RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A larger cube has 8 cubic inch as a volume and in the cube there are 8 smaller cubes such that their volume is 1 cubic inch. What is the difference between the surface areas’ sum of the 8 smaller cubes and the surface area of the larger cube, in square inch?
A.24
B.64
C.81
D.108
Answer: A.24
Explanation: Volume of larger cube = 8 = 2^3
Side of larger cube = 2
Volume of smaller cube = 1 --> Side of smaller cube = 1
Surface area of larger cube = 6 * 2^2 = 24
Surface area of 27 smaller cubes = 8 * 6 * 1 = 48
Difference = 48 - 24 = 24
Answer: A
Question: A certain club has 11 members, including Harry. One of the 11 members is to be chosen at random to be the president, one of the remaining 10 members is to be chosen at random to be the secretary, and one of the remaining 9 members is to be chosen at random to be the treasurer. What is the probability that Harry will either be the secretary or the member chosen to be the treasurer?
A.1/4
B.2/11
C.3/11
D.5/11
Answer: B.2/11
Explanation: Each member out of 11, including Harry, has equal chances to be selected for any of the positions (the sequence of the selection is given just to confuse us). The probability that Harry will be selected to be the secretary is 1/11 and the probability that Harry will be selected to be the treasurer is also 1/11. So, the probability that Harry will be selected to be either the secretary or the the treasurer is 1/11+1/11=2/11.
Answer: B.
Question: In how many ways can the letters of the word "PROBLEC" be rearranged to make 7 letter words such that none of the letters repeat?
A.4!
B.5!
C.7!
D.8!
Answer: C.7!
Explanation: There are seven positions to be filled.
The first position can be filled using any of the 7 letters contained in PROBLEM.
The second position can be filled by the remaining 6 letters as the letters should not repeat.
The third position can be filled by the remaining 5 letters only and so on.
758
Therefore, the total number of ways of rearranging the 7 letter word = 7*6*5*4*3*2*1 = 7! Ways.
C
Question: Tub A and tub B contain 540 liters of water each. Every minute tub A loses 25 liters of water while tub B loses 15 liters. If in X minutes tub B will contain 6 times as much water as tub A, what is X?
A.15
B.20
C.25
D.30
Answer: B.20
Explanation: The equation is 6(540−25X)=540−15X from where X=20
Answer: B
Question: Two pipes A and B can fill a cistern in 20 and 30 minutes respectively, and a third pipe C can empty it in 40 minutes. How long will it take to fill the cistern if all the three are opened at the same time?
A.17 1/7
B.17 1/6
C.17 1/7
D.17 1/1
Answer: C.17 1/7
Explanation: 1/20 + 1/30 - 1/40
= 7/120
120/7
= 17 1/7
Answer: C
Question: Find the number which is nearest to 3105 and is exactly divisible by 21.
A.1208
B.3108
C.241
D.217
Answer: B.3108
Explanation: Sol. On dividing 3105 by 21, we get 18 as remainder.
Number to be added to 3105 = (21 - 18) - 3.
Hence, required number = 3105 + 3 = 3108.
Option B
Question: Raj is working on a set of Data Sufficiency problems for his December GMAT: a geometry problem, an algebra problem, and a data interpretation problem. He has determined that statement 1 of the geometry problem is insufficient on its own, that both statement 1 and 2 of the algebra problem are insufficient on their own, and that statement 2 of the data interpretation problem is insufficient on its own. If the probabilities are expressed as percents Q, approximately how much greater is the probability that all three answers are “C” after Raj figures out that statement 1 of the data interpretation problem is also insufficient on its own?
A.Q=2.3%
B.Q=2.8%
C.Q=3.3%
D.Q=5.6%
Answer: B.Q=2.8%
Explanation: Step 1: Figure out what we need to know.We have two probabilities that we need to figure out: the one before Raj figures out that statement 1 of the data interpretation problem is also insufficient, and the one after. The answer is the difference between them, in the form of a percent.
Step 2: The first probability.
If statement 1 of the geometry problem is insufficient, then the only valid answer choices are B, C, and E; the probability that it is C is 1/3.
If both statements of the algebra problem are insufficient on their own, then the only remaining valid answers are C and E; the probability that it is C is 1/2
If statement 2 of the data interpretation problem is insufficient, then the remaining answers are A, C, and E, and the probability that C is correct is 1/3.
The probability of all three occurring is the product of the probability fractions: (1/3)*(1/2)*(1/3) = 1/18.
Step 3: The second probability.
Only the third problem has changed; if Raj now knows that statement 1 is also insufficient, the valid answer choices are only C and E, leaving a 1/2 probability that the answer is C.
The probability of all three occurring is still the product of those fractions, but this time they are (1/3)*(1/2)*(1/2) = 1/12.
Step 4: The answer.Note that here, as will sometimes happen on the GMAT, values that you compute “along the way” appear as wrong answer choices. This problem calls for the difference between our two numbers,Q (1/12)-(1/18) = 1/36, which is a 2.77777% chance, rounded to 2.8% —the correct answer is Choice B.
Question: A 5% stock yields 10%. The market value of the stock is:
A.Rs.56
B.Rs.55
C.Rs.50
D.Rs.90
Answer: C.Rs.50
Explanation: Explanation:
For an income of Rs. 10, investment = Rs. 100.
For an income of Rs 5, investment =Rs.100/10 X5 =Rs 50
Market value of Rs. 100 stock = Rs.50
Answer is C
Question: If two numbers are in the ratio 2:3. If 5 is subtracted from both of the numbers then the ratio becomes 3:4 then find the smallest number?
A.5
B.10
C.20
D.40
Answer: B.10
Explanation: Given Ratio -> 2:3
2x - 5 : 3x - 10 = 3 : 4
4[2x - 5] = 3[3x - 5]
8x - 20 = 9x - 15
9x - 8x = 20 - 15
x = 5
Then smallest number is = 2x
2x = 10
Ans - B
Question: The average of numbers 0.44204, 0.44203, 0.44202 and 0.44201 is ?
A.0.44202
B.0.44204
C.0.442022
D.0.442025
Answer: D.0.442025
Explanation: Answer
Average = (0.44204 + 0.44203 + 0.44202 + 0.44201)/ 4
=1.7681/ 4
=0.442025
Correct Option: D
Question: The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
A.76 m
B.178 m
C.245 m
D.187 m
Answer: C.245 m
Explanation: Speed = [45 X 5/18] m/sec
= [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30 = 25/2
=> 2(130 + x)
= 750 => x = 245 m.
Answer: C
Question: Walking 7/6 of his usual rate, a boy reaches his school 4 min early. Find his usual time to reach the school?
A.22
B.87
C.66
D.28
Answer: D.28
Explanation: Speed Ratio = 1:7/6 = 6:7
Time Ratio = 7:6
1 -------- 7
4 --------- ? è 28 m
Answer: D
Question: In a classroom, the average age of boys (b) is g and the average age of girls (g) is b. The average age of all is b+g. At the time of calculation, the class teacher, who is 42 years old was also present in the class. Can you find the value of b+g?
A.8
B.3
C.7
D.9
Answer: A.8
Explanation: A
b+g = 8
for b in range(1,99):
for g in range(1,99):
sum1=2*b*g+42
sum2=(b+g)*(b+g+1)
if(sum1==sum2):
print(b,g,sum1)
(b,g)=(3,5) => b+g=8
Question: 6 friends visited a book stall and brought 6 books, and everyone decided to contribute equally to the total bill of $400. If one of the friends had a coupon for 5% off the total bill, and if each friend still contributed equally after the coupon was applied to the bill, how much did each friend pay?
A.62.12
B.63
C.63.33
D.64
Answer: C.63.33
Explanation: At the non-discounted price, each friend would pay $66.66, as $400 divided by 6 friends is $66.66 per friend. But if the bill is 5% off, then each friend would pay 5% less. 5% of $66.66 is $3.33, so each friend saves $3.33 and pays the remaining $63.33
CORRECT OPTION:OPTION C
Question: The average age of seven persons sitting in a row facing east is 28 years. If the average age of the first three persons is 21 years and the average age of the last three persons is 34 years, then find the age of the person sitting in the middle of the row?
A.76 years
B.31 years
C.45 years
D.13 years
Answer: B.31 years
Explanation: Total age seven persons = (28 * 7)years
Total age of the first three persons and the last three persons are (21 * 3) years and (34 * 3) years respectively.
Age of the person sitting in the middle of the row
= 28 * 7 - 21 * 3 - 34 * 3 = 196 - 63 - 102
= 31 years.
Answer: B
Question: Bob wants a bunch of bananas and insists that the bunch contains a prime number of bananas. The bunches contain the following number of bananas. Which bunch should Bob buy?
A.4
B.5
C.6
D.8
Answer: B.5
Explanation: Bunch B has a prime number of bananas.
Question: Two trains travelling in the same direction at 58 and 22 kmph completely pass off another in 1 minute. If the length of the first train is 110 m, what is the length of the second train?
A.800 m
B.110 m
C.600 m
D.490 m
Answer: D.490 m
Explanation: RS = 58 â€“ 22= 36 * 5/18 = 10 mps
T = 60 sec
D = 10 * 60 = 600 m
110
--------
490 m
Answer: D
Question: By selling an umbrella for Rs. 300, a shopkeeper gains 20%. During a clearance sale, the shopkeeper alows a discount of 10% on the marked price. His gain percent during the sale is :
A.6
B.7
C.8
D.9
Answer: C.8
Explanation: Sol.
Marked price = Rs. 300. C.P. = Rs. [100 / 120 * 300] = Rs.250.
Sale price = 90% of Rs. 300 = Rs. 270.
∴ Required gain% = [20 / 250 * 100] % = 8%.
Answer C
Question: Which among the following represents a sum of 3 consecutive even integers?
A.200
B.303
C.400
D.564
Answer: D.564
Explanation: Sum of three consecutive Even Integers must be a multiple of 2 as well as a multiple of 3 because such a sum is always 3 times the middle number (applicable to all equally spaced numbers)
Divisibility of 3: Sum of the digits of the number must be divisible by 3
Divisibility of 2: Unit digit of the number must be divisible by 2
A. 200NOT A MULTIPLE OF 3 SO RULED OUT
B. 303NOT A MULTIPLE OF 2 SO RULED OUT
C. 400NOT A MULTIPLE OF 3 SO RULED OUT
D. 564 A MULTIPLE OF 3 and 2 THE CORRECT ANSWER!!!
D
Question: The probability that A speaks truth is 4/5 and that of B speaking truth is 3/4. What is the probability that they agree in stating the same fact?
A.18/35
B.12/35
C.9/10
D.19/35
Answer: C.9/10
Explanation: If both agree stating the same fact, either both of them speak truth of both speak false.
Probability = 4/5 * 3/4 + 3/5 * 2/4
= 12/20 + 6/20 = 18/20 = 9/10
ANSWER:C
Question: For each hour of production, a certain factory requires 1 assembly line worker for every 25 units to be produced in that hour. The factory also requires 10 managers regardless of the number of units to be produced. Which of the following expressions represents the total number of assembly line workers and managers that this factory requires to produce 50N in one hour, where N is a positive integer?
A.12 + 50N
B.12 + 2N
C.10 + 2N
D.37N
Answer: C.10 + 2N
Explanation: 25 units = 1 worker;
50N units = 50N/25 = 2N workers.
So, the answer is 2N workers plus 10 managers.
Answer: C.
Question: The compound interest earned by Sunil on a certain amount at the end of two years at the rate of 8% p.a. was Rs.2828.80. Find the total amount that Sunil got back at the end of two years in the form of principal plus interest earned
A.19828.88
B.19828.8
C.19828.87
D.19828.81
Answer: B.19828.8
Explanation: Let the sum be Rs.P
P{ [ 1 + 8/100]2 - 1 } = 2828.80
P(8/100)(2 + 8/100) = 2828.80 [a2 - b2 = (a - b) ( a + b)] P = 2828.80 / (0.08)(2.08) = 1360/0.08 = 17000 Principal + Interest = Rs. 19828.80
Answer: B
Question: Income of A is 25% more than the income of B. What is the income of B in terms of income of A?
A.80%
B.8%
C.82
D.27
Answer: A.80%
Explanation: Explanation:
One of the most basic questions.
Let income of B be 100. Income of A is 25% more than income of B which means Income of A becomes 125
Now income of B in terms of A = 100/125 *100 = 80%
ANSWER: A
Question: A solution is made of water and pure acid. If 75% of the solution is water, how many litters of pure acid are in 20 litters of this solution?
A.10
B.35
C.27
D.5
Answer: D.5
Explanation: If 75% of the solution is water then
100% - 75% = 25% is acid.
If the solution is 20 litters, then
25% of 20 = 25% * 20 = 5 litters are pure acid.
correct answer D
Question: Find compound interest on $ 16000 at 15% per annum for 2 years 4 months, compounded annually.
A.6109
B.6209
C.6218
D.6107
Answer: C.6218
Explanation: Time = 2 years 4 months = 2(4/12) years = 2(1/3) years.
Amount = $ [16000 X (1+­(15/100))2 X (1+((1/3)*15)/100)]
=$ [16000 * (23/20) * (23/20) * (21/20)]
= $ 22218	.
:. C.I. = Rs. (22218 - 16000) = $ 6218
Answer C.
Question: Tough and Tricky questions: Exponents.
If 3^m3^m3^m = 7^n, then m/n =
A.1/3
B.2/3
C.1
D.3/2
Answer: A.1/3
Explanation: I also soved it, but a bit differently. Thank you for reminding me of this much easier and logical way!
What I did was to test powers of 3 that would lead to 9.
So, we have 3 raised to the same power 3 times and 9 raised to another power one time: 3^m3^m3^m = 9^n
What I did was test 3 raised to the power of 2 like this:
3^2*3^2*3^2 = 9*9*9 = 9^3. This means that m=2 and n=3. So, m/n=1/3.A
Question: What is the ratio of y to x if (x + 3y) / ( x - y) = 3/7?
A.-15/4
B.-1/6
C.-1/15
D.3/5
Answer: B.-1/6
Explanation: Solving for y/x gives, -1/6 (B)
Question: If x : y = 3 : 5, find the value of (2x + 4y) : (3x – y)
A.13 : 2
B.11 : 2
C.13 : 3
D.13 : 4
Answer: A.13 : 2
Explanation: Explanation:
Given: x/y = 3/5
(2x + 4y)/(3x – y)
= (2*3 + 4*5) : (3*3 – 5)
= 26:4
= 13 : 2
ANSWER: A
Question: If n is a positive integer and the product of all integers from 1 to n, inclusive, is a multiple of 840, what is the least possible value of n?
A.5
B.6
C.7
D.8
Answer: C.7
Explanation: 840 = 2*2*2*3*5*7, so n must be at least 7.
The answer is C.
Question: What is the median from the below series 90, 93, 93, 88, 95, 88, 97, 87, and 98
A.80
B.85
C.93
D.97
Answer: C.93
Explanation: Ordering the data from least to greatest, we get:
87, 88, 88, 90, 93, 93, 95, 96, 98
The median quiz score was 93. (Four quiz scores were higher than 93 and four were lower.)
C
Question: Rs. 1300 is divided into three parts A, B and C. How much A is more than C if their ratio is 1/2:1/3:1/4?
A.222
B.300
C.99
D.88
Answer: C.99
Explanation: 1/2:1/3:1/4 = 6:4:3
3/13*1300 = 300
Answer:C
Question: On a race track a maximum of 5 horses can race together at a time. There are a total of 25 horses. There is no way of timing the races. What is the minimum number R of races we need to conduct to get the top 3 fastest horses?
A.5
B.7
C.8
D.10
Answer: B.7
Explanation: R=7 is the correct answer.
Good solution Buneul.B
Question: Calculate the value of n from the below equation: y^4âˆ’20y+1=22
A.5
B.3
C.6
D.2
Answer: B.3
Explanation: Use elimination method to find the correct option. you find that of all the options 3 is the correct value for y
Answer: B
Question: Find the area of trapezium whose parallel sides are 18 cm and 12 cm long, and the distance between them is 14 cm?
A.288 cm2
B.277 cm2
C.224 cm2
D.226 cm2
Answer: C.224 cm2
Explanation: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)
= 1/2 (18 + 12) * (14)
= 224 cm2
Answer: C
Question: A and B’s salaries together amount to Rs. 2,000. A spends 95% of his salary and B spends 85% of his. If now their savings are the same, what is A’s salary?
A.Rs.500
B.Rs.750
C.Rs.1250
D.Rs.1500
Answer: D.Rs.1500
Explanation: Explanation:
(5/100) A = (15/100) B
A = 3B
A + B = 2000
4B = 2000 => B = 500
A = 1500
ANSWER IS D
Question: The sum of the two numbers is 12 and their product is 35.What is the sum of the reciprocals of these numbers?
A.12/35
B.12/38
C.12/31
D.12/32
Answer: A.12/35
Explanation: Explanation:
Let a and b are the numbers.Then a+b is 12 and ab is 35.
Answer: A
Question: Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 70 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
A.22
B.36
C.48
D.99
Answer: B.36
Explanation: Relative speed = 70 + 30 = 100 km/hr.
100 * 5/18 = 250/9 m/sec.
Distance covered = 500 + 500 = 1000 m.
Required time = 1000 * 9/250= 36 sec
Answer: B
Question: In N is a positive integer less than 200, and 14N/60 is an integer, then N has how many different positive prime factors A?
A.2
B.3
C.5
D.6
Answer: B.3
Explanation: I like to put the numbers in prime factors so it is easier and faster to visualize.
14*n/60
If we write the factors of 14 --> 2, 7, and the factors of 60 --> 2, 2, 3, 5, we have
(2*7*n)/(2^2*3*5)
Simplifying
7*n/(2*3*5)
The only way the equation above has an integer value is if n has AT LEAST the factors 2, 3 and 5, so we can simplify again and we have the number 7.
The number could be 2*3*5, or 2*3*5*2, or 2*3*5*.....
However to be less than 200 we can not add any prime number.
2*3*5 = 120
If we added the next prime factor 7, we would have A=2*3*5*7 = 840
Thus, answer B
Question: The population of a village is 13400. It increases annually at the rate of 21% p.a. What will be its population after 2 years?
A.10000
B.12000
C.19619
D.18989
Answer: C.19619
Explanation: Formula :
( After =100 denominator
Ago = 100 numerator)
13400 × 121/100 × 121/100 = 19619
C
Question: Speed of a boat in standing water is 9 kmph and the speed of the stream is 1.5 kmph. A man rows to place at a distance of 210 km and comes back to the starting point. The total time taken by him is:
A.12 hours
B.24 hours
C.36 hours
D.48 hours
Answer: D.48 hours
Explanation: Sol.
Speed upstream = 7.5 kmph; Speed downstream = 10.5 kmph.
∴ total time taken = [210/7.5 + 210/10.5] hours = 48 hours.
Answer D
Question: Lucy invested $10,000 in a new mutual fund account exactly three years ago. The value of the account increased by 10 percent during the first year, increased by 7 percent during the second year, and decreased by 10 percent during the third year. What is the value of the account today?
A.$10,350
B.$10,395
C.$10,593
D.$11,500
Answer: C.$10,593
Explanation: the amount at the end of first year will become the principle for 2nd year, applying this trick and calculating we get the amount at the end of third year to be 10593. So the answer is (C).
Question: What is the sum of all three digit integers formed using the digits 3,4 and 5 (repetition is allowed)
A.11982
B.11984
C.11985
D.11988
Answer: D.11988
Explanation: n = 3*3*3 = 27
= (555 + 333) / 2 = 444
Sum = number of integers x average value
n * = 27 * 444 = 11988
answer = D
Question: What is the remainder when 7^74 - 5^74 is divided by 12?
A.1
B.0
C.2
D.3
Answer: B.0
Explanation: easiest way for me: 7^74 - 5^74 = (49)^37-25^37 = (12*4+1)^37 - (12*2+1)^37 -> remainder is 1^37 - 1^37 = 0
Ans : B
Question: 40 persons like apple. 7 like orange and mango dislike apple. 10 like mango and apple and dislike orange. 4 like all. How many people like apple?
A.47
B.46
C.54
D.58
Answer: A.47
Explanation: orange+mango-apple=7
mango+apple-orange=10
apple=40
orange+mango+apple=4
40+10+4-7=47 like apple
ANSWER:A
Question: Which of the following numbers is divisible by 12?
A.1332
B.1021
C.3221
D.4211
Answer: A.1332
Explanation: 1332. This is the only option with last two digits divisible by 12
Answer:A
Question: An advertising agency finds that, of its 200 clients, 115 use Television, 110 use Radio and 130 use Magazines. Also, 85 use Television and Magazines, 75 use Television and Radio, 95 use Radio and Magazines. How many use all the three?
A.100
B.70
C.90
D.98
Answer: A.100
Explanation: Total=200
Television=115
Radio=110
Magazine=130
All the three =200-115-110-130+85+75+95=100
ANSWER A
Question: A rectangular room has the rectangular shaped rug shown as above figure such that the rug’s area is 180 square feet and its length is 8 feet longer than its width. If the uniform width between the rug and room is 8 feet, what is the area of the region uncovered by the rug (shaded region), in square feet?
A.32
B.36
C.704
D.46
Answer: C.704
Explanation: Rug's area = 180
which is (x) x (8+x) = 180
so x= 10
rug maintains a uniform distance of 8 feet
so room has dimension 10+16 and 18+16 i.e. 26 and 34
area of room 26x34 = 884 area covered is 180
so uncovered area is 884-180=704 (ANSWER C)
Question: Gita, Hussain, Inge, Jeong, Karen, and Leila are seated in a row of six chairs. How many seating arrangements are possible if Gita cannot sit next to Inge and Jeong must sit next to Leila?
A.288
B.240
C.144
D.120
Answer: C.144
Explanation: taking he initials of each for reference... Since, J and L have to be together, lets combine them into 1. So, now we have 5 things which can be arranged in 5! ways. ALso, J and L can be arranged in two ways (JL, LJ) .
This gives total ways, 5! * 2 = 240
Now, we are given G and I can not be together, therefore subtract the cases when they (G and I) are together. Now, see we have 4 people (JL and GI) are combined as one. Total no of arrangement = 4!
But, J and L can be arranged internally in 2 ways (JL and LJ). Similarly, G and I can be internally arranged in two ways (GI and IG).
Therefore, total such cases will be 4! * 2 * 2 = 96. Subtract this from 240.
240 - 96 = 144. Hence, C
Question: How many such pairs of digits are there in the number 421579368 each of which has as many digits between them in the number as when they are arranged in ascending order?
A.4
B.5
C.6
D.3
Answer: D.3
Explanation: Explanation:
Given Number: 4 2 1 5 7 9 3 6 8
Ascending order: 1 2 3 4 5 6 7 8 9
Hence the required pairs are
Answer: D) Three
Question: If the speed of a man is 63 km per hour, then what is the distance traveled by him in 25 seconds ?
A.275m
B.360m
C.375 m
D.437.5 m
Answer: D.437.5 m
Explanation: The distance traveled in 25 sec = 63*(5/18) *25 =437.5m
ANSWER:D
Question: What is the product of the greatest 2 digit multiple of 3 and the greatest 2 digit prime number?
A.9,312
B.9,603
C.9,506
D.9,649
Answer: B.9,603
Explanation: the greatest 2 digit multiple of 3: 99
the greatest 2 digit prime numebr: 97
97*99.
9603
B
Question: If X is the sum of first 30 positive even integers and Y is the sum of first 30 positive odd integers, what is the value of x-y?
Please try to explain your answers
A.10
B.25
C.30
D.75
Answer: C.30
Explanation: First even minus first odd = 2-1 = 1;
The sum of first 2 even integers minus the sum of first 2 odd integers = (2+4)-(1+3) = 2;
The sum of first 3 even integers minus the sum of first 3 odd integers = (2+4+6)-(1+3+5) = 3;
We can see the patterns here, so the sum of first 30 positive even integers minus the sum of first 30 positive odd integers will be 30.
Answer: C.
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 ?
A.3 days
B.4 days
C.4 days
D.6 days
Answer: D.6 days
Explanation: 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.
Option 'D'
Question: What is the units digit of 33^2 * 17^3 * 49^3?
A.1
B.3
C.5
D.7
Answer: B.3
Explanation: The units digit of 33^2 is the units digit of 3*3 = 9 which is 9.
The units digit of 17^3 is the units digit of 7*7*7 = 343 which is 3.
The units digit of 49^3 is the units digit of 9*9*9 = 729 which is 9.
The units digit of 9*3*9 = 243 is 3.
The answer is B.
Question: 10x + 2y = -6
6x + y = 1
In the system of equations above, what is the value of x?
A.2
B.3
C.4
D.5
Answer: C.4
Explanation: 10x + 2y = -6 can be written as 5x + y = -3
Let's subtract the second equation from this equation.
-x = -4
x = 4
The answer is C.
Question: In how many ways can the letters of wordINTELLIGENTbe arranged such that all the Consonants always appear together?
A.9!
B.5!*4!
C.5!*5!
D.5!*7!
Answer: D.5!*7!
Explanation: Let the arrangment be: _ _ _ _ _ _ _ _ _ _ (11 letters, 4 vowels I, E, I, E and 7 consonant N, T, L, L, G, N, T)
For all consonants together, consider them as 1 group {N, T, L, L, G, N, T} I E I E --> this gives us 5! arrangements with {} group considered as 1 . Now {} group can in itself be arranged in 7! ways
Thus total arrangements with all consonants together = 5!*7! --> D is the correct answer.