speed in miles/hour will be.
(1.86*10^6)*3600 = (1.86*10^6)*(3.6*10^3) = some number*10^9..
The key is realizing that thesome numberhas to be bigger thatn 1.86 (because 1.86*3.6), and the only answer that fits that is D
Answer: D
Question: If y > 0, (8y)/20 + (3y)/10 is what percent of y?
Options:
A)40%
B)50%
C)60%
D)70%
E)80%
Rationale: can be reduced to 4y/10+3y/10 =7y/10=70%
Answer D
Answer: D
Question: If p, q and r are positive integers and satisfy x = (p + q -r)/r = (p - q + r)/q = (q + r - p)/p, then the value of x is?
Options:
A)-1
B)1
C)2
D)-2
E)-3
Rationale: When two or more ratios are equal, each of the ratios are equal to sum of the numerators divided by the sum of the denominators, provided sum of the denominators is non-zero.
Hence, x = (p + q -r)/r = (p - q + r)/q = (q + r - p)/p
=> x = (p + q - r + p - q + r + q + r - p) / (r + q + p)
=> x = (r + q + p) / (r + q + p) = 1
p + q + r is non-zero.
Answer: B
Answer: B
Question: A train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?
Options:
A)999
B)279
C)120metre
D)99
E)21
Rationale: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec.
Length of the train = 20 * 6
= 120 m.
Answer: C
Answer: C
Question: Ravi purchased a refrigerator and a mobile phone for Rs. 15000 and Rs. 8000 respectively. He sold the refrigerator at a loss of 4 percent and the mobile phone at a profit of 10 percent. Overall he make a.?
Options:
A)277
B)209
C)121
D)200
E)128
Rationale: Let the SP of the refrigerator and the mobile phone be Rs. r and Rs. m respectively.
r = 15000(1 - 4/100) = 15000 - 600
m = 8000(1 + 10/100) = 8000 + 800
Total SP - Total CP = r + m - (15000 + 8000) = -600 + 800 = Rs. 200
As this is positive, an overall profit of Rs. 200 was made.
Answer: D
Answer: D
Question: A diagonal is a line segment that connects non-adjacent vertices in a polygon. How many diagonals does an octagon have?
Options:
A)20
B)40
C)60
D)90
E)80
Rationale: Select one vertex and you can draw 5 diagonals.
If you draw 5 such diagonals for each of the 8 vertices, you will draw a total of 5 × 8 = 40 diagonals. But you actually draw each diagonal twice, once from each of its ends. Therefore, there are a total of 40 ÷ 2 = 20 different diagonals
correct answer A
Answer: A
Question: The slant height of a cone is 18 cm and radius of the base is 8cm, find the curved surface of the cone?
Options:
A)26
B)452
C)450
D)440
E)28
Rationale: π * 18 * 8
= 452
Answer:B
Answer: B
Question: A watch was sold at a loss of 10%. If it was sold for Rs.140 more, there would have been a gain of 4%. What is the cost price?
Options:
A)1000
B)2287
C)2677
D)2887
E)2688
Rationale: 90%
104%
--------
14% ---- 140
100% ---- ? => Rs.1000
Answer: A
Answer: A