RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: John deposited $10,000 to open a new savings account that earned 2 percent annual interest, compounded quarterly. If there were no other transactions in the account, what was the amount of money in John’s account 6 months after the account was opened?
A.$10,100.25
B.$10,101.50
C.$10,200.75
D.$10,201.00
Answer: A.$10,100.25
Explanation: 2 percent annual interest compounded quarterly --> 0.5% in 3 moths.
For the first 3 moths interest was 0.5% of $10,000, so $50;
For the next 3 moths interest was 0.5% of $10,000,plus0.25 earned on previous interest of $100, so $50+$0.25=$50.25;
Total interest for 6 months was $50+$50.25=$100.25, hence balance after 6 months was $10,000+ $100.25=$10,100.25.
Answer: A.
Question: If 3<(7-x)/3, which of the following must be true?
I. 5<x
II. |x+3|>2
III. -(x+5) is positive
A.II only
B.III only
C.I and II only
D.II and III only
Answer: C.I and II only
Explanation: 12<7-x
x<-5
x+5<0
1.5<x...not possible
2.True.....Check for values x=-6,-7,-8....... etc
3.True.. Since x+5<0 -(x+5) will always be positive
Hence, Ans is C..
Question: Listed below are the mean temperatures measured in the Tokharian desert in a certain month. What is the median temperature T in that particular month?
Mean Temp (C°) No. of days
29 --------------------> 5
30 --------------------> 11
31 --------------------> 8
32 --------------------> 6
A.29
B.30
C.30.5
D.31
Answer: B.30
Explanation: to find out median===>they must be arranged in ascending order.
29 29 29...(5 times)30 30 30 30.....(11 times)31 31 31.....(8 times)32 32 32 .....(6 times)
total days=5+11+8+6=30
therefore 30 numbers ...median T will be==>mean of 15 and 16 th place temperature===>(30+30)/2=30
hence B
Question: Find the number of terms in the series 8, 12, 16, . . .72
A.17
B.18
C.19
D.20
Answer: A.17
Explanation: SOLUTION:
a = 8
l = 72
d = 12 – 8 = 4
ANSWER IS A
Question: As part of her MBA program, Karen applied for three different Spring Break outreach projects, each of which selects its students by a random lottery of its applicants. If the probability of her being accepted to each individual project is 25%, what is the probability that Karen will be accepted to at least one project?
A.37/64
B.23/64
C.15/32
D.7/16
Answer: A.37/64
Explanation: Since the probability of Karen's being accepted to each individual project is 25%, the probability of her not being accepted to each project is 75%. The probability that she will be accepted to none is, therefore, (3/4)*(3/4)*(3/4)=27/64.
P(Karen will be accepted to at least one project) = 1 - (27/64) = 37/64.
The answer is A.
Question: AB
+BA
___
202
In the addition problem above, A and B represent digits in two different two-digit numbers. What is the sum of A and B?
A.6
B.8
C.9
D.20
Answer: D.20
Explanation: two ways to do it..
1) straight logic..
only 20 fits in..
D
Question: A fraction bears the same ratio to 1/27 as 3/7 does to 5/9. The fraction is?
A.1/24
B.1/35
C.1/34
D.1/37
Answer: B.1/35
Explanation: Let the fraction be x. Then,
x:1/27 = 3/7 : 5/9
x × 5/9 = 1/27 × 3/7
x × 5/9 = 1/9 × 1/7
x × 5/9 = 1/63
x × 5 = 9/63
5x = 1/7 = 1/35
B
Question: The set S consists of 5 numbers: {1,2,3,4,5}. If all possible subsets including the null set are created and one subset is chosen at random, what is the probability that the subset has 4 or 5 as its largest number?
A.1/2
B.2/3
C.3/4
D.5/8
Answer: C.3/4
Explanation: The set S has 2^5 = 32 subsets.
The number 5 is in half of these subsets.
Thus 5 is the largest number in 16 subsets of S.
Of the remaining 16 subsets, 4 is an element in 8 of them.
Thus 4 is the largest number in 8 subsets of S.
The probability that 4 or 5 is the largest number is 24/32 = 3/4.
The answer is C.
Question: What will be 50 percent of a number whose 200 percent is 90 ?
A.144
B.72
C.22.5
D.None of these
Answer: C.22.5
Explanation: Answer
∵ 200% of N = 90
⇒ N = (90 x 100) / 200 = 45
∴ 50% of N = (50 x 45) / 100 = 22.5
Correct Option: C
Question: The difference between the local value and the face value of 6 in the numeral 85475641 is
A.459
B.954
C.594
D.584
Answer: C.594
Explanation: Explanation:
(Local value of 6) - (Face value of 6) = (600 - 6) = 594
C)
Question: In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.40 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for ?
A.	160
B.	175
C.	180
D.	195
Explanation:
A.160
B.175
C.180
D.185
Answer: B.175
Explanation: Suppose the man works overtime for x hours.
Now, working hours in 4 weeks = (5 x 8 x 4) = 160.
160 x 2.40 + x x 3.20 = 432
3.20x = 432 - 384 = 48
x = 15.
Hence, total hours of work = (160 + 15) = 175.
Answer: Option B
Question: When positive integer s is divided by 6, the remainder is 1. Which of the following must be true?
I. s is a prime number
II. s is odd
III. s is divisible by 7
A.I only
B.II only
C.III only
D.I and II only
Answer: B.II only
Explanation: s=6q+1
Examine II) put q=0,1,2,3....... we have s=1,7,13,...25 so s must be odd
Examine III) 14/6 has reminder 249/7 has reminder 1 so not always true
Examine I) s= 7 true but while 2 is prime, it does not give reminder 1
Answer: B
Question: If a carpenter completes 3/8th of his work in 6 days, then how many more days will he require completing his remaining work?
A.10
B.12
C.6
D.16
Answer: A.10
Explanation: Explanation:
As 3/8th of the work is completed, the work remaining is 5/8th of the total.
(3/8):6::(5/8):x
x = 6*(5/8)/(3/8)
x = 10
ANSWER A
Question: Listed below are the mean temperatures measured in the Tokharian desert in a certain month. What is the median temperature Q in that particular month?
Mean Temp (C°) No. of days
29 --------------------> 5
30 --------------------> 11
31 --------------------> 8
32 --------------------> 6
A.29
B.30
C.30.5
D.31
Answer: B.30
Explanation: to find out median===>they must be arranged in ascending order.
29 29 29...(5 times)30 30 30 30.....(11 times)31 31 31.....(8 times)32 32 32 .....(6 times)
total days=5+11+8+6=30
therefore 30 numbers ...median will be==>mean of 15 and 16 th place temperature Q===>(30+30)/2=30
hence B
Question: A man can row upstream at 10kmph and downstream at 28 kmph. The speed of the stream is
A.2 km/hr
B.4 km/hr
C.5 km/hr
D.10.5 km/hr
Answer: B.4 km/hr
Explanation: Sol.
Speed of stream = 1/2(28-10) kmph = 4 kmph.
Answer B
Question: Pascal has 96 miles remaining to complete his cycling trip. If he reduced his current speed by 4 miles per hour, the remainder of the trip would take him 16 hours longer than it would if he increased his speed by 50%. What is his current speed T?
A. 6
B. 8
C. 10
D. 12
Answer: B. 8
Explanation: Let the current speed be x miles per hour.
Time taken if speed is 50% faster (i.e. 3x/2 = 1.5x) = 96/1.5x
Time taken if speed is reduced by 4 miles/hr (i.e. (x-4)) = 96/(x-4)
As per question, 96/(x-4) - 96/1.5x = 16
Solving this T we get x = 8.
B.
Question: Which of the following must be true if b=x^5
I. b is positive.
II. x is non-negative.
III. If x is positive then b is positive.
A.I only
B.II and III only
C.II only
D.I and III only
Answer: D.I and III only
Explanation: I. b is negative --> true
II. b is non-negative. b can take ANY value: positive, negative, zero. We don't have any restrictions on its value;
III. If x is positive then b is positive.
Answer: D (I and III only).
Question: If 2 >p > 1> q > 1, which of the following must be greater than 1?
I.	p/q
II.	pq
III.	p-q
A.I and II
B.I and III
C.I only
D.II only
Answer: A.I and II
Explanation: We could solve this easily using counter examples.
I is true since p>q and both are positive
II is false. Take p=4/3, q=3/4. pq=1
III is false. Take p=1.2, q=0.3. p-q=0.9
So, the answer is A
Question: The average of 9 numbers is 104. Average of the first 5 of them is 99 and that of the last 5 is 100. Find the 5th number?
A.46
B.59
C.63
D.75
Answer: B.59
Explanation: Sum of all the 9 numbers = 9 * 104 = 936Sum of the first 5 of them = 5 * 99 = 495Sum of the last 5 of them = 5 * 100 = 500So, the 5th number = 495 + 500 - 936= 59.Answer: B
Question: There are 28 stations between Kolkatta and Chennai. How many second class tickets have to be printed, so that a passenger can travel from any station to any other station?
A.870
B.970
C.1070
D.1000
Answer: A.870
Explanation: The total number of stations = 30
From 30 stations we have to choose any two stations and the direction of travel (i.e., Kolkatta to Chennai is different from Chennai to Kolkatta) in 30P2 ways.
30P2= 30 * 29 = 870
ANSWER: A
Question: If Y > X and XM < YM, what must be true?
A.M > 0.
B.M < Y.
C.X < 0.
D.M < 0.
Answer: A.M > 0.
Explanation: X<Y, bus as soon as M is multiplied to both sides inequality sign changes.
This is only possible when ve is multiplied on both sides. That means M is ve
A is the answer
Question: The tax on a commodity is diminished by 20% and its consumption increased by 15%. The effect on revenue is?
A.8
B.6
C.5
D.5
Answer: B.6
Explanation: 100 * 100 = 10000
80 * 115 = 9200
-----------
10000-----------800
100-----------? => 8% decrease
Answer:B
Question: A simple interest amount of rs 5000 for six month is rs 200. what is the anual rate of interest?
A.10%
B.6%
C.8%
D.9%
Answer: C.8%
Explanation: S.I=P*N*R/100
200=5000*0.5*R/100
R=200*100/(5000*0.5)
R=8%
ANSWER:C
Question: f n = 3^5 - 2^5, which of the following is NOT a factor of n?
A.211
B.422
C.633
D.100
Answer: D.100
Explanation: =243-32 =211 is prime number.any number not a factor of 211
D
Question: In how many ways can be 6 boys and 6 girls sit around circular table so that no two boys sit next to each other?
A.(5!)^2
B.(6!)^2
C.5!6!
D.11!
Answer: C.5!6!
Explanation: first fix one boy and place other 5 in alt seats so total ways is 5!
now place each girl between a pair of boys... total ways of seating arrangement of girls 6!
total is 5!*6!
ANS C
Question: A, B and C completed a piece of work, A worked for 6 days, B for 9 days and C for 4 days. Their daily wages were in the ratio of 3:4:5. Find the daily wages of C, if their total earning was Rs.1480?
A.Rs.109
B.Rs.108
C.Rs.100
D.Rs.103
Answer: C.Rs.100
Explanation: 3x 4x 5x
6 9 4
18x + 36x + 20x = 1480
74x = 1480 => x = 20
5x = 100 Rs.
Answer:C
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.200 m
B.225 m
C.245 m
D.250 m
Answer: C.245 m
Explanation: Let the length of the bridge:L
The equation now is L+130/12.5m/s(45km/hr or12.5m/s)=30
Solving, L =245m
ANSWER:C
Question: A car owner buys petrol at 7.50, 8.00 and 8.50 per litre for three successive years. What approximately is his average cost per litre of petrol if he spends 4000 each year?
A.8
B.9
C.7.98
D.8.50
Answer: C.7.98
Explanation: Let average cost of petrol per litre be x
Then x = 12000 /4000/7.5+4000/8+4000/8.5
= 3 /2/15+1/8+2/17=6120/767= Rs. 7.98 per litre
Answer C
Question: 128% of 5/8 =
A.0.2
B.0.5
C.0.6
D.0.8
Answer: D.0.8
Explanation: Should be simple.
1.28*5/8 = 6.4/8= 0.8
Correct Option : D
Question: 0, 1, 2, 4, 6, 9, 12, 16, ?
What number should replace the question mark?
A.24
B.20
C.19
D.26
Answer: B.20
Explanation: B
20
add 1, 1, 2, 2, 3, 3, 4, 4.
Question: The product of x and y is a constant. If the value of x is increased by 60%, by what percentage must the value of y be decreased?
A.30%
B.32%
C.35%
D.37.5%
Answer: D.37.5%
Explanation: x*y = constt.
Let x = y = 100 in beginning
i.e. x*y = 100*100 = 10000
x (100) ---becomes---> 1.6x (120)
i.e. 160*New 'y' = 10000
i.e. New 'y' = 10000/160 = 62.5
i.e. y decreases from 100 to 62.5 i.e. Decrease of 37.5%
Answer: option D
Question: Two trains 300 m and 450 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
A.10.6
B.27
C.10.4
D.10.8
Answer: B.27
Explanation: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other = 300 + 450 = 750 m.
Required time = 700 * 9/250 = 27 sec.
Answer: B
Question: a, b, c are non negitive integers such that 28a+30b+31c = 365. a + b + c = ?
A.22
B.12
C.88
D.73
Answer: B.12
Explanation: In a calender,
Number of months having 28 days = 1
Number of months having 30 days = 4
Number of months having 31 days = 7
28 x 1 + 30 x 4 + 31 x 7 = 365
Here, a = 1, b = 4, c = 7.
a+b+c = 12
Answer:B
Question: Write 880,000,000,000 in scientific notation.
A.8.8 * 10^11
B.800.900 * 10^11
C.8.900 * 10^11
D.80.9000* 10^11
Answer: A.8.8 * 10^11
Explanation: a * 10 n , where a is a real number such that 1 * |a| < 10 and n is an integer.
880,000,000,000 = 8.8* 100,000,000,000 = 8.8 * 10 11**
correct answer A
Question: If rupee one produces rupees nine over a period of 40 years, find the rate of simple interest?
A.20 %
B.10 %
C.15 %
D.22 1/2%
Answer: D.22 1/2%
Explanation: Explanation:
9 = (1*40*R)/100
R = 22 1/2 %
ANSWER IS D
Question: If n is a prime number, which of the following could be true
A.n^n/4 = 1^(n-1)
B.n^2/4= is even
C.(n)(n^n) = is negative
D.n^2+n^3= n^5
Answer: A.n^n/4 = 1^(n-1)
Explanation: A should be the answer.
2^2/4 = 1^(2-1)
Question: How many multiples of 4 are there between 20 and 112, inclusive?
A.21
B.22
C.23
D.24
Answer: D.24
Explanation: The multiples of 4 are from 4*5 up to 4*28.
28-5+1 = 24.
The answer is D.
Question: A certain company’s profit in 1996 was 20 percent greater than its profit in 1995, and its profit in 1997 was 20 percent greater than its profit in 1996. The company’s profit in 1997 was what percent greater than its profit in 1995?
A.5%
B.18%
C.33%
D.44%
Answer: D.44%
Explanation: Profit in 1995 - 100
Profit in 1996 - 120
%increae Profit in 1997 in comparison to 1995 = 20 + 120*20%= 44
Correct Option : D
Question: Suppose you have three identical prisms with congruent equilateral triangles as the end-polygons. Suppose you attach them by the rectangular faces so they are perfectly aligned. There will be some large faces created by two or more co-planar faces of the individual prisms: count each such large face as one. Given that, how many faces does the resultant solid have
A. 4
B. 6
C. 9
D. 5
Answer: D. 5
Explanation: To arrange them as described I did as follows on my scratch paper (see the file attached), where I counted 4 sides and added top , hence 4+1 = 5.
D
Question: Linda spent 3/4 of her savings on furniture and the rest on a TV. If the TV cost her $240, what were her original savings?
A.$900
B.$800
C.$960
D.$700
Answer: C.$960
Explanation: If Linda spent 3/4 of her savings on furnitute, the rest
4 / 4 - 3 / 4 = 1 / 4 on a TV
But the TV cost her $240. So 1 / 4 of her savings is $240. So her original savings are 4 times $240 = $960
correct answer C
Question: A apple costs Rs 20 each and a watermelon costs Rs. 7 each. If I spend Rs 47 on total what is the number of apple I purchased?
A.5
B.6
C.2
D.7
Answer: C.2
Explanation: 2 * 20 +7 = 47
Answer : 2 apple
Answer : C
Question: A boy rides his bicycle 10 km at an average speed of 12 km/hr and again travels 12 km at an average speed of 10 km/hr. His average speed for the entire trip is approximately?
A.10.6 km/hr
B.10.8 km/hr
C.18.8 km/hr
D.80.8 km/hr
Answer: B.10.8 km/hr
Explanation: Total distance traveled = 10 + 12
= 22 km /hr.
Total time taken = 10/12 + 12/10
= 61/30 hrs.
Average speed = 22 * 30/61
= 10.8 km/hr.
Answer: B
Question: In 1979 approximately 1/3 of the 37.3 million airline passengers traveling to or from the United States used Kennedy Airport. If the number of such passengers that used Miami Airport was 1/2 the number that used Kennedy Airport and 5 times the number that used Logan Airport, approximately how many millions of these passengers used Logan Airport that year?
A. 18.6
B. 9.3
C. 1.2
D. 3.1
Answer: C. 1.2
Explanation: number of
passengers using Kennedy airport = 37/3 =~12.43
Passengers using Miami airport = 12.43/2=~6.2
passengers using logan airport = 6.2/5 =~1.24
so C
Question: What will come in place of the x in the following Number series? 5, 10, 20, x , 55
A.33
B.37
C.55
D.50
Answer: C.55
Explanation: (C)
The pattern is + 5, + 10, + 15, +20 â€¦â€¦â€¦..
So the missing term is = 20 + 15 = 55
Question: In a certain pond, 50 fish were caught, tagged, and returned to the pond. A few days later, 50 fish were caught again, of which 2 were found to have been tagged. If the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, what`s the approximate number of fish in the pond?
A.400
B.625
C.1250
D.2500
Answer: C.1250
Explanation: If x is total number of fish in the pond :
4 = 50/x * 100
=> x = 1250
So answer is C
Question: A man had to make 3 trips to the store because he kept forgetting items his wife had requested. The store was 500 meters from his home. It took the man 45 minutes to complete the store run. What was the man's speed in kilometers per hour.
A.2
B.1.5
C.2.25
D.3
Answer: C.2.25
Explanation: The distance between the man's home and the store is 500 meters.
3 times means that the man made the 500 meter trip 6 times in total.
6 * 500 = 3000 meters or 3 km.
Since the man's total time was 45 min, we need to multiply 3000 by 3/4 or .075.
Correct answer is 2.25 km per hour
Question: Triangle STV has sides ST = TV = 13, and SV = 10. What is the area?
A.60
B.100
C.120
D.136
Answer: A.60
Explanation: Let the base B of the triangle be SV = 10. Then we need to find the height H.
H^2 = 13^2 - 5^2 = 144 and then H = 12.
The area is (1/2)*B*H = 5*12 = 60
The answer is A.
Question: A student committee that must consists of 6 members is to be formed from a pool of 8 candidates. How many different committees are possible
A.5
B.28
C.40
D.56
Answer: B.28
Explanation: Out of 8 people, any 6 can be selected for a committee. So 8c6= 28 is the answer.
B
Question: 2^1 + 2^1 + 2^1 + 2^1 =
A.2^2
B.4^6
C.4^8
D.4^9
Answer: A.2^2
Explanation: Hi shakticnb,
Certain Quant questions on the GMAT are just about 'organizing' the information in a specific way. If you find yourself getting confused by a prompt, think about how you might change the way that the information is presented to you.
Here, for example, we're asked for....
2^1 + 2^1 + 2^1 + 2^1 =
Now, the GMAT doesn't really expect us to calculate this sum (but we could if we had to), but we are expected to find a way to organize this information... If, instead of all of those exponents, we had...
X + X + X + X =
What would the sum be?
Clearly, it would be 4(X) = 4X.....since we're just combining 'like' terms. Take that same idea with this prompt and you have...
2^1 + 2^1 + 2^1 + 2^1 =
2(2^1)
This can be re-written as...
(2^1)(2^1)
...and now we can use exponent rules; since we're MULTIPLYING 'bases' that are the same, we ADD the exponents...
(2^1)(2^1) = 2^2
Final Answer:
A
Question: If M = 2N+1 where M is an Integer then which of the following is true?
A.M is even if N is a non integer and a multiple of 0.5
B.M is always Even
C.M is a non multiple of 2
D.M= 1
Answer: A.M is even if N is a non integer and a multiple of 0.5
Explanation: A
Question: A man purchases 2 watches for $ 500. He sells one at 15% profit and the other at a loss of 10%. He neither gains nor loses on the whole. Thus, the cost price of two watches are :
A.$ 260 and $ 300
B.$200 and $ 300
C.$224 and $336
D.$560 and $560
Answer: B.$200 and $ 300
Explanation: x + y = 500 --- (1)
1.15x + 0.9y = 500 --- (2)
(2) - (1) --> 0.15x - 0.1y = 0
15x = 10y
x/y = 2/3 = (2*100)/(3*100) = 200/300
Answer: B
Question: A man can row downstream at the rate of 10 Km/hr and upstream at 6 Km/hr. Find man's rate in still water and the rate of current?
A.9,6
B.8,2
C.9,3
D.6,6
Answer: B.8,2
Explanation: Explanation:
Rate of still water = 1/2 (10 + 6) = 8 Km/hr
Rate of current = 1/2 (10-6) = 2 Km/hr
Answer: Option B
Question: The price of cooking oil has increased by 25%. The percentage of reduction that a family should effect in the use of cooking oil so as not to increase the expenditure on this account is?
A.25%
B.20%
C.23%
D.24%
Answer: B.20%
Explanation: Reduction in consumption
= [(P/(100 + P)] X 100)%
= [(25/(100 + 25)] X 100)%
= 20%
ANSWER:B
Question: In the quiet town ofNothintodothere are 600 inhabitants, 400 are unemployed and 200 are somnambulists. If half of the somnambulists are unemployed, how many are employed and are not somnambulists?
A.50.
B.100.
C.150.
D.200.
Answer: B.100.
Explanation: Total = 600
unemployed=400
employed=600-400=200
som=200
unemployed som = 200/2=100
employed som = 100
employed that are not som = 200-100=100
Answer : B
Question: What is the sum of this series?
1, 3, 5, 7, 9, ...... 35.
A.324
B.350
C.384
D.444
Answer: A.324
Explanation: Number of odd numbers between 1 and 35 is (35+1)/2=18
Therefore Sum of odd numbers 18*18= 324
ANSWER: A
Question: A can do half the work in one day where as B can do it full. B can also do half the work of C in one day. Ratio in their efficiency will be?
A.1:2:8
B.1:2:0
C.1:2:5
D.1:2:4
Answer: D.1:2:4
Explanation: WC of A: B = 1:2
B: C = 1:2
---------------------
A: B: C = 1:2:4
Answer:D
Question: The price of 357 mangoes is Rs. 1517.25 what will be the approximate price of 9 dozens of such mangoes ?
A.Rs. 3000
B.Rs. 3500
C.Rs. 4000
D.Rs. 2500
Answer: D.Rs. 2500
Explanation: Solution
Let the required price be Rs. x. Then, More mangoes, More price
∴ 357 : (49 × 12) : : 1517.25 : x
⇔ 357 x = (49 × 12 × 1517.25) ⇔ x = 49x12x1517.25/357⇔ x = 2499.
Hence, the approximate price is Rs. 2500 . Answer D
Question: If x, y, and z are consecutive odd integers, with x < y < z, then which of the following must be true?
I. x + y is even
II. (x+z)/y is an integer
III. xz is even
A.I only
B.II only
C.III only
D.I and II only
Answer: D.I and II only
Explanation: x, y, and z are consecutive integers ⇒
Y = X+2
Z = X+4
1- x+y is even - Correct: sum of any 2 odd integers is even
2- (x+z)/y is an integer - Correct: x+z = x+x+4 = 2x+4 = 2(x+2)
and x+z/y = 2(x+2)/x+2 = 2 ⇒ integer
3- xz is even - Not Correct: multiplication of any 2 odd integers is always odd
Answer: D
Question: If a 3-member subcommittee is to be formed from a certain 6-member committee, how many different such subcommittee are possible?
A.6
B.18
C.20
D.108
Answer: C.20
Explanation: 1st member can be selected in 6 ways
2nd can be selected in 5 ways
3rd can be selected in 4 ways
So total ways : 120
But to avoid the similar scenarios 120/3!=20
ANS:C
Question: If a committee of 3 people is to be selected from among 4 married couples so that the committee does not include two people who are married to each other, how many such committees are possible?
A.20
B.32
C.54
D.80
Answer: B.32
Explanation: You now have your Committee of 3 people. But you've selected them in an order, when order doesn't matter.
Selection #1 = Jack
Selection #2 = Susan
Selection #3 = Mary
Assume this is a good committee where Jack is not married to Susan or Mary and Susan and Mary are not married. The above committee will be the same as the following committee:
Selection #1 = Susan
Selection #2 = Mary
Selection #3 = Jack
To account for the fact that the order does not matter, we must divide out the number of ways a single committee can be the same members but in different order. 3 places = 3!, 3*2*1 = 6.
8*6*4 / 6 = 32. Answer B.
Question: A and B complete a work in 80 days. A alone can do it in 40 days. If both together can do the work in how many days?
A.1.0875 days
B.0.1875 days
C.0.0675 days
D.0.0375 days
Answer: D.0.0375 days
Explanation: 1/80 + 1/40 = 0.0375 days
ANSWER:D
Question: A composer’s guild is planning its spring concert, and eight pieces have been submitted for consideration. The director of the guild knows that they will only have time to present five of them. If the pieces can be played in any order, how many combinations of pieces are possible?
A.56
B.21
C.10
D.50
Answer: A.56
Explanation: Combination question..
8C5 = 56..
IMO option A is correct..