divelab/Sys2Bench huggingface dataset:
Question: If a, b, and c are consecutive even positive integers, which of the following could be equal to a + b + c ?
Options:
A)141
B)200
C)606
D)391
E)412
Rationale: The key to answering this question quickly is to realize that a+b+c is a multiple of BOTH 2 and 3. With that information, you can quickly eliminate answer choices. If you don't recognize those two Number Properties though, then you can still get to the correct answer (but it will require a bit more work).
We're told that a, b and c are CONSECUTIVE EVEN INTEGERS, so we could write them algebraically as...
A + (A+2) + (A+4) = 3A + 6
We know that 3A + 6 COULD equal one of those five answers; we just have to find it...
Could 3A + 6 = 141
3A = 135
A = 45
This is NOT an EVEN INTEGER, so 141 is NOT the answer
Could 3A + 6 = 200
3A = 194
A = 64.6666
This is NOT an EVEN INTEGER, so 200 is NOT the answer
Could 3A + 6 = 606
3A = 600
A = 200
This IS an EVEN INTEGER! The numbers would be 200, 202 and 204. This IS the answer
Final Answer:
C
Answer: C
Question: James invested a certain sum of money in a simple interest bond whose value grew to $700 at the end of 3 years and to $ 800 at the end of another 2 years. What was the rate of interest in which he invested his sum?
Options:
A)9.09%
B)12.5%
C)6.67%
D)6.25%
E)8.33%
Rationale: Lets assume the Principal Amount (initial amount invested) to be P
rate of interest to beRand time as T. We need to find R
Now After a time of 3years the principal P amounts to $700 and after a time of 5years ( question says after another 2years so 3+2) P becomes $800.
Formulating the above data
Amount (A1) at end of 3years
A1= P(1 + 3R/100) = 700
Amount (A2) at end of 5years
A2 = P(1 + 5R/100) = 800
Dividing A2 by A1 we get
(1 + 5R/100)/(1 + 3R/100) = 8/7
after cross multiplication we are left with 11R =100 which gives R = 9.09%
Option: A
Answer: A
Question: If 0.5% of A =65 paise, then the value of A is ?
Options:
A)Rs. 130
B)Rs. 17
C)Rs. 1.70
D)Rs. 4.25
E)None
Rationale: Answer
∵ 0.5/100 of A = 65/100
∴ A = Rs. (65 / 0.5) = Rs. 130
Correct Option: A
Answer: A
Question: A boy and a girl appear for an interview against 2 vacant posts in an office. The probability of the boy's selection is 1/5 and that of the girl's selection is 1/3. What is the probability that only 1 of them is selected?
Options:
A)1/3
B)2/5
C)2/7
D)3/7
E)3/8
Rationale: Probability that only one of them is selected = (prob. that brother is selected) × (prob. that sister is not selected) + (Prob. that brother is not selected) × (Prob. that sister is selected)
= = 2/5
B
Answer: B
Question: If the length of an edge of cube P is twice the length of an edge of cube Q, what is the ratio of the volume of cube Q to the volume of cube P?
Options:
A)1/8
B)1/4
C)1/3
D)1/7
E)1/9
Rationale: The length of cube Q = 1;
The length of cube P = 2;
The ratio of the volume of cube Q to the volume of cube P = 1^3/2^3 = 1/8.
Answer: A
Answer: A
Question: For which of the following functions does f(−y)=−f(y) for all real number values of x?
Options:
A)y^8−y^4
B)y^2−y^6
C)y^5/y^7
D)y^9/(y^5+1)
E)-32/5 putting y=2 on y^5/(y^2+1)
Rationale: all even root cannot be matched eliminated
put y=2
f(−y)=(−2)^5/(−2^)2+1=−32/5, and
−f(y)=−2^5/2^2+1=−32/5, for a match.
ANSWER: A
Answer: A
Question: The area of circle O is added to its diameter. If the circumference of circle O is then subtracted from this total, the result is 12. What is the radius of circle O?
Options:
A)–2/pi
B)2
C)3
D)4
E)6
Rationale: pi*r^2 + 2r -2*pi*r = 12
Simplifying the equation: pi*r(r-2)+2r=12
Without much algebraic: We can Test the answers quickly, then 6 is the only possible answer that will eliminate pi from equation.
Answer is E
Answer: E
Question: A crow leaves its nest, and flies back and forth from its nest to a nearby ditch to gather worms. The distance between the nest and the ditch is 100 meters. In one and a half hours, the crow manages to bring worms to its nest 15 times. What is the speed of the crow in kilometers per hour?
Options:
A)1
B)2
C)3
D)5
E)7
Rationale: The distance between the nest and the ditch is 100 meters.
15 times mean = A crow leaves its nest, and flies back ( going and coming back) i.e. 2 times we get total 30 rounds.
So the distance is 30 * 100 = 3000.
D = ST
3000/1.5 = T , I think we can take 3000 meters as 3 km, then only we get T = 2.( 1000 meters = 1 km)
D)
Answer: D
Question: Three 6 faced dice are thrown together. The probability that no two dice show the same number on them is
Options:
A)7/12
B)5/9
C)1/36
D)5/12
E)8/9
Rationale: No two dice show same number would mean all the three faces should show different numbers. The first can fall in any one of the six ways. The second die can show a different number in five ways. The third should show a number that is different from the first and second. This can happen in four ways.
Thus 6 * 5 * 4 = 120 favourable cases.
The total cases are 6 * 6 * 6 = 216.
The probability = 120/216 = 5/9.
ANSWER:B
Answer: B
Question: What is the greatest positive integer x such that 3^x is a factor of 9^5?
Options:
A)5
B)9
C)10
D)20
E)30
Rationale: What is the greatest positive integer x such that 3^x is a factor of 9^5?
9^5 = (3^2)^5 = 3^10
C. 10
Answer: C
Question: A fort had provision of food for 150 men for 45 days. After 10 days, 25 men left the fort. The number of days for which the remaining food will last, is:
Options:
A)33
B)38
C)42
D)12
E)17
Rationale: Explanation:
After 10 days : 150 men had food for 35 days.
Suppose 125 men had food for x days.
Now, Less men, More days (Indirect Proportion)
\inline {\color{Blue} \therefore } 125 : 150 :: 35 : x 125 x x = 150 x 35
=> x=
=> x= 42
Answer: C
Answer: C
Question: What is the smallest positive integer x, such that 2160 x is a perfect cube?
Options:
A)100
B)6
C)8
D)12
E)18
Rationale: Take out the factors of 2160 that will come 6^3*10. for perfect cube you need every no. raise to the power 3. for 2160 to be a perfect cube, you need two 2 and two 5 that means 100
A is the answer.
Answer: A
Question: A certain computer manufacturing firm last year produced 80 percent of its computers using parts made by its subsidiary company. If the remaining 10,800 computers were produced using parts purchased from another parts manufacturer, how many computers were produced by the computer manufacturing firm altogether?
Options:
A)54,000
B)64000
C)62000
D)60000
E)68000
Rationale: 80% parts used of subsidary company, so 20% parts used of other companies.
Now, 20% parts = 10,800 computers
So, 1% parts = 10,800/20
Or, 100% parts = 54,000 computers.
Hence answer is (A)
Answer: A
Question: A takes twice as much time as B or thrice as much time to finish a piece of work.Working together they can finish the work in 2 days.B can do the work alone in:
Options:
A)5 hours
B)6 hours
C)7 hours
D)8 hours
E)4 hours
Rationale: Let B takes =x hours
A takes=x/2
1/x + 1/(x/2)=1/2
3/x=1/2
x = 6 hours
ANSWER:B
Answer: B
Question: The average of 10 numbers is calculated as 16. It is discovered later on that while calculating the average, one number namely 36 was wrongly read as 26. The correct average is?
Options:
A)A)17
B)B)18
C)C)19
D)D)22
E)E)24
Rationale: Explanation:
10 * 16 + 36 – 26=170 => 170/10 = 17
A)
Answer: A
Question: A college has 10 basketball players. A 5 member's team and a captain will be selected out of these 10 players. How many different selections can be made?
Options:
A)1260
B)210
C)10C6 *6!
D)10C5 *6
E)None
Rationale: Solution:
A team of 6 members has to be selected from the 10 players. This can be done in 10C6 or 210 ways.
Now, the captain can be selected from these 6 players in 6 ways.
Therefore, total ways the selection can be made is 210 *6= 1260.
Alternatively, we can select the 5 member team out of the 10 in 10C5 ways = 252 ways.
The captain can be selected from amongst the remaining 5 players in 5 ways.
Therefore, total ways the selection of 5 players and a captain can be made,
=252 *5= 1260
Answer: Option C
Answer: C
Question: Two numbers are respectively 20% and 50% more than a third number. The percentage that is first of the second is?
Options:
A)77%
B)78%
C)79%
D)80%
E)81%
Rationale: I II III
120 150 100
150----------120
100-----------? => 80%
Answer:D
Answer: D
Question: Joe's current weekly caloric intake is 20,000 calories. His physician has advised Joe to reduce the number of calories he consumes weekly to 14,000. By what percent does Joe need to reduce his weekly caloric intake?
Options:
A) 20%
B) 30%
C) 50%
D) 60%
E) 70%
Rationale: A certain percentage of questions in the Quant section of the GMAT are just 'math questions' - you'll use a formula, do some calculations and you'll have the answer. This is one of those types of questions. You still have to write everything down and stay organized, but the work involved is relatively straight-forward.
Here, we're told that the original amount of calories is 20,000 and that the reduced amount of calories is 14,000. We're asked what PERCENT should the original amount of calories be REDUCED BY?
Original Calories= 20,000
Reduced Calories = 14,000
The percent of reduced calories is relative to the original calories as shown:
14,000/20,000 = 7/10 = 70%. So, 14,000 calories is 70% of 20,000 calories (100%). But the question is BY what PERCENT should the original amount of calories be REDUCED. 100% - 70% = 30%.
B
Answer: B
Question: Evaluate: |4 - 8(3 - 12)| - |5 - 11| = ?
Options:
A)40
B)50
C)60
D)70
E)80
Rationale: According to order of operations, inner brackets first. Hence
|4 - 8(3 - 12)| - |5 - 11| = |4 - 8*(-9)| - |5 - 11|
According to order of operations, multiplication within absolute value signs (which may be considered as brackets when it comes to order of operations) next. Hence
= |4 + 72| - |5 - 11|
= |76| - |-6|
= 76 - 6 = 70
correct answer D)70
Answer: D
Question: A certain sum amounts to Rs.675 in 3 years and Rs.850 in 6 years. Find the rate % per annum?
Options:
A)10%
B)8%
C)11%
D)9%
E)7%
Rationale: 3 --- 675
6 --- 850
--------------
3 --- 175
N = 1 I = 55 R = ?
P = 675 - 175= 500
55 = (500*1*R)/100
R = 11%
Answer: C
Answer: C
Question: If (a – b) is 7 more than (c + d) and (a + b) is 3 less than (c – d), then (a – c) is:
Options:
A)6
B)2
C)3
D)4
E)5
Rationale: (a – b) – (c + d) = 7 and (c – d) – (a + b) = 3
=> (a – c) – (b + d) = 7 and (c – a) – (b + d) = 3
=> (b + d) = (a – c) – 7 and (b + d) = (c – a) – 3
=> (a – c) – 7 = (c – a) – 3 => 2(a – c) = 4 => (a – c) = 2
ANSWER:B
Answer: B
Question: Frank the Fencemaker needs to fence in a rectangular yard. He fences in the entire yard, except for one full side of the yard, which equals 40 feet. The yard has an area of 480 square feet. How many feet offence does Frank use?
Options:
A)14
B)47
C)54
D)180
E)64
Rationale: Area = Length x Breadth
480 = 40 x Breadth
So, Breadth = 12 Units
Fencing required is -
Breadth + Breadth + Length
12 + 12 + 40 => 64 feet
Answer must be (E) 64
Answer: E
Question: A man buys 12 lts of liquid which contains 10% of the liquid and the rest is water. He then mixes it with 10 lts of another mixture with 30% of liquid. What is the % of water in the new mixture?
Options:
A)80.91
B)76.45
C)77.45
D)74.45
E)73.45
Rationale: 10% in 12 lts is 1.2. So water = 12-1.2 = 10.8 lts. 30% of 10 lts = 3. So water in 2nd mixture = 10-3 = 7 lts. Now total quantity = 12 + 10 = 22 lts. Total water in it will be 10.8 + 7 = 17.8 lts. % of water = (100*17.8)/22 = 80.91. Answer:A
Answer: A
Question: If in a box of dimensions 6 m * 5 m * 4 m smaller boxes of dimensions 60 cm * 50 cm * 40 cm are kept in it, then what will be the maximum number of the small boxes that can be kept in it?
Options:
A)500
B)1000
C)900
D)800
E)700
Rationale: 6 * 5 * 4 = 60/100 * 50/100 * 40/100 * x
1 = 1/10 * 1/10 * 1/10 * x => x = 1000
ANSWER:B
Answer: B
Question: If a and b are each greater than x and y, which of the following must be true?
I. a + b < x + y
II. ab > xy
III.a + b > x + y
Options:
A)I only
B)II only
C)I and II
D)III only
E)I, II and III
Rationale: I. a + b > x + y. Since a and b are each greater than x and y, then the sum of a and b will also be greater than the sum of x and y.
II. ab > xy. Not necessarily true, consider a = b = 0 and x = y = -1 --> ab = 0 < 1 = xy.
III. |a| + |b| > |x| + |y|. Not necessarily true, consider a = b = 0 and x = y = -1 --> |a| + |b| = 0 < 2 = |x| + |y|.
Answer: D.
Answer: D
Question: A rummy( card game) player has 13 cards in his hand with 2 Aces, one of spades and other of hearts. All other cards are unique. How many ways can he hold the 13 cards?
Options:
A)14!
B)11!
C)12!
D)10!
E)13!
Rationale: Even though the player has 2 Aces, both of them are of different colour and sign. So we can't consider them as a single object. Ace (spade)Ace(heart) is different to Ace(heart)Ace(spades). So there are 13! Ways to arrange the cards. Answer is E. 13!.
Answer: E
Question: The units digit of (35)^(87) + (93)^(55) is:
Options:
A)2
B)4
C)6
D)8
E)0
Rationale: The units digit of powers of 3, cycles in a group of 4: {3, 9, 7, 1}
55 has the form 4k+3, so the units digit of 93^55 is 7.
The units digit of powers of 5 is always 5.
7+5 = 12, so the units digit is 2.
The answer is A.
Answer: A
Question: If X gets 25% more than Y and Y gets 20% more than Z, the share of Z out of Rs. 740 will be:
Options:
A)Rs. 300
B)Rs. 200
C)Rs. 240
D)Rs. 350
E)None of these
Rationale: Z share = Z,
Y = 1.2Z
X = 1.25×1.2Z,
X+Y+Z =740
(1.25× 1.2+1.2+1)Z=74
3.7Z=740, Z=200
Answer: . B.
Answer: B
Question: When 27 is divided by positive integer n, the remainder is 4. For how many values of n is this true?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: When 27 is divided by n, the remainder is 4 i.e. 4 apples left over after grouping, so n must be greater than 4.
It also means that 23 is completely divisible by n.
The factors of 23 are 1 and 23.
Out of these, n can be 23.
Answer (B).
Answer: B
Question: Two pipes can fill the cistern in 10hr and 12 hr respectively, while the third empty it in 25hr. If all pipes are opened simultaneously, then the cistern will be filled in
Options:
A)7.5 hr
B)6.98 hr
C)8.5 hr
D)10 hr
E)None of these
Rationale: Solution:
Work done by all the tanks working together in 1 hour.
1/10+1/12−1/25=1/7
Hence, tank will be filled in 6.98 hour
Option(B)
Answer: B
Question: A carpenter constructed a rectangular sandbox with a capacity of 10 cubic feet. If the carpenter were to make a similar sandbox twice as long, twice as wide, and twice as high as the first sandbox, what would be the capacity, in cubic feet, of the second sandbox?
Options:
A) 20
B) 40
C) 60
D) 80
E) 100
Rationale: A quick note on doubling. When you double a length you have 2*L1. When you double all lengths of a rectangle you have (2*L1)(2*L2) = A. An increase of 2^2 or 4. When you double all lengths of a rectangular prism you have (2*L1)(2*L2)(2*L3) = V. An increase of 2^3 or 8.
This leads to the basic relationship:
Line: 2*original size
Rectangle: 4*original size
Rectangular Prism: 8*original size answer is D
Answer: D
Question: A house seller can deduct 5 percent from the total sales value. If he has sold 5 houses, and the price of two houses is between $150,000 and $250,000, one of them is $400,000 house, two houses are between $500,000 and 750,000, what is the range of his revenue?
Options:
A)790
B)785
C)795
D)800
E)810
Rationale: taking away '000 thousand sfor easy calculation
(1) 2(150)+400+2(500) = 1700
1700*0.95=1615 (Revenue considering the minimum values with the discount)
(2) 2(250)+400+2(750) = 2400 (Revenue considering the maximum values without the discount)
So, the the revenue range could be = 2400 - 1615 = 785
B
Answer: B
Question: Salaries of Ravi and Sumit are in the ratio 2 : 3. If the salary of each is increased by Rs. 4000, the new ratio becomes 40 : 57. What is Sumit's salary?
Options:
A)32000
B)38000
C)35000
D)33000
E)39000
Rationale: Let the original salaries of Ravi and Sumit be Rs. 2x and Rs. 3x respectively.
Then, 2x + 4000/3x + 4000 = 40/57
57(2x + 4000) = 40(3x + 4000)
6x = 68,000
3x = 34,000
Sumit's present salary = (3x + 4000) = Rs.(34000 + 4000) = Rs. 38,000.
Answer is B.
Answer: B
Question: Rs. 800 becomes Rs. 956 in 3 years at a rate of S.I. If the rate of interest is increased by 4%, what amount will Rs. 800 become in 3 years?
Options:
A)1059
B)1028
C)1052
D)1028
E)1012
Rationale: S.I. = (956 - 800) = Rs. 156.
Rate = (100 * 156) / (800 * 3) = 6 1/2 %
Now rate = (6 1/2 + 4) = 10 1/2 %
New S.I. = (800 * 21/2 * 3/100) = Rs. 252
New amount = (800 + 252) = Rs. 1052.Answer:C
Answer: C
Question: Three pipes A, B and C can fill a tank from empty to full in 30 minutes, 20 minutes and 10 minutes respectively. When the tank is empty, all the three pipes are opened. A, B and C discharge chemical solutions P, Q and R respectively. What is the proportion of solution R in the liquid in the tank after 3 minutes?
Options:
A)6/19
B)6/11
C)6/12
D)6/10
E)6/38
Rationale: Part filled by (A + B + C) in 3 minutes = 3(1/30 + 1/20 + 1/10) = 11/20
Part filled by C in 3 minutes = 3/10
Required ratio = 3/10 * 20/11 = 6/11
Answer:B
Answer: B
Question: 9 men working 8 hours per day dig 30 m deep. How many extra men should be put to dig to a depth of 50 m working 6 hours per day?
Options:
A)33
B)66
C)88
D)11
E)281
Rationale: (9 * 8)/30 = (x * 6)/50 => x = 20
20 – 9 = 11
Answer: D
Answer: D
Question: The total cost of 100 paper plates and 200 paper cups is $6.00 At the same rates what is the total cost of 20 of the plates and 40 of the cups?
Options:
A)$.90
B)$1.00
C)$1.20
D)$1.50
E)$1.60
Rationale: U dont need to go through all this
What u have with u is
100 P + 200 C = $6.00
Just divide the equation by 5 and you will get what u are looking for
20P + 40 C = $1.20
Therefore OA is C
Answer: C
Question: What is the least number of squares tiles required to pave the floor of a room 15 m 17 cm long and 9 m 2 cm broad?
Options:
A)617
B)746
C)808
D)812
E)814
Rationale: Length of largest tile = H.C.F. of 1517 cm and 902 cm = 41 cm.
Area of each tile = (41 x 41) cm2.
Required number of tiles = (1517 x 902)/(41X41) = 814.
Answer: Option E
Answer: E
Question: A train is 400 meter long is running at a speed of 60 km/hour. In what time will it pass a bridge of 800 meter length?
Options:
A)72 seconds
B)27 seconds
C)40 seconds
D)128 seconds
E)18 seconds
Rationale: Speed = 60 Km/hr = 60*(5/18) m/sec = 150/9 m/sec
Total distance = 400+ 800 = 1200 meter
Time = Distance/speed
= 1200 * (9/150) = 72 seconds
Answer: A
Answer: A
Question: The percentage profit earned by selling an article for Rs. 1920 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 25% profit?
Options:
A)Rs. 2000
B)Rs. 2200
C)Rs. 2400
D)Rs. 2600
E)None of these
Rationale: Let C.P. be Rs. x.
Then, (1920 - x)/x * 100 = (x - 1280)/x * 100
1920 - x = x - 1280
2x = 3200 => x = 1600
Required S.P. = 125 % of Rs. 1600 = 125/100 * 1600 = Rs. 2000.
ANSWER:A
Answer: A
Question: Stacy and Heather are 15 miles apart and walk towards each other along the same route. Stacy walks at constant rate that is 1 mile per hour fast than heather's constant rate of 5 miles/hour. If Heather starts her journey 24 minutes after Stacy, how far from the original destination has Heather walked when the two meet?.
Options:
A)6.5mile
B)5.7mile
C)7.0mile
D)8.0mile
E)12 mile
Rationale: Ss - Stacy's speed = 6m/hr
Sh - Heather's speed = 5m/hr
In 24 minutes Stacy will cover = (24/60)*6 = 2.4miles
Now since both are walking in opposite directions, add their speeds - 6+5 =11m/hr and distance to cover is 15 -2.4 = 12.6
Time taken = Distance/ Speed = 12.6/11 = 1.145 hrs
Heather will cover = 5*1.145 = 5.72miles.
Answer B
Answer: B
Question: Look at this series: 2, 4, 6, 8, 10, ... What number should come next?
Options:
A)11
B)12
C)13
D)14
E)15
Rationale: Explanation: This is a simple addition series. Each number increases by 2.
Answer: Option B
Answer: B
Question: A man gets a simple interest of Rs.500 on a certain principal at the rate of 5% p.a in two years. Find the compound interest the man will get on twice the principal in two years at the same rate.
Options:
A)256.29
B)256.22
C)256.28
D)256.21
E)256.25
Rationale: Let the principal be Rs.P
S.I at 5% p.a in 8 years on Rs.P = Rs.500
(P)(8)(5)/100 = 500
P = 1250
C.I on Rs.2P i.e., Rs.2500 at 5% p.a in two years
=2500{ [1 + 5/100]2 - 1} = 2500{ 212 - 202 /202}
= 2500/400(441 - 400)
= 25/4(41) = 1025/4 = Rs.256.25
Answer:E
Answer: E
Question: The area of a square garden is A square feet and the perimeter is p feet. If a=2p+14.25, what is the perimeter of the garden, in feet?
Options:
A)38
B)36
C)40
D)56
E)64
Rationale: Perimeter of square = P
Side of square = P/4
Area of Square = (P^2)/16 =A
Given that A = 2P + 14.25
(P^2)/16 = 2P + 9
P^2 = 32P + 228
P^2 -32P -228 = 0
P^2 -38P + 6P -228 = 0
P(P-38)+6(P+38) = 0
(P-38)(P+6) = 0
P = 38 or- 6
Discarding negative value , P = 38
Answer is A
Answer: A
Question: A gym offers 11 levels of fitness classes, and in an attempt to reward those who progress toward higher levels of fitness it charges $50 less per course for each level of fitness. Jessica completed all 11 levels by taking one course at each level, and her total cost was $4675. What is the cost X for a course at the gym's highest level?
Options:
A)$175
B)$245
C)$425
D)$675
E)$725
Rationale: Let the cost of a course in level 1 = x
=> Cost of level 2 = x-(50*1)... and so on
=> cost of level 11 = x-(50*10) = x-500
=> Total cost X of 1 course in each of the 11 levels = x+(x-50)+(x-100)+.....+(x-500)
= 11x -50 (1+2+....+10)
= 11x - (50*55)
=> 11x-2750 = 4675
11x = 7425
x= 675
x-500=175
Answer A
Answer: A
Question: If the average marks of three batches of 62, 60 and 45 students respectively is 50, 55, 60, then the
average marks of all the students is
Options:
A)54.48
B)54.68
C)54.6
D)54.49
E)None of these
Rationale: Explanation:
(62Ã—50)+(60Ã—55)+(45Ã—60)/(62+60+45)=54.49
Answer: Option D
Answer: D
Question: Seven children — A, B, C, D, E, F, and G — are going to sit in seven chairs in a row. Child A has to sit next to both BG, with these two children immediately adjacent to here on either side. The other four children can sit in any order in any of the remaining seats. How many possible configurations E are there for the children?
Options:
A)240
B)480
C)720
D)1440
E)3600
Rationale: MAGOOSHOFFICIAL SOLUTION:
First, we will consider the restricted elements — children ABG have to be in three seats in a row. How many “three in a row” seats are there in a row of seven seats?
X X X _ _ _ _
_ X X X _ _ _
_ _ X X X _ _
_ _ _ X X X _
_ _ _ _ X X X
There are five different “three in a row” locations for these three children. Now, for any given triplet of seats, we know A has to be in the middle, so the children could be seated B-A-G or G-A-B — just those two orders. This means the total number of configurations for these three children is 5*2 = 10.
Now, consider the non-restricted elements, the other four. Once ABG are seated, the remaining four children can be seated in any order among the remaining four seats — that’s a permutation of the 4 items —- 4P4 = 4! = 24. For any single configuration of ABG, there are 24 ways that the other children could be seated in the remaining seats.
Finally, we’ll combine with the Fundamental Counting Principle. We have 10 ways for the first three, and 24 ways for the remaining four. That’s a total number of configurations E of 24*10 = 240.
Answer = A
Answer: A
Question: In how many different ways can 2 girls and 2 boys form a circle such that the boys and the girls alternate?
Options:
A)8
B)1
C)7
D)5
E)2
Rationale: Explanation :
In a circle, 2 boys can be arranged in 2! ways
Given that the boys and the girls alternate.
Hence there are 2 places for girls which can be arranged in 2! ways
Total number of ways = 1! x 2! = 1 x 2 = 2. Answer : Option E
Answer: E
Question: A sum amounts to Rs.8820 in 2 years at the rate of 5% p.a. If interest was compounded yearly then what was the principal?
Options:
A)s.4000
B)s.5000
C)s.4500
D)s.4800
E)s.8000
Rationale: CI=8820,R=5,N=2
CI=P[1+R/100]^2
=P[1+5/100]^2
8820=P[21/20]^2
8820[20/21]^2
8000
ANSWER:E
Answer: E