divelab/Sys2Bench huggingface dataset:
Question: Matt is touring a nation in which coins are issued in two amounts, 2¢ and 5¢, which are made of iron and copper, respectively. If Matt has five iron coins and fiveteen copper coins, how many different sums from 1¢ to 160¢ can he make with a combination of his coins?
Options:
A)80
B)85
C)81
D)160
E)157
Rationale: The total sum is 5*2 + 15*5 = 85¢. If you can make each sum from 1 to 85 (1¢, 2¢, 3¢, ..., 85¢), then the answer would be 85 (maximum possible).
Now, with 2¢ and 5¢ we cannot make 1¢ and 3¢. We also cannot make 84¢ and 82¢ (since total sum is 85¢ we cannot remove 1¢ or 3¢ to get 84¢ or 82¢).
So, out of 85 sums 4 are for sure not possible, so the answer must be 85 - 4 = 81 sums or less. Only A fits.
Answer: C.
Answer: C
Question: A ladder 30 feet long is leaning against a wall that is perpendicular to level ground. The bottom of the ladder is 10 feet from the base of the wall. If the top of the ladder slips down 5 feet, how many feet will the bottom of the ladder slip?
Options:
A)14
B)15
C)18.92
D)19
E)25
Rationale: 30^2-10^2=800
it means that the height is equal to 28.28.
since the top of the ladder slips down 5 feet, then the height of the wall =28.28-5=23.28
the bottom =sqrt(30^2-23.28^2)=sqrt(900-541.95)=18.92
ans is C
Answer: C
Question: Rs. 6000 is lent out in two parts. One part is lent at 7% p.a simple interest and the other is lent at 10% p.a simple interest. The total interest at the end of one year was Rs. 450. Find the ratio of the amounts lent at the lower rate and higher rate of interest?
Options:
A)5:1
B)5:6
C)5:2
D)5:8
E)5:2
Rationale: Let the amount lent at 7% be Rs. x
Amount lent at 10% is Rs. (6000 - x)
Total interest for one year on the two sums lent
= 7/100 x + 10/100 (6000 - x) = 600 - 3x/100
=> 600 - 3/100 x = 450 => x = 5000
Amount lent at 10% = 1000
Required ratio = 5000 : 1000 = 5:1
Answer:A
Answer: A
Question: The current of a stream at 1 kmph. A motor boat goes 35 km upstream and back to the starting point in 12 hours. The speed of the motor boat in still water is?
Options:
A)6
B)9
C)5
D)1
E)4
Rationale: S = 1
M = x
DS = x + 1
US = x - 1
35/(x + 1) + 35/(x - 1) = 12
x = 6
Answer: A
Answer: A
Question: In the seaside summer camp there are 50 children. 90% of the children are boys and the rest are girls. The camp administrator decided to make the number of girls only 5% of the total number of children in the camp. How many more boys must she bring to make that happen?
Options:
A)50.
B)45.
C)40.
D)30.
E)25.
Rationale: Given there are 50 students In the seaside summer camp , 90% of 50 = 45 boys and remaining 5 girls.
Now here 90% are Boys and 10% are Girls.
Now question is asking about how many boys do we need to add, to make the girls percentage to 5 or 5%..
If we add 50 to existing 45 then the count will be 95 and the girls number will be 5 as it.
Now boys are 95% and girls are 5%. ( out of 100 students = 95 boys + 5 girls ).
IMO option A is correct.
Answer: A
Question: If in a game of 80, P can give 16 points to Q and R can give 20 points to P, then in a game of 150, how many points can R give to Q?
Options:
A)60
B)28
C)26
D)17
E)81
Rationale: Explanation:
When P scores 80, Q scores 64.
When R scores 80, P scores 60
Hence, when R scores 150, Q scores (60 * 64 * 150) / (80 * 80) = 90
Therefore, in a game of 150, R can give 60 points to Q.
ANSWER: A
Answer: A
Question: The remainder when 1!+2!+3!...+50! divided by 8! will be
Options:
A)21
B)5193
C)77
D)9275
E)19
Rationale: The remainder when the terms greater than 8! are divided by 8! becomes 0 so we need to consider the terms upto 7!.
So remainder will be whatever is obtained by dividing 1!+2!+3!+4!+5!+6!+7! with 8!.
So remainder is obtained by dividing (1+2+6+24+120+720+5040)= 5193 with 8! ( 40320)
So remainder is 5193.
Answer:B
Answer: B
Question: In Township K each property is taxed at 10 percent of its assessed value. If the assessed value of a property in Township K is increased from $20,000 to $24,000, by how much will the property tax increase?
Options:
A) $32
B) $50
C) $320
D) $400
E) $500
Rationale: Increase in house value = $24,000 - $20,000 =$4000
So, tax increase = 10% of$4000= $400
Answer: D
Answer: D
Question: For any integer n greater than 1, #n denotes the product of all the integers from 1 to n, inclusive. How many prime numbers are there between #6 +2 and #6 +6 , inclusive?
Options:
A)None
B)One
C)Two
D)Three
E)Four
Rationale: Given that n* denotes the product of all the integers from 1 to n, inclusive so, 6*+2=6!+2 and 6*+6=6!+6.
Now, notice that we can factor out 2 our of 6!+2 so it cannot be a prime number, we can factor out 3 our of 6!+3 so it cannot be a prime number, we can factor out 4 our of 6!+4 so it cannot be a prime number, ... The same way for all numbers between 6*+2=6!+2 and 6*+6=6!+6, inclusive. Which means that there are no primes in this range.
Answer: A.
Answer: A
Question: A circular rim 35 inches in diameter rotates the same number of inches per second as a circular rim 42 inches in diameter. If the smaller rim makes x revolutions per second, how many revolutions per minute does the larger rim makes in terms of x ?
Options:
A)48pi/x
B)50x
C)48x
D)24x
E)x/75
Rationale: C = (pi)d
C(small): (pi)*35
C(large): (pi)*42
Lets say the time horizon is 60 seconds, so during that time the smaller rim covers a distance of (pi)*35*60 = (pi)*(2100) inches
(pi)*(2100) = (pi)*(42)(x)
pi*(50) = pi*(x)
50=x
Answer: B.
Answer: B
Question: If the integer p is rounded to the nearest hundred, the result represents a 66 2/3 % increase over the value obtained when p is rounded to the nearest ten. which of the following is a possible value of p?
Options:
A)64
B)67
C)99
D)133
E)147
Rationale: We have to check options 1 by 1.
64 rounded to nearest hundred = 100
64 rounded to nearest ten = 60
now difference = 40
the result represents a 66 2/3 % increase over the value obtained when x is rounded to the nearest ten.
therefore 40/60)*100 = 66 2/3 ==>this is the answer.
99 rounded to nearest ten = 100
133 rounded to nearest ten = 130
133 rounded to nearest hundred p= 100=A
Answer: A
Question: A parking garage rents parking spaces for $10 per week or $25 per month. How much does a person save in a year by renting by the month rather than by the week?
Options:
A) $120
B) $160
C) $220
D) $240
E) $260
Rationale: 10$ per week!
An year has 52 weeks.
Annual charges per year = 52* 10 = 520$
30$ per month!
An year has 12 months.
Annual charges per year = 12 * 25 = 300$
520 - 300 = 120
Ans A
Answer: A
Question: A two years older than B who is twice as old as C. if the total of the ages of A , B and C be 27, the how old B ?
Options:
A)7
B)8
C)9
D)10
E)12
Rationale: C's age be X years. the B's age = 2X years, A's age= (2X+2)years
therefore (2X+2)+2X+X=27
5X=25
X=5
B's age 2X=10 years. correct answer (D)
Answer: D
Question: The symphony sells two kinds of tickets: orchestra, for $30, and upper tiers, for $12. On a certain night, the symphony sells 90 tickets and gets $1836 in revenue from the sales. How many orchestra tickets did they sell?
Options:
A)38
B)42
C)46
D)50
E)54
Rationale: Let x be the number of orchestra tickets.
Then 90-x is the number of upper tier tickets.
30x + 12(90-x) = 1836
18x = 1836-1080
x = 42
The answer is B.
Answer: B
Question: Pipe A can fill a tank in 8 hours, pipe B in 16 hours and pipe C in 16 hours. If all the pipes are open, in how many hours will the tank be filled?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: Part filled by A + B + C in 1 hour = 1/8 + 1/16+ 1/16= 1/4
All the three pipes together will fill the tank in 4 hours.
Answer: C
Answer: C
Question: If x^2 + 9/x^2 = 42, what is the value of x - 3/x
Options:
A)6
B)25
C)9
D)5
E)3
Rationale: To find : x-3/x. Let it be t.
=> x-3/x = t
=> (x^2 + 9/x^2) - 2*x*3/x = t^2 (Squaring both sides).
=> (42) - 2*3 = 36
=> t^2 = 36. Thus t=6 or t=-6.
Answer A
Answer: A
Question: Express 25 mps in kmph?
Options:
A)299
B)29
C)90
D)77
E)11
Rationale: 25 * 18/5 = 90 kmph Answer:C
Answer: C
Question: X, Y, and Z are different prime numbers. The product X^3*Y^2*Z^2 is divisible by how many different positive numbers?
Options:
A)24
B)36
C)48
D)60
E)72
Rationale: The exponents of X^3*Y^2*Z^2 are 3, 2, and 2.
The number of factors is (3+1)(2+1)(2+1) = 36
The answer is B.
Answer: B
Question: If x is an integer, then x(x - 1)(x - b) must be evenly divisible by three when b is any of the following values EXCEPT
Options:
A)-4
B)-2
C)-1
D)2
E)5
Rationale: here's another approach
x(x - 1)(x - b)
all three are consecutive, so the product MUST be a multiple of 3
we don't know the value of b just yet ... so let's extend the series ... the extension itself reveals the answers
..(x-5)..(x-2)(x-1)x(x+1)..(x+4)..
we can see the possible values of b too from the series
b = 2 OR 2+3n [25]
b = -1 OR -1+3n [-1-4]
B i.e. -2 does not fit in any value of b
so B it is
Answer: B
Question: Which of the following is a divisible by 11 number ?
Options:
A)92
B)80
C)30
D)120
E)121
Rationale: Explanation :
E 121 is divisible by 11
Answer : Option E
Answer: E
Question: What is the speed of the train in km/hr whose length is 360 metres which passes a pole in 18 seconds?
Options:
A)59/9 km/hr
B)50/9 km/hr
C)25/6 km/hr
D)55/18 km/hr
E)60/18 km/hr
Rationale: Speed=(18x5/18)=5 m/sec.
Length of the train= 360 metre
Time=18s
Speed=length / time
Speed=(360/8)=20 m/sec = 20*5/18 km/hr = 50/9 km/hr
Answer: B
Answer: B
Question: A man is walking at the rate of 8 km/hr crosses a bridge in 15 minutes. The length of the bridge is
Options:
A)1000 meters
B)1050 meters
C)1200 meters
D)2000 meters
E)None of these
Rationale: Explanation:
We need to get the answer in meters. So we will first of change distance from km/hour to meter/sec by multiplying it with 5/18 and also change 15 minutes to seconds by multiplying it with 60.
Speed=8âˆ—5/18=20/9m/sec
Time=15âˆ—60seconds=900seconds
Distance=Timeâˆ—Speed/Distance=20/9âˆ—900=2000meter
Option D
Answer: D
Question: Rahul's mother is the only daughter of Monika's father. How is Monika's husband related to Rahul ?
Options:
A)Uncle
B)Father
C)Grandfather
D)Brother
E)SISTER
Rationale: Explanation:
Clearly, the only daughter or Monika's father is Monika herself
So, Rahul's mother is Monika
Thus, Monika's husband is the father of Rahul.
Answer: B) Father
Answer: B
Question: Three partners shared the profit in a business in the ratio 5 : 7 : 8. They had partnered for 14 months, 8 months and 7 months respectively. What was the ratio of their investments?
Options:
A)5 : 7 : 8
B)20 : 49 : 64
C)38 : 28 : 21
D)None of these
E)Cannot be determined
Rationale: Solution: Let their investments be Rs. x for 14 months, Rs. y for 8 months and Rs. z for 7 months respectively.
Then, 14x : 8y : 7z = 5 : 7 : 8.
Now, 14x/8y = 5/7 => 98x = 40y
=> y = 49/20 x
And, 14x/7z = 5/8
=> 112x = 35z
=> z = 112/35 x = 16/5 .x.
So x : y : z = x : 49/20 x : 16/5 x = 20 : 49 : 64.
Answer: Option B
Answer: B
Question: In 1982 and 1983, Company B’s operating expenses were $12.0 million and $14.0 million, respectively, and its revenues were $15.6 million and $18.8 million, respectively. What was the percent increase in Company B’s profit (revenues minus operating expenses) from 1982 to 1983 ?
Options:
A)3%
B)16 2/3%
C)25%
D)33 1/3%
E)60%
Rationale: Profit in 1982=15.6-12.0=3.6
profit in 1983=18.8-14.0=4.8
increase in profit=4.8-3.6=1.2
percentage increase
12*100/36 =33.33 ; ANSWER:D
Answer: D
Question: Two trains of equal lengths are running at speeds of 30 kmph and 60 kmph. The two trains crossed each other in 30 seconds when travelling in opposite direction. In what time will they cross each other when travelling in the same direction?
Options:
A)90 sec
B)18 sec
C)19 sec
D)15 sec
E)11 sec
Rationale: Let the length of each train be x m.
(x + x) / (60 + 30)5/18 = (750 * 18) / (30 * 5)
= 90 sec.
Answer:A
Answer: A
Question: An accurate clock shows 8 o’clock in the morning. Through how many degrees will the hour hand rotate when the clock shows 2 o’clock in the afternoon?
Options:
A)144°
B)150°
C)168°
D)180°
E)None of these
Rationale: Angle traced by the hour hand in 6 hours
= (360⁄12 × 6)° = 180°
Answer B
Answer: B
Question: 5355 x 51 = ?
Options:
A)273105
B)273243
C)273247
D)273250
E)273258
Rationale: 5355 x 51	= 5355 x (50 + 1)
= 5355 x 50 + 5355 x 1
= 267750 + 5355
= 273105
A
Answer: A
Question: (786×74) ÷ ? = 3635.25
Options:
A)A)4.8
B)B)48
C)C)16
D)D)68
E)E)48
Rationale: Explanation:
58164/x = 3635.25 => x = 58164/3635.25 = 16
Answer: Option C
Answer: C
Question: Sides of a rectangular park are in the ratio 3: 2 and its area is 3750 sq m, the cost of fencing it at 50 ps per meter is?
Options:
A)Rs.150
B)Rs.100
C)Rs.125
D)Rs.175
E)Rs.275
Rationale: 3x * 2x = 3750 => x = 25
2(75 + 50) = 250 m
250 * 1/2 = Rs.125
ANSWER:C
Answer: C
Question: There are two cars. One is 300 miles north of the other. Simultaneously, the car to the north is driven westward at 20 miles per hour and the other car is driven eastward at 60 miles per hour. How many miles apart are the cars after 5 hours?
Options:
A)300
B)360
C)400
D)450
E)500
Rationale: Here, drawing a quick sketch of the 'actions' described will end in a diagonal line that you canbuilda right triangle around:
The right triangle will have a base of 400 and a height of 300. The hidden pattern here is a 3/4/5 right triangle (the 300 lines up with the '3' and the 400 lines up with the '4'). In this way, you can deduce that each side is '100 times' bigger than it's corresponding side:
3/4/5 becomes
300/400/500
Thus the distance between the two cars is the length of the hypotenuse of this larger right triangle...
Final Answer:E
Answer: E
Question: The average salary of all the workers in a workshop is Rs.8000. The average salary of 7 technicians is Rs.10000 and the average salary of the rest is Rs.6000. The total number of workers in the workshop is
Options:
A)20
B)21
C)22
D)23
E)14
Rationale: Solution
Let the toatl number of workers be x.
Then 8000x=(10000 x 7) + 6000 (x -7)
x= 14.
Answer E
Answer: E
Question: A and B go around a circular track of length 600 m on a cycle at speeds of 36 kmph and 60 kmph. After how much time will they meet for the first time at the starting point?
Options:
A)120 sec
B)176 sec
C)178 sec
D)187 sec
E)180 sec
Rationale: Time taken to meet for the first time at the starting point
= LCM { length of the track / speed of A , length of the track / speed of B}
= LCM { 600/ (36 * 5/18) , 600/ (60 * 5 /18) }
= 180 sec.
Answer: E
Answer: E
Question: A train 240 m long passes a pole in 24 seconds. How long will it take to pass a platform 650 m long?
Options:
A)80 sec
B)89 sec
C)99 sec
D)86 sec
E)85 sec
Rationale: Explanation:
Speed = (240/24) m/sec = 10 m/sec.
Required time =[ (240 + 650)/10) ] sec = 89 sec.
Answer:B
Answer: B
Question: There are k members in a certain department, including Michael. Two representatives are to be selected to attend a company conference. If there are 55 possible combinations in which Michael is not selected, what is the value of k?
Options:
A)11
B)12
C)15
D)18
E)22
Rationale: Combinations of two persons, in which Michael was not selected = 55
number of ways two persons can be selected from m people = m*(m-1)/2
Let m be the number of people excluding Michael, then m*(m-1) = 110 => m=11
Thus, k = m + 1(Michael) = 12
option B
Answer: B
Question: A circular rim 20 inches in diameter rotates the same number of inches per second as a circular rim 30 inches in diameter. If the smaller rim makes x revolutions per second, how many revolutions per minute does the larger rim makes in terms of x ?
Options:
A)40x
B)75x
C)48x
D)24x
E)x/75
Rationale: Revolutions - circumference of the rim.
=> 20pi*X*60 = 30pi*Revolutions
=> 2/3 *X *60 = Revolutions => 40X - Option A
Answer: A
Question: If a coin has an equal probability of landing heads up or tails up each time it is flipped , what is the probability that the coin will land Tails up exactly once in 3 consecutive flips ?
Options:
A)0.125
B)0.375
C)0.325
D)0.5
E)0.666
Rationale: Total number of ways in which H or T can appear in 3 tosses of coin is
= 2 * 2 * 2 = 8 ways
For 2 T and 1 TH
Thus probability is
= P(HTT) + P(TTH) + P(THT)
= 1/8 + 1/8 + 1/8
= 3/8
= .375
Answer :B
Answer: B
Question: Which is smallest prime number?
Options:
A)37
B)47
C)24
D)67
E)107
Rationale: Answer:A
Answer: A
Question: A man sitting in a bullet train which is travelling at 50 kmph observes that a goods bullet train , travelling in opposite direction, takes 9 seconds to pass him. If the goods bullet train is 280 m long, find its speed.?
Options:
A)44 kmph.
B)52 kmph.
C)75 kmph.
D)83 kmph.
E)62 kmph.
Rationale: E
62 kmph.
Relative speed = 280/9 m / sec = ((280/9)*(18/5)) kmph = 112 kmph.
Speed of goods train = (112 - 50) kmph = 62 kmph.
Answer: E
Question: What is the smallest integer n for which 25^n > 5^12 ?
Options:
A) 6
B) 7
C) 8
D) 9
E) 10
Rationale: To solve, we want to get the bases the same. Thus we need to break 25^n into prime factors.
25^n = (5^2)^n = 5^(2n) (Remember that when we have a power to a power, we multiply the exponents.)
We can use the new value in the given inequality:
5^(2n)> 5^12
Since we have the same bases on either side of the inequality we can drop the bases and set up an equation involving just the exponents.
2n > 12
n > 6
Because n is greater than 6, the smallest integer that satisfies the inequality 25^n > 5^12 is 7.
The answer is B.
Answer: B
Question: Two integers are in the ratio of 1 to 4. If 12 is added to the smaller number, the ratio becomes 1 to 2. Find the larger integer.
Options:
A)8
B)16
C)32
D)48
E)54
Rationale: One option is to set up the equations and solve:
If the ratio of two integers x and y is 1 to 4, then 4x=y, where x is the smaller integer.
If adding 12 to the smaller integer makes the ratio 1 to 2, then 2(x+12)=y.
Substituting y=4x into the second equation yields 2x+24=4x.
So, x=12 (smaller integer) and, y=4x=48 (larger integer) so D is the correct answer.
Another option is to TEST the answer choices.
A) the larger number is 8
Given: the two integers are in the ratio of 1 to 4
So, the smaller number must be 2
If 12 is added to the smaller number, the ratio becomes 1 to 2
If we add 12 to the smaller number (2), we get 14.
So, the new ratio is 14 to 8 which is the same as 7 to 4.
No good. We want a resulting ratio of 1 to 2
ELIMINATE A
B) the larger number is 16
Given: the two integers are in the ratio of 1 to 4
So, the smaller number must be 4
If 12 is added to the smaller number, the ratio becomes 1 to 2
If we add 12 to the smaller number (4), we get 16
So, the new ratio is 16 to 16 which is 1 to 1.
No good. We want a resulting ratio of 1 to 2
ELIMINATE B
C) the larger number is 32
Given: the two integers are in the ratio of 1 to 4
So, the smaller number must be 8
If 12 is added to the smaller number, the ratio becomes 1 to 2
If we add 12 to the smaller number (8), we get 20
So, the new ratio is 20 to 32 which is 5 to 8.
No good. We want a resulting ratio of 1 to 2
ELIMINATE C
D) the larger number is 48
Given: the two integers are in the ratio of 1 to 4
So, the smaller number must be 12
If 12 is added to the smaller number, the ratio becomes 1 to 2
If we add 12 to the smaller number (12), we get 24
So, the new ratio is 24 to 48. This is the same as the ratio of 1 to 2
Therefore (D) is correct
E) the larger number is 54
Given: the two integers are in the ratio of 1 to 4
So, the smaller number must be 13.5 (which is not an integer)
Since both numbers are integers, the larger number cannot be 54.
ELIMINATE E
Therefore D is the only correct choice.
Answer: D
Question: On a sum of money, the simple interest for 2 years is Rs. 324, while the compound interest is Rs. 340, the rate of interest being the same in both the cases. The rate of interest is
Options:
A)15%
B)14.25%
C)9.87%
D)10.5%
E)11.5%
Rationale: The difference between compound interest and simple interest on Rs. P for 2 years at R% per annum
= (R Ã— SI)/(2 Ã— 100)
Difference between the compound interest and simple interest = 340 - 324 = 16
(R Ã— SI)/(2 Ã— 100) = 16
(R Ã— 324)/(2 Ã— 100) = 16
R = 9.87%
Answer: Option C
Answer: C
Question: A two-digit number is such as the product of the digits plus the sum of the digits
is equal to the number. What is the number?
Options:
A)num 1
B)num 3
C)num 5
D)num 7
E)num 9
Rationale: Assume the 2 digit number is of the form xy, with x 6= 0. The statement indicates
that these two digits satisfy the equation xy + x + y = 10x + y. A quick simplification gives y = 9.
correct answer E
Answer: E
Question: Simplify: 1398 x 1398
Options:
A)1945450
B)1945440
C)1954440
D)1954044
E)1954404
Rationale: 1398 x 1398 - (1398)^2
= (1400 - 2)^2
= (1400)^2 + (2)^2 - 2 x 1400 x 2
=1960000 + 4 - 5600 = 1954404.
Answer is E.
Answer: E
Question: The reflex angle between the hands of a clock at 10.25 is:
Options:
A)180º
B)192	1/2 º
C)195º
D)197	1/2 º
E)197 º
Rationale: Angle traced by hour hand in 125/12 hrs ={(360/12)x(125/2)}º	= 312 1/2 º	. Angle traced by minute hand in 25 min =(360/60)x 25	º= 150º. Reflex angle = 360º -(312	1/2- 150º	)= 360º - 162 1/2º= 197 1/2º	.Answer: D
Answer: D
Question: The two trains of lengths 400 m, 600 m respectively, running at same directions. The faster train can cross the slower train in 180 sec, the speed of the slower train is 48 km. then find the speed of the faster train?
Options:
A)60
B)68
C)67
D)69
E)70
Rationale: Length of the two trains = 600m + 400m
Speed of the first train = X
Speed of the second train= 48 Kmph
1000/X - 48 = 180
1000/x - 48 * 5/18 = 180
50 = 9X - 120
X = 68 Kmph
Answer: Option B
Answer: B
Question: Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1120?
Options:
A)1000
B)2217
C)2889
D)2777
E)2991
Rationale: 1120 = P [1 + (5*12/5)/100]
P= 1000
Answer: A
Answer: A
Question: Today my car meter reads as 72927 kms. I notes that this is a palindrome. How many minimum kms i need to travel so my car meter find another palindrom.
Options:
A)100 kms
B)115 kms
C)110 kms
D)210 kms
E)120 kms
Rationale: C
110 kms
72927+110 = 73037 , a palindrome
Answer: C
Question: The difference between the place value and the face value of 9 in the numeral 856973 is
Options:
A)973
B)891
C)5994
D)6084
E)None of these
Rationale: (Place value of 9) - (Face value of 9) = (900 - 9) = 891
Answer: Option B
Answer: B
Question: The number of people who purchased book A is twice the number of people who purchased book B. The number of people who purchased both books A and B is 500, which is twice the number of people who purchased only book B. What is the number of people X who purchased only book A?
Options:
A)250
B)500
C)750
D)1000
E)1500
Rationale: This is best solved using overlapping sets or a Venn Diagram. We know that A = 2B, and that 500 people purchased both A and B. Further, those purchasing both was double those purchasing B only. This gives us 250 people purchasing B only. With the 500 that pruchased both, we have a total of 750 that purchased B and this is 1/2 of those that purchased A. So, 1500 purchased A. Less the 500 that purchased both, X=1000 purchased A only. (This is much simpler to solve using the Venn diagram).
Correct answer is D. 1000
Answer: D
Question: Look at this series: __, VIII, XI, XIV, XVII, XX, ... What number should fill the blank?
Options:
A)IX
B)XXIII
C)XV
D)V
E)None
Rationale: Explanation: This is a simple addition series; each number is 3 more than the previous number.
Answer: D
Answer: D
Question: The variable x is inversely proportional to the square of the variable y. If y is divided by 7a, then x is multiplied by which of the following?
Options:
A)1/49a
B)1/49a^2
C)1/7a
D)49a
E)49a^2
Rationale: initially - did x= 1/y^2
But this yielded the wrong answer,
I then re examined the question and tried y^2/x =1
Which I then got y = SQR(X)
subbing into y/7a I got answer E)
Answer: E
Question: A certain sum of money at simple interest amounted Rs.1200 in 12 years at 6% per annum, find the sum?
Options:
A)337
B)268
C)198
D)697
E)168
Rationale: 1200 = P [1 + (12*6)/100]
P = 697'
Answer:D
Answer: D