RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: B as a percentage of A is equal to A as a percentage of (A+B). Find B as a percentage of A.
A.62%
B.73%
C.41%
D.71%
Answer: A.62%
Explanation: Explanation :
According to the question:-
=>B/A=A/(A+B).
As B is a percent of A, let us assume B=Ax.
Then, equation (1) can be re-written as
=>x=11+x.
=>x(1+x)=1.
=>x2+x+1=0.
=>x=−1±5/√2
Thus,
x=−1+5 /√2
=>0.62.
=>62%.
Answer : A
Question: The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 8100 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units?
A.140 sq.units
B.360 sq.units
C.367sq.units
D.178sq.units
Answer: B.360 sq.units
Explanation: Given that the area of the square = 8100 sq.units
=> Side of square = √8100 = 90 units
The radius of the circle = side of the square = 90 units Length of the rectangle = 2/5 * 90 = 36 units
Given that breadth = 10 units
Area of the rectangle = lb = 36 * 10 = 360 sq.units
Answer:B
Question: At a certain store, the price of a pair of shoes is thirty dollars more than three times the price of a pair of jeans and the price of a sweater is fifty percent more than the price of a pair of shoes. If the price of a pair of jeans is j dollars at this store, then what is the price, in dollars, of a pair of shoes, a sweater and a pair of jeans, in terms of j ?
A.1.5j + 10
B.3j + 20
C.8.5j + 75
D.5.5j + 30
Answer: C.8.5j + 75
Explanation: Ans C
Given
Price of Jeans = J
Price of shoes = 30+3J
Price of Sweater = 1.5(30+3J)
Total Price of all three items = J+30+3J+1.5(30+3J) = 75+8.5J
Question: The cost of a one-family home was $ 120,000 in 1980. In 1988, the price had increased to $ 192,000. What was the percent increase in the cost of the home?
A.60%
B.50%
C.55%
D.40%
Answer: A.60%
Explanation: Increase = 192000-120000 = 72000
% increase = 72000*100/120000 = 60%
Answer: option A
Question: The ratio between the speeds of two trains is 8 : 9. If the second train runs 405 kms in 5 hours, then the speed of the first train is
A.87.5 km/h
B.72 km/h
C.70 km/h
D.80 km/h
Answer: B.72 km/h
Explanation: B
72 km/h
Question: There are 5 competitors in a race (John, mary and 3 other ones) in which there are no ties, what is the probability that mary finish ahead of john?
A.1/6
B.1/3
C.1/2
D.2/3
Answer: C.1/2
Explanation: Mary has equal chances of finishing ahead of John as John has chances of finishing ahead of mary
But, Probability for Mary finishing ahead of John + Probability for John finishing ahead of Mary = 1
Hence Probability for Mary finishing ahead of John = 1/2
Answer: Option C
Question: You hold some gold in a vault as an investment. Over the past year the price of gold increases by 30%. In order to keep your gold in the vault, you must pay 2% of the total value of the gold per year. What percentage has the value of your holdings changed by over the past year.
A.27.5%
B.27.4%
C.27.6%
D.27.7%
Answer: B.27.4%
Explanation: (100%+30%)*(100%-2%) = 130*0.98= 127.4% an increase of 27.4%
Your gold holdings have increased in value by 27.4%.
The Answer is B
Question: George while driving along the highway saw road markers which are at equal distances from each other. He crosses the markers every 20 seconds. If he increases his speed by x meters per second, he crosses the markers at every 15 seconds. But if he increases his speed by y meters per second, he crosses the marker at every 10th second. If y-x = 40 meters per second, then what is the distance between two markers.
A.2377
B.2788
C.1200
D.2778
Answer: C.1200
Explanation: Let speed be =z m/s then Distance= 20z m
(z+x)15=20z; (z+y)10=20z
Also given that y - x = 40
solving we get 20z=1200
Answer:C
Question: Ratio between Rahul and Deepak is 4:3, After 6 Years Rahul age will be 26 years. What is Deepak present age.
A.14
B.15
C.20
D.22
Answer: B.15
Explanation: Explanation:
Present age is 4x and 3x,
=> 4x + 6 = 26 => x = 5
So Deepak age is = 3(5) = 15
Option B
Question: The distance between Delhi and Mathura is 110 kms. A starts from Delhi with a speed of 40 kmph at 7 a.m. for Mathura and B starts from Mathura with a speed of 25 kmph at 8 p.m. from Delhi. When will they meet?
A.9.04 a.m.
B.10.00 a.m.
C.12.00 a.m.
D.18.00 a.m.
Answer: A.9.04 a.m.
Explanation: Explanation:
D = 110 â€“ 40 = 70
RS = 40 + 25 = 65
T = 70/65 = 1 hours 04 minutes
8 a.m. + 1 hours 04 minutes = 9:04 a.m.
Answer: Option A
Question: The difference between the place values of two nines in the numerical 62039295 is
A.89
B.891
C.8910
D.0
Answer: C.8910
Explanation: Required difference = (9000-90)
=8910.
Answer is C
Question: A boy wants to go abroad by boat and return by flight. He has a choice of 4 different boat to go and 5 flight to return. In how many ways, can the boy perform his journey?
A.20
B.30
C.43
D.45
Answer: A.20
Explanation: Ans.(a)
Sol. Number of choices to go by ship = 4 Number of choices to return by airline = 5 From, fundamental principle, total number of ways of performing the journey = 4 x 5 = 20 ways
Question: If p#q denotes the least common multiple of p and q, then P=((12#16)#(18#24)) = ?
A. 216
B. 180
C. 144
D. 108
Answer: C. 144
Explanation: There are several ways to find the Least Common Multiple of two numbers. In this case, the most efficient method is to use the Greatest Common Factor: (A * B) / (GCF AB) = LCM AB
The greatest common factor of 12 and 16 is 4. So, 12#16 = 12*16/4 = 48.
The greatest common factor of 18 and 24 is 6. So, 18#24 = 18*24/6 = 72
Finally, the greatest common factor of 48 and 72 is 24. So,P= ((12#16)#(18#24)) = 48#72 = (48*72)/24 = 2*72 = 144
The correct answer is C.
Question: If f=1 and (f-b)/c = 1 which of the following is NOT a possible value of b?
A.-2
B.-1
C.0
D.1
Answer: D.1
Explanation: Equation is:
(f-b)/c = 1 where f = 1
so plug in 1 for f and look at it again
(1-b)/c = 1
now C can be anything we want, so if b = -2 we can plug it in and make it work
(1-(-2))/c = 1
3/c = 1
c = 3 and it works
HOWEVER, if we have a 0 in the numerator there isn't a number on earth that makes 0/C = 1
(1-1)/c = 1
0/c = 1
there aren't any matches for C to make this true
B cannot be 1.
Answer is D
Question: In covering a distance of 36 km, A takes 2 hours more than B. If A doubles his speed, then he would take 1 hour less than B. A's speed is:
A.5 km/h
B.6 km/h
C.10 km/h
D.15 km/h
Answer: B.6 km/h
Explanation: Let A's speed be X km/hr.
Then, 36/x - 36/2x = 3
6x = 36
x = 6 km/hr.
Answer : B.
Question: The sum of the first k positive integers is equal to k(k+1)/2. What is the sum of the integers from p to q, inclusive, where 0<p<q?
A.q(q+1)/2 - (p+1)(p+2)/2
B.q(q+1)/2 - p(p+1)/2
C.q(q+1)/2 - (p-1)p/2
D.(q-1)q/2 - (p+1)(p+2)/2
Answer: C.q(q+1)/2 - (p-1)p/2
Explanation: Or try plug-in method: let q=4 and p=3 --> then q+p=7. Let see which option yields 7.
A. q(q+1)/2 - (p+1)(p+2)/2 = 10-10=0;
B. q(q+1)/2 - p(p+1)/2 = 10-6=4;
C. q(q+1)/2 - (p-1)p/2 = 10-3=7 --> OK;
D. (q-1)q/2 - (p+1)(p+2)/2 = 6-10=-4;
E. (q-1)q/2 - p(p+1)/2 = 6-6=0.
Answer: C.
Question: A sum of Rs. 2900 amounts to Rs. 3422 in 3 years. Had the rate of interest be 1% higher then what would the sum amount in the same time period?
A.Rs. 3509
B.Rs. 3683
C.Rs. 3596
D.Data inadequate
Answer: A.Rs. 3509
Explanation: 3422=2900+(2900*R*3/100)
R=6
If R is 1 more.
Then R=7
Sum=2900+(2900*7*3/100)
Sum=3509
ANSWER:A
Question: Calculate the speed of a boat in still water (in km/hr) if in one hour, the boat goes 13 km/hr downstream and 10 km/hr upstream.
A.3 kmph
B.9 kmph
C.4 kmph
D.8 kmph
Answer: B.9 kmph
Explanation: Speed in still water = (13 + 5)1/2 kmph = 9 kmph.
answer :B
Question: A man can do a piece of work in 5 days, but with the help of his son, he can do it in 4 days. In what time can the son do it alone?
A.15
B.17
C.20
D.8
Answer: C.20
Explanation: Son's 1day's work = (1/4)-(1/5) = 1/20
The son alone can do the work in 20 days
Answer is C
Question: The average (arithmetic mean) of 20, 40, and 60 is 5 more than the average of 10, 60, and what number?
A.30
B.35
C.40
D.45
Answer: B.35
Explanation: a1 = 120/3 = 40
a2 = a1 -5 = 35
sum of second list = 35*3 = 105
therefore the number = 105 -70 = 35
B
Question: A man can row upstream at 5km/hr and down stream at 13km/hr find mans rate in still water ?
A.7.5km/hr
B.3.5km/hr
C.9km/hr
D.4km/hr
Answer: C.9km/hr
Explanation: given upstream(u) =5km/hr
down stream (v)= 13km/hr rate in still water =1/2(u+v)=1/2(5+13)=9km/hr Answer is (C)
Question: If g is a number such that –2 ≤ g ≤ 2, which of the following has the largest possible absolute value?
A.3g – 1
B.x^2 + 1
C.3 – x
D.x – 3
Answer: A.3g – 1
Explanation: Ans is A .. leads to the max value of 7 for g = -2
Question: Find the number of different prime factors of 441
A.4
B.2
C.3
D.5
Answer: B.2
Explanation: Explanation:
L.C.M of 441 = 3 x 3 x 7 x 7
3, 7
Number of different prime factors is 2.
Answer: Option B
Question: Bhanu spends 30% of his income on petrol on scooter 12% of the remaining on house rent and the balance on food. If he spends Rs.300 on petrol then what is the expenditure on house rent?
A.62
B.140
C.84
D.60
Answer: C.84
Explanation: Given 30% (Income ) = 300 ⇒⇒ Income = 1000
After having spent Rs.300 on petrol, he left with Rs.700.
His spending on house rent = 12% (700) = Rs.84
Answer:C
Question: Elvin's monthly telephone bill is the sum of the charge for the calls he made during the month and a fixed monthly charge for Internet service. Elvin's total telephone bill for January was $48 and Elvin's total telephone bill for February was 90$. If Elvin's charge for the calls he made in February was twice the charge for the calls he made in January, what is Elvin's fixed monthly charge for Internet service?
A.$5
B.$10
C.$14
D.$6
Answer: D.$6
Explanation: Bill = Fixed Charge + Charge of Calls made
in Jan, Bill = Fixed Charge(Let, y) + Charge of calls made in Jan (Let, x) = $48
in Feb, Bill = Fixed Charge (Let, y) + Charge of calls made in Feb (Then, 2x) = $90
i.e. x+y = 48
and 2x+y = 90
Take the difference if two equations
i.e. (2x+y) - (x+y) = 90 - 48
i.e. x = 42
i.e. Fixed Monthly Charge, y = 6
Answer: Option
D
Question: Chloe has $27 dollars to go to the fair. she is bringing 2 other friends along. Admission to the fair is $3. Each ride costs $1.70. How many rides can she and her friends go on and how much money will be left over?
A.They can go on 15 rides and $1.50 will be left over.
B.They can go on 3 rides and $2.70 will be left over.
C.They can go on 7 rides and $0 will be left over.
D.They can go on 6 rides and $0 will be left over.
Answer: B.They can go on 3 rides and $2.70 will be left over.
Explanation: Admission to the fair is $3 per person. If she wants her and her friends to go, the cost will be $9. 27-9 is 18. To go on a ride is $5.10. 5.10 x 3 is 15.30. 18-15.30 is 2.70. They can go on 3 rides and $2.70 will be left over. The correct answer is B.
Question: On one side of a coin there is the number 0 and on the other side the number 1. What is the probability that the sum of three coin tosses will be 1?
A.1/8.
B.1/2.
C.3/8.
D.5/8.
Answer: C.3/8.
Explanation: Assume the coin is unbiased.
Possible sums from 3 tosses = 0,1,2,3
O and 3 are possible in only 1 case each. (0,0,0 or 1,1,1)
1 is possible in 3C1 = 3 cases. (1,0,0; 0,1,0 or 0,0,1) or
similarly, 2 is possible in 3C2=3 cases (1,0,1; 1,1,0; 0,1,1)
So answer will be 3/8. Option 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?
A.4082.8
B.408
C.40
D.4082.4
Answer: D.4082.4
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 * 7) = 315 (13 - 0.04) = 4095 - 12.6 = Rs. 4082.40
Answer: Option D
Question: Three numbers are in the ratio of 3 : 4 : 6 and their product is 1944. The largest of these numbers is
A.6
B.12
C.18
D.26
Answer: C.18
Explanation: Solution
Let the numbers be 3x, 4x and 6x.
Then, 3x × 4x × 6x = 1944
‹=›72x3 = 1944
‹=›x3 = 27
‹=›x = 3
Therefore, Largest number = 6x = 18.
Answer C
Question: How many Numbers can be formed with digits 2,4,6,8 without repetition?
A.124
B.256
C.64
D.84
Answer: C.64
Explanation: Number of one digit numbers = 4
Number of two digit numbers = 4 P 2 = 12
Number of Three digit numbers = 4 P 3 = 24
Number of four digit numbers = 4 P 4 = 24
So, total = 24 + 24 + 12 + 4 = 64
ANSWER:C
Question: The ratio of two numbers is 4 : 7 and their H.C.F. is 4. Their L.C.M. is
A.112
B.22
C.56
D.27
Answer: A.112
Explanation: Explanation:
Let the numbers be 4x and 7x. Then, their H.C.F. = x. So, x = 4.
So, the numbers 16 and 28.
L.C.M. of 16 and 28 = 112.
Answer: Option A
Question: The list price of an article is Rs.65. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is?
A.3%
B.4%
C.7%
D.8%
Answer: B.4%
Explanation: Explanation:
65*(90/100)*((100-x)/100) = 56.16
x = 4%
Answer: Option B
Question: Two whole numbers whose sum is 42 cannot be in the ratio
A.2:5
B.1:6
C.2:4
D.3:8
Answer: D.3:8
Explanation: D) 3:8
Question: If |r+s|=|r-s|, then r*s must be equal to:
A.-2
B.2
C.0
D.-3
Answer: C.0
Explanation: Solution 1: Distance perspective
|r-s| = |r+s| ==> The distance of r and s is equal to the distance of r and -s.
<=======(-s)=======0=======(s)======>
Only 0 is the value that has a distance equal to s and -s.
Solution 2:
|r-s| = |r+s| (square both)
r^2 -2rs + s^2 = r^2 + 2rs + s^2
4rs = 0
rs = 0
Answer: C
Question: 105,100,...,90,85,80,75
Insert the missing number
A.95
B.78
C.83
D.84
Answer: A.95
Explanation: Missing number : 95
Answer : A
Question: Mr. Thomas invested an amount of Rs. 13,900 divided in two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be Rs. 3508, what was the amount invested in scheme B?
A.6400
B.6408
C.6406
D.6405
Answer: A.6400
Explanation: Let the sum invested in scheme A be Rs. x and that in scheme B be Rs. (13900 - x). Then,
(x * 14 * 2)/100 + [(13900 - x) * 11 * 2]/100 = 3508
28x - 22x = 350800 - (13900 * 22)
6x = 45000 => x = 7500
So, sum invested in scheme B = (13900 - 7500) = Rs. 6400.
Answer: A
Question: A passenger sitting near the window in a train moving at 40 km/h, noticed that it took 3 sec. for the oncoming train to pass by. What was the speed of the oncoming train if the length of the oncoming train was 69 metres?
A.a)50km/h
B.b)42.8km/h
C.c)56km/h
D.d)60km/h
Answer: B.b)42.8km/h
Explanation: im getting A
3 secs to pass a 75 mts train , therefore speed = 23 meters/sec
to convert m/s to km/hrs multiply by 3.6
23*3.6 = 90
so its 82.8-40 = 42.8 .
B
Question: The ratio, by weight, of coffee to sugar to water in a pot of coffee is 4:1:15. The ratio is then altered so that the ratio of coffee to sugar is halved while the ratio of coffee to water is doubled. If the altered pot of coffee contains 16 grams of sugar, how many grams of water does it contain after alteration?
A.64
B.60
C.56
D.52
Answer: B.60
Explanation: The new ratio of coffee to sugar is 2:1
The new ratio of coffee to water is 8:15.
The new ratio of coffee to sugar to water is 8:4:15.
If there are 16 grams of sugar, then there are (15/4)*16=60 grams of water.
The answer is B.
Question: A person covered one-fourth of the total distance at 25 kmph and remaining distance at 24 kmph. What is the average speed for the total distance?
A.21 (1/8)
B.21 (1/33)
C.24 (8/33)
D.29 (1/33)
Answer: C.24 (8/33)
Explanation: Let the total distance be x km
total time taken = (x/4)/25 + (3x/4)/24 = x/100+ x/32 = 33x/800
Average speed = x/(33x/800) = 24 8/33 kmph.
Answer: C
Question: The cost per liter of petrol during a 4 year period is as follows:
Year 1, $1 per liter ;
Year 2, $1.5 per liter ;
Year 3, $1.2 per liter ;
Year 4, $2 per liter .
If a factory spent equal dollars on petrol each year, what was the average cost of a liter of petrol during the 4 year period?
A.$1.22
B.$1.333
C.$1.425
D.$1.175
Answer: B.$1.333
Explanation: Let money spent each year = $6
liters bought first year = 6
liters bought second year = 4
liters bought third year = 5
liters bought fourth year = 3
Total number of liters = 18
Total money spent = 6*4 = 24
Average = 24/18 = 4/3 = 1.33
Answer is B
Question: If n denotes a number to the left of 0 on the number line such that the square of n is less than 1/36, then the reciprocal of n must be
A.Less than -6
B.Between -1 and -1/6
C.Between -1/6 and 0
D.Between 0 and 1/6
Answer: A.Less than -6
Explanation: n^2 < 1/36
abs(n) < 1/6
Since n<0, then 0 > n > -1/6
1/n < -6
The answer is A.
Question: Everyone shakes hands with everyone else in a room. Total number of handshakes is 105. Number of persons=?
A.14
B.12
C.11
D.15
Answer: D.15
Explanation: In a room of n people, the number of possible handshakes is C(n,2) or n(n-1)/2
So n(n-1)/2 = 105 OR n(n-1)=210 OR n=15
Answer is (D)
Question: Average score in 10 matches is 32, How many runs one should should score to increase his average by 4
runs.
A.70
B.76
C.78
D.80
Answer: B.76
Explanation: Average after 11 innings should be 36
So, required score = (11 * 36) - (10 * 32)
= 396 - 320 = 76
Answer: Option B
Question: The simple interest accrued on an amount of Rs.49500 at he end of three is Rs.17820. What would be the compound interest accured on the same amount at teh same rate in the same period? (Round off your answer to two decimal places)
A.Rs.20043.94
B.Rs.20043.97
C.Rs.20043.96
D.Rs.20043.16
Answer: A.Rs.20043.94
Explanation: Let the rate of interest be R% p.a.
(49500)(3)(R)/100 = 17820
495R = 5940
R = 12
CI on Rs.49500 at 12% p.a. for three years
= 49500{[1 + 12/100]3 - 1} = 69543.936 - 49500 = Rs.20043.94
when rounded off to two decimal places.
Answer:A
Question: Rahim bought 42 books for Rs.520 from one shop and 22 books for Rs.248 from another. What is the average price he paid per book ?
A.s.17
B.s.18
C.s.12
D.s.11
Answer: C.s.12
Explanation: Average price per book
= (520 + 248) / (42 + 22) = 768/ 64
= Rs.12
Answer:C
Question: In a class total 34 students, 16 are have a brother, 15 are have sisters, 9 students don't have either brothers or sisters.Find the number of students having both brother and sisters.
A.4
B.5
C.6
D.7
Answer: C.6
Explanation: Total Number of students = 34
Let A be the Number of students have a brothers.
Let B be the number of students have a sisters.
AUB = Number of students have either brothers or sisters=34-9=25
n(AUB)= n(A)+n(B)-n(AnB)
25=16+15-n(AnB)
n(AnB)=31-25
n(AnB)=6
The number of students having both brother and sisters = 6
ANSWER:C
Question: What is the greatest 5-digit number when divided by 6, 7 ,8 , 9, and 10 leaves a remainder of 4, 5, 6, 7, and 9 respectively?
A.56780
B.78910
C.97479
D.97918
Answer: C.97479
Explanation: When you divide a positive integer by 10, the remainder will just be the units digit. We know the remainder is 9 when we divide by 10, so C is the only possible answer.
Question: The inverse ratio of 6: 2: 1 is?
A.2:3:7
B.2:3:9
C.2:3:2
D.1:3:6
Answer: D.1:3:6
Explanation: 1/6: 1/2: 1/1 = 1:3:6
Answer:D
Question: If f(x) = ax^5 – 3x^2 + ax^2 – x, then f(b) – f(-b) will equal:
A.0
B.2ab
C.2ab^4 – 6
D.2ab^5-2b
Answer: D.2ab^5-2b
Explanation: f(x)=ax^5 – 3x^2 + ax^2 – x
f(b) = ab^5 – 3b^2 + ab^2 – b
f(-b) = -ab^5 – 3b^2 + ab^2 + b
f(b) - f(-b) = ab^5 – 3b^2 + ab^2 – b + ab^5 + 3b^2 - ab^2 – b
=2ab^5-2b
Answer D
Question: For the set { 3, 3, 4, 4, 5, 5, x}, which of the following values of x will most increase the standard deviation?
A.(-3)^2
B.2
C.3
D.4
Answer: A.(-3)^2
Explanation: Standard Deviation Step 1, as pointed out by others, is to find out the mean = 4
Step 2, For each number: subtract the Mean and square the result =
(1-4)^2=(-3)^2
(2-4)^2=(-2)^2
(3-4)^2 =(-1)^2
(4-4)^2=(.0)^2
(5-4)^2=(1)^2
Clearly (1-4)^2=(-3)^2 will give you the greatest value among all the other options.
Hence A
Question: Gold is 10 times as heavy as water and copper is 5 times as heavy as water. In what ratio should these be mixed to get an alloy 9 times as heavy as water?
A.3:2
B.1:2
C.4:1
D.5:2
Answer: C.4:1
Explanation: G = 10W
C = 5W
Let 1gm of gold mixed with x gm of copper to get 1+x gm of the alloy
1gm gold + x gm copper = x+1 gm of alloy
10W+5Wx = x+1 * 9W
10+5x = 9(x+1)
x = 1/4
Ratio of gold with copper = 1:1/4 = 4:1
Answer is C
Question: How many 6 digit telephone numbers can be formed if each number starts with 35 and no digit appears more than once?
A.720
B.360
C.1420
D.1680
Answer: D.1680
Explanation: 6 digit number where first 2 digit are fixed .
1*1*8*7*6*5 =1680
ANSWER:D
Question: The number of arrangement of letters of the word BANANA in which the two N's do not appear adjacently is:
A.40
B.50
C.. 60
D.80
Answer: A.40
Explanation: Total # of arrangements of BANANA is 6!/(3!2!) = 60 (arrangement of 6 letters {B}, {A}, {N}, {A}, {N}, {A}, where 3 A's and 2 N's are identical).
The # of arrangements in which the two N's ARE together is 5!/3!=20 (arrangement of 5 units letters {B}, {A}, {A}, {A}, {NN}, where 3 A's are identical)..
The # of arrangements in which the two N's do not appear adjacently is {total} - {restriction} = 60 - 20 = 40.
Answer: A.
Question: Bill has a small deck of 14 playing cards made up of only 2 suits of 7 cards each. Each of the 7 cards within a suit has a different value from 1 to 7; thus, there are 2 cards in the deck that have the same value. Bill likes to play a game in which he shuffles the deck, turns over 4 cards, and looks for pairs of cards that have the same value. What is the chance that Bill finds at least one pair of cards that have the same value?
A.8/67
B.61/130
C.17/33
D.63/143
Answer: D.63/143
Explanation: P(no pairs) = 12/13*10/12*8/11 = 80/143
P(at least one pair) = 1 - 80/143 = 63/143
The answer is D.
Question: In a theater, the first row has 15 seats and each row has 2 more seats than previous row. If the last row has 53 seats, what is the total number of seats in the theater?
A.600
B.640
C.680
D.720
Answer: C.680
Explanation: The number of seats in the theater is
15 + (15+2) + ...+ (15+38)=
20(15) + 2(1+2+...+19)=
20(15) + 2(19)(20)/2=
20(15+19) = 20(34) = 680
The answer is C.
Question: In an xy-coordinate plane, a line is defined by y = kx + 1. If (4, b), (a,3), and (a, b+1) are three points on the line, where a and b are unknown, then k = ?
A. 1/2
B. 1/4
C. 3/2
D. 2
Answer: B. 1/4
Explanation: b=4k+1...(1)
b+1=ak+1...(2)
3=ak+1...(3)
Taking (2) and (3)
3=b+1
b=2
Taking (1)
2=4k+1
k=1/4
Answer : B
Question: What is the greatest prime factor of 8^13 - 2^30?
A.23
B.37
C.59
D.73
Answer: D.73
Explanation: 8^13 - 2^30
=(2^3)^13 - 2^30
= 2^39 - 2^30
= 2^30 (2^9 -1)
= 2^30 * (512-1)
= 2^30 * 511
= 2^30 * 7 * 73
The greatest prime factor is 73.
The answer is D.
Question: Ten identical machines, running continuously at the same constant rate, take 6 days to complete a shipment. How many additional machines, each running at the same constant rate, would be needed to reduce the time required to complete a shipment by four days?
A.25
B.20
C.14
D.9
Answer: B.20
Explanation: From the question you know that 10R = 1/6. The question asks you (partially) to make the rate from 1/6 to 1/2 (drop from 6 day to 2). So the only thing that you need to do is to find the magic number than can convert 1/6 to 1/2.
So 1/6 * x = 1/2 (1 equation with one unknown). So by solving this you get x = 6/2 or 3/1. Thats it then! Take the magic number 3/1 and multiply BOTH sides of the original equation and you have:
10*(3/1)*R = (3/1) * 1/6
10 * 3 * R = 1/2, Hence 30R = 1/2, therefore 20 more machines!
B