RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: If n is a positive integer and n^2 is divisible by 134, then the largest positive integer that must divide n is
A.6
B.12
C.24
D.36
Answer: C.24
Explanation: The question asks aboutthe largest positive integer that MUST divide n, not COULD divide n. Since the least value of n for which n^2 is a multiple of 72 is 12 then the largest positive integer that MUST divide n is 12.
Complete solution of this question is given above. Please ask if anything remains unclear.
I spent a few hours on this one alone and I'm still not clear. I chose 12 at first, but then changed to 48.
I'm not a native speaker, so here is how I interpreted this question:the largest positive integer that must divide n=the largest positive factor of n. Since n is a variable (i.e. n is moving), so is its largest factor. Please correct if I'm wrong here.
I know that if n = 12, n^2 = 144 = 2 * 72 (satisfy the condition). When n = 12, the largest factor of n is n itself, which is 12. Check: 12 is the largest positive number that must divide 12 --> true
However if n = 48, n^2 = 48 * 48 = 32 * 72 (satisfy the condition too). When n = 48, the largest factor of n is n itself, which is 48. Check: 48 is the largest positive number that must divide 48 --> true
So, I also notice that the keyword isMUST, notCOULD. The question is, why is 48 notMUST divide 48, but instead onlyCOULD divide 48? I'm not clear right here. Why is 12MUST divide 12? What's the difference between them?
Only restriction we have on positive integer n is that n^2 is divisible by 72. The least value of n for which n^2 is divisible by 72 is 12, thus nmustbe divisible by 12 (n is in any case divisible by 12). For all other values of n, for which n^2 is divisible by 72, n will still be divisible by 12. This means that n is always divisible by 12 if n^2 is divisible by 72.
Now, ask yourself: if n=24, is n divisible by 48? No. So, n is not always divisible by 48.
C
Question: An bus covers a certain distance at a speed of 250 kmph in 5 hours. To cover the samedistance in 1hr, it must travel at a speed of?
A.600 km/hr
B.720 km/hr
C.730 km/hr
D.750 km/hr
Answer: D.750 km/hr
Explanation: Distance = (250 x 5) = 1250 km.
Speed = Distance/Time
Speed = 1250/(5/3) km/hr. [We can write 1 hours as 5/3 hours]
Required speed = 1250 x 3 km/hr = 750 km/hr.
D
Question: Angelo and Isabella are both salespersons. In any given week, Angelo makes $580 in base salary plus 8 percent of the portion of his sales above $1,000 for that week. Isabella makes 10 percent of her total sales for any given week. For what amount of weekly sales would Angelo and Isabella earn the same amount of money?
A.23,500
B.24,500
C.25,000
D.26,500
Answer: C.25,000
Explanation: Let the weekly sales of both = x
580+(x−1000)8/100=10/100x
x = 25000
ANSWER:C
Question: A, B and C enter into partnership. A invests some money at the beginning, B invests double the amount after 6 months, and C invests thrice the amount after 8 months. If the annual gain be Rs.18000. A's share is?
A.2299
B.2779
C.6000
D.2878
Answer: C.6000
Explanation: x* 12 : 2x* 6: 3x* 4
1:1:1
1/3 * 18000 = 6000.Answer: C
Question: A train 140 m long crosses a platform 160 m long in 16 sec; find the speed of the train?
A.87 kmph
B.65 kmph
C.68 kmph
D.16 kmph
Answer: C.68 kmph
Explanation: D = 140 + 160 = 300
T = 16
S = 300/16 * 18/5 = 67.5 kmph
Answer:C
Question: There are 10 solid colored balls in a box, including 1 Green and 1 Yellow. If 3 of the balls in the box are chosen at random, without replacement, what is the probability that the 3 balls chosen will include the Green ball but not the yellow ball.
A.1/6
B.7/30
C.1/4
D.3/10
Answer: B.7/30
Explanation: But we ARE told that there is is only 1 green ball and only 1 yellow ball in the box, becausethere are 10 solid colored balls in a box,including 1 Green and 1 Yellowmeans exactly that. How else?
Would it make ANY sense if there were for example 2 green balls and we were told thatthere are 10 solid colored balls in a box,including 1 Green and 1 Yellow?
Hmm.. yeah, that does make sense. I'm a non-native English speaker so I tend to over-analyze simple things. In this case, since the wordonlywas missing i.e. there are 10 solid colored balls in a box, includingexactly/only1 Green and 1 Yellow . But yeah, in retrospect this is a Quant question not a Verbal SCThanks for the explanation answer is B
Question: Four friends, Patricia, Melyssa, Tania, and Cassandra, are pooling their money to buy a $1100 item. Patricia has twice as much money as Melyssa. Tania has $10 more than Patricia. Cassandra has 20% more than Tania. If they put all their money together and spend the $1100, they will have $32 left. How much money does Patricia have?
A.$200
B.$420
C.$300
D.$315
Answer: C.$300
Explanation: P= 2M ; T= P+10 ; C= 1.2(T)
P+M+T+C-1100=32
P+0.5P+P+10+1.2(P+10) = 1132
P+0.5P+P+10+1.2P+12=1132
P+0.5P+P+1.2P+22=1132
P+0.5P+P+1.2P=1110
3.7P=1110
P=300
Answer:C
Question: If two numbers are in the ratio 2:3. If 10 is added to both of the numbers then the ratio becomes 3:4 then find the smallest number?
A.18
B.20
C.22
D.25
Answer: A.18
Explanation: 2:3
2x + 10 : 3x + 10 = 3 : 4
4[2x + 10] = 3[3x + 10]
8x + 40 = 9x + 30
9x - 8x = 40 - 30
x = 10
Then smallest number is = 2
2x = 20
A
Question: Simplify : 5793405 x 9999
A.57928256595
B.59278256595
C.57928262559
D.59722422582
Answer: A.57928256595
Explanation: 5793405x9999=5793405(10000-1)=57934050000-5793405=57928256595.
Answer is A
Question: A bakery has 6 employees. It pays annual salaries of $16,000 to each of 2 employees, $18,000 to 1 employee, and $19,000 to each of the remaining 3 employees. Which number is closest to the average (arithmetic mean) annual salary of these employees?
A.$17,200
B.$17,500
C.$17,800
D.$18,000
Answer: C.$17,800
Explanation: average = 2(16000)+(18000)+3(19000) / 6 = $17,833
The answer is C.
Question: In the first week of last month, Company X realized an average wholesale profit of $5712 per day from the sale of q units of Product Y. Which of the following CANNOT be the difference between Product Y’s sale price and cost per unit?
A.$3
B.$4
C.$7
D.$13
Answer: D.$13
Explanation: The key operator that everyone seems to have missed is the average. The average profit of $5304 per day is equivalent to a total profit of $39984 for the whole week.
Therefore, the difference between sale price and cost per unit is equal to $39984, which is divisible by all of the answer choices, except for 13.
So, D is the answer.
Question: If a and b are different positive integers and a + b = b(a + b), then which of the following must be true?
I. a = 1
II. b < a
III. b = 1
A.I only
B.II only
C.III only
D.II and III
Answer: D.II and III
Explanation: b has to equal a squared, and that only works if b is 1. There are no positive integers less than 1, soII and III are correct.
Answer : D
Question: A train sets off at 2 p.m. at the speed of 70 kmph. Another train starts at 1:30 p.m. in the same direction at the rate of 85 kmph. At what time the trains will meet?
A.10.18 p.m
B.10.29 p.m
C.8.30 p.m
D.10.38 p.m
Answer: C.8.30 p.m
Explanation: D = 70 * 1 ½ = 105 km
RS = 85 – 70 = 15
T = 105/15 = 7 h
1.30 + 7 h = 8.30 p.m.
Answer:C
Question: If f(x) = x^3/(x^4 - 1), what is f(1/x) in terms of f(x)?
A.-f(x)
B.f(x)
C.2*f(x)
D.1/f(x)
Answer: A.-f(x)
Explanation: If x = 2 then f(x) = 8/15 and f(1/x) = -8/15 which is equal to -f(x)
answer A
Question: The function f is defined for all positive integers u by the following rule. f(u) is the number of positive integers each of which is less than u and has no positive factor in common with u other than 1. If p is any prime, number then f(p)=
A.(p+1)/2
B.p-2
C.p-1
D.(p-1)/2
Answer: C.p-1
Explanation: If not the wording the question wouldn't be as tough as it is now. The GMAT often hides some simple concept in complicated way of delivering it.
This question for instance basically asks: how many positive integers are less than given prime number p which have no common factor with p except 1.
Well as p is a prime, all positive numbers less than p have no common factors with p (except common factor 1). So there would be p-1 such numbers (as we are looking number of integers less than p).
For example: if p=5 how many numbers are less than 5 having no common factors with 5: 1, 2, 3, 4, --> 5-1=4.
Answer: C.
Question: A rectangular paper when folded into two congruent parts had a perimeter of 34cm foer each part folded along one set of sides and the same is 38cm. When folded along the other set of sides. What is the area of the paper?
A.140
B.788
C.277
D.288
Answer: A.140
Explanation: Explanation:
when folded along the breadth
we have 2(l/2 +b) = 34 or l+2b = 34...........(1)
when folded along the length, we have 2(l+b/2)=38 or 2l+b =38.....(2)
from 1 &2 we get l=14 and b=10
Area of the paper = 14*10 = 140 sq cm
Answer: A) 140
Question: Five percent of a certain grass seed is timothy. If the amount of the mixture needed to plant one acre contains 2 pounds of timothy, how many acres can be planted with 600 pounds of the seed mixture?
A.12
B.15
C.20
D.24
Answer: B.15
Explanation: If the mixture contains 2 pounds of timothy, the mixture must be 40 pounds.
Thus we need 40 pounds of mixture per acre.
600 / 40 = 15 acres
The answer is B.
Question: If Jan spent 40% of her monthly income on housing and 20% less than she spent on housing on a car payment, what percent of her monthly income did she have left after making both her housing payment and her car payment?
A.20%
B.28%
C.42%
D.50%
Answer: B.28%
Explanation: Lets say the total income of Jan is 100
Then
She spends 40 on Housing
20% less than she spent on Housing = 40−20/100∗40=3240−20/100∗40=32
Total expenditure = 40 + 32 = 72
Remaining = 100 - 72 = 28
Hence the answer is B 28 %
Question: The speed of a boat in still water is 70kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?
A.kmph
B.kmph
C.kmph
D.kmph
Answer: D.kmph
Explanation: Speed downstream = 70 + 20 = 90 kmph
Speed upstream = 70 - 20 = 50 kmph
Answer:D
Question: A mixture of 125 gallons of wine and water contains 20% of water. How much water must be added to the mixture in order to increase the percentage of water to 25% of the new mixture?
A.8.33
B.8.39
C.8.36
D.8.31
Answer: A.8.33
Explanation: Explanation:
Initially water in the mixture = 20%(125) = 25
Let x gallons of water be added to change to water concentration to 25% or 1/4
⇒25+x125+x=14⇒25+x125+x=14
⇒x=253⇒x=253 = 8.33 gallons.
Answer:A
Question: Two trains started from the same point. At 8:00 am the first train traveled East at the rate of 80 mph. At 9:00 am, the second train traveled West at the rate of 100 mph. At what time were they 530 miles apart?
A.11:30 am
B.10:30 am
C.8:30 am
D.7:30 am
Answer: A.11:30 am
Explanation: When the first train has traveled for t hours the second train will have traveled (t - 1) hours since it started 1 hour late. Hence if D1 and D2 are the distances traveled by the two trains, then
D1 = 80 t and D2 = 100 (t - 1)
Since the trains are traveling in opposite direction, the total distance D between the two trains is given by
D = D1 + D2 = 180 t - 100
For D to be 530 miles, we need to have
180 t - 100 = 530
Solve for t
t = 3 hours 30 minutes.
8 am + 3:30 = 11:30 am
Answer A
Question: What will come in place of the x in the following Number series? 1. 0, 6, 24, 60, 120, 210, x
A.336
B.350
C.380
D.430
Answer: A.336
Explanation: (A)
The given series is : 13 – 1, 23 – 2, 33 – 3, 43 – 4, 53 – 5, 63 – 6,
So the missing term = 73 – 7 = 343 – 7 = 336
Question: An article cost is Rs 912 after decreasing 24%. So find the actual cost of the article?
A.1200
B.1500
C.1300
D.1000
Answer: A.1200
Explanation: CP* (76/100) = > 912
CP = 12*100 = 1200
ANSWER A
Question: Six machines at a certain factory operate at the same constant rate. If five of these machines, operating simultaneously, take 42 hours to fill a certain production order, how many fewer hours does it take all six machines, operating simultaneously, to fill the same production order?
A.4
B.6
C.7
D.9
Answer: C.7
Explanation: The total work is 5*42 = 210 machine hours
The time required for six machines is 210/6 = 35 hours, thus 7 fewer hours.
The answer is C.
Question: Grace has 17 jellybeans in her pocket. She has 9 red ones, 4 green ones, and 4 blue ones. What is the minimum number of jellybeans she must take out of her pocket to ensure that she has one of each color?
A.4
B.8
C.12
D.14
Answer: D.14
Explanation: The worst scenario is when she takes 9 red and 4 green, total of 13 jellybeans, and still doesn't have 3 distinct colors. But the next draw (14th) will surely be the third color jellybean (blue) as there is no other color jellybeans left in pocket.
Answer: D.
Question: 3 pumps, working 8 hours a day, can empty a tank in 2 days. How many hours a day must 12 pumps work to empty the tank in 1 day?
A.4
B.10
C.11
D.12
Answer: A.4
Explanation: 3 pumps take 16 hrs total (8 Hrs a day)
If 1 pump will be working then, it will need 16*3=48 hrs
1 pump need 48 Hrs
If I contribute 12 pumps then
48/12=4 hrs.
answer :A
Question: The sides AB, BC & CA of a triangle ABC have 3, 4 and 5 interior points respectively on them. Find the number of triangles that can be constructed using these points as vertices.
A.220.
B.205.
C.250
D.105
Answer: B.205.
Explanation: different ways..
1) EASIEST approach..
lets see how many total can be made if none of the points were colliner that is NO three were in one line = 12C3 = 12!/9!3! = 220...
Due to collinear, extra triangles considered above = 3C3 + 5C3 +4C3 = 1+10+4 = 15..
total = 220-15 = 205
ANSWER:B
Question: A stationary engine has enough fuel to move 12 hours when its tank is 4/5 full, how much
hours will it run when the tank is 1/3 full
A.3 hours
B.4 hours
C.5 hours
D.6 hours
Answer: C.5 hours
Explanation: when engine is (4/5) full,it moves for 12 hr
so, when tank is full, it will move = 12/(4/5) = 15 hr
So, when it is 1/3 full, it will move = 15*(1/3)= 5 hours
ANSWER:C
Question: Miguel is 46 years old. He is 6 years older than thrice his son’s age. Find the age of his son.
A.11years
B.12years
C.13years
D.14years
Answer: C.13years
Explanation: sons age=x
46-3x=6
x=13years
ANSWER:C
Question: Each of the 11 letters A, H, I, M, O, T, U, V, W, X and Z appears same when looked at in a mirror. They are called symmetric letters. Other letters in the alphabet are asymmetric letters. How many two letter computer passwords can be formed (no repetition allowed) with at least one symmetric letter
A.2,145
B.6,435
C.12,100
D.2420
Answer: D.2420
Explanation: Since we are given atleast one symmetric letter in the three letter word we can take the following cases
1. All two
2. One symmetry and other two non
4. All the two letters can be arranged in 2 ways
( 11c2+ 11c1 * 15c2) *2
( 11*10/ 2 + 11 * 15 * 14 / 2 ) * 2
2420
IMO option D is the correct answer..
OA please...will correct if I missed anything..D
Question: If each edge of cube increased by 50%, the percentage increase in
A.100
B.114
C.115
D.125
Answer: D.125
Explanation: 100 × (150)/100 × (150)/100 = 225 => 125%
Answer is D.
Question: What is the simplified result of following the steps below in order?
(1)	add 5y to 2z
(2)	multiply the sum by 3
(3)	subtract z + y from the product
A.5z + 14y
B.5x + 16y
C.5x + 5y
D.6x + 4y
Answer: A.5z + 14y
Explanation: 3(5Y+2Z) -Z-Y= 14Y+5Z
'A' is the answer
Question: In paper A, one student got 18 out of 70 and in paper B he got 14 out of 30. In which paper he did fare well?
A.46.6
B.46.9
C.46.7
D.46.2
Answer: A.46.6
Explanation: Find the percentages. Paper A = 18/70 x 100 = 25.7
Paper B = 14/30 x 100 = 46.6
Answer:A
Question: A parallelogram has a base that is four time the size of it's height. The total area of this parallelogram is 2,304 Sq ft. What is the height of the parallelogram?
A.19
B.23
C.24
D.16
Answer: C.24
Explanation: 4x * x = 2304 => x
= 24
Answer: C
Question: A certain number X when divided by 233 leaves a remainder of 87. Which of the following can be subtracted from X to make X divisible by 91?
A.17
B.27
C.37
D.47
Answer: D.47
Explanation: Least possible value of the number is 233 + 87 = 320
Further it is given the number must be divisible by 91 .
320/91 = Gives remainder as 47
So, 47 must be subtracted from the number , answer is (D)
Question: A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
A.40 sec
B.42 sec
C.45 sec
D.48 sec
Answer: A.40 sec
Explanation: Explanation:
Formula for converting from km/hr to m/s: X km/hr =(X x 5/8)m/s.
Therefore, Speed =(45 x5/18)m/sec	=	25/2 m/sec.
Total distance to be covered = (360 + 140) m = 500 m.
Formula for finding Time =(Distance/Speed)
Required time =(500x 2 / 25)sec	= 40 sec.
ANSWER IS A
Question: S is a set containing 7 different positive odd primes. T is a set containing 8 different numbers, all of which are members of S. Which of the following statements CANNOT be true?
A. The median of S is prime.
B. The median of T is prime
C. The median of S is equal to the median of T.
D. The sum of the terms in S is prime.
Answer: A. The median of S is prime.
Explanation: Here is my explanation. The question states:S is a set containing 9 different positive odd primes. T is a set containing 8 different numbers, all of which are members of S. Which of the following statements CANNOT be true?
(A) The median of S is prime.
Thismust be true. If there are an odd number of members of a set, then the median is a member of the set: it's the middle number, when all the numbers are ranked from smallest to biggest. Every number in S is a positive odd prime, so the median is one of them, and is prime.
(B) The median of T is prime.
Thismay or may not be true. If a set has an even number of members, the median is average of the two numbers in the middle, when ranked from smallest to biggest. The average of two odd numberscould beeven (average of 71 and 73 is 72), and hence not prime, or itcould beodd (the average of 71 and 79 is 75). For particularly well chosen odd numbers, the average can be not only odd but also prime -- for example, the average of 89 and 113 is 101, another prime number. If the two middle numbers of T were 89 and 113, the median would be 101, a prime number.
(C) The median of S is equal to the median of T.
Under most configurations for S and T, this wouldn't happen. If you weren't trying to make it happen, it would be unlikely to happen by chance. BUT, if the number dropped going from from S to T was the median of S (say, 101), and if the two middle numbers of T happen to have an average of that number that was dropped (for example, if the two numbers were 89 and 113), then the medians would be equal. In other words, the three middle numbers of S would have to be {. . ., 89, 101, 133, . . .}, and when 101 is dropped in going to T, the median of two would be the average of 89113, which happens to be 101. It's an exceptional case, but itcouldbe true.
(D) The sum of the terms in S is prime.
Thismay or may not be true. The sum of 9 odd numbermustbe an odd number. That odd numbercould beprime. For example, the sum of the first nine odd prime numbers {3, 5, 11, 13, 17, 19, 23, 29} is 127, which is prime. If you drop 3 and include the next prime, 31, the set {5, 11, 13, 17, 19, 23, 29, 31} has a sum of 155, which is clearly not prime.
(E) The sum of the terms in T is prime.
Thismust be false. The sum of eight odd numbers must be an even number. Only 2 is prime, and all other even numbers are not. Therefore, the sum of eight odd prime numbers will be an even number bigger than two, and absolutely cannot be prime.
A
Question: Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 108 kmph and 72 kmph. In how much time will the trains cross each other?
A.8
B.7
C.9
D.2
Answer: A.8
Explanation: Relative speed = (108 + 72)* 5/18 = 50 mps.
The time required = d/s = (100 + 100 + 200)/50
= 400/50 = 8 sec.
Answer:A
Question: A train 110 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?
A.5
B.6
C.7
D.8
Answer: B.6
Explanation: Speed of train relative to man = 60 + 6 = 66 km/hr.
= 66 * 5/18 = 55/3 m/sec.
Time taken to pass the men = 110 * 3/55 = 6 sec.
Answer: Option B
Question: Which of the following correctly lists the data sets in order of least to greatest standard deviation?
I. 56, 56, 56, 56, 56, 56
II. 5, 7, 16, 18, 25, 32
III. 6,7,8,9,10,11,12
A.I, II, III
B.I, III, II
C.II, I, III
D.I, III, II
Answer: D.I, III, II
Explanation: out of three given sets,
I has all numbers same, so it has zero standard deviation hence it is Least
only answer choices C and E have I in least position.
Out of I ans III
III has consecutive numbers , hence all are closedly spaced hence std deviation will be less
while in II,numbers are spread widely hence std deviation should be more than III
hence order should be I, III,II
IMO D
Question: A certain sum of money is divided among A, B and C so that for each Rs. A has, B has 65 paisa and C 40 paisa. If C's share is Rs.24, find the sum of money?
A.288
B.262
C.72
D.123
Answer: D.123
Explanation: A:B:C = 100:65:40
= 20:13:8
8 ---- 24
41 ---- ? => Rs.123
Answer: D
Question: A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 10 hrs and a machine of type S does the same job in 5 hours. If the company used the same number of each type of machine to do the job in 2 hours, how many machines of type R were used?
A.A)3
B.B)4
C.C)6
D.D)9
Answer: C.C)6
Explanation: Rate of machine R =1/10
Rate of machine S =1/5
since same no of machines used for R and S to do the same work in 2 hrs
So collective rate needed to finish the work in 2 hrs= 1/2
Let the no of machine be x
So, x/10 +x/5 =1/2
3x/10=1/2
x=30/5=6
So no of machine R is 6
Answer C
Question: What is the units digit of 18! + 2 ?
A.1
B.2
C.3
D.4
Answer: B.2
Explanation: Any number above 4!, such as 5!, 6!, etc... are always multiples of 10, so their units digit is 0.
The units digit of 18! + 2 is 2.
The answer is B.
Question: A and B can finish a work in 14 days while A alone can do the same work in 24 days. In how many days B alone will complete the work?
A.33 1/3 days
B.35 2/3 days
C.33 2/3 days
D.31 2/3 days
Answer: C.33 2/3 days
Explanation: B = 1/14 – 1/24 = 5/168
=> 168/5 days
=>33 2/3 days
ANSWER:C
Question: A company has two types of machines, type R and type S. Operating at a constant rate a machine of R does a certain job in 36 hours and a machine of type S does the job in 12 hours. If the company used the same number of each type of machine to do job in 12 hours,how many machine R were used?
A.3
B.4
C.6
D.9/2
Answer: D.9/2
Explanation: yes there is a typo in the question, I got the same ques on my GMAT PREP last week, and the questions goes as:
A company has two types of machines,type R and type S.Operating at a constant rate a machine of R does a certain job in 36 hours and a machine of type S does the job in 12 hours .If the company used the same number of each type of machine to do job in2 hours,how many machine R were used?
So for a job to be done in 2 hours R = 1/2
R_a(Rate of Machine R) = 1/36
R_s(Rate of Machine S) = 1/12
Lets say x machines are used to attain the desired rate, thus
x/36+x/12 = 1/2 (Desired R =1/2 i.e. to complete the job in 2 hours)
(x+3x)/36 = 1/2
4x/36 = 1/2
x = 9/2.
QA = 9/2 (ANSWER D)
Question: Subtracting 10% from X is the same as multiplying X by what number?
A.97%
B.90%
C.80%
D.98%
Answer: B.90%
Explanation: X - (10/100) X = X * ?
? = 90%
Answer: B
Question: A bag contains 6 red, 5 blue and 2 green balls. If 2 balls are picked at random, what is the probability that both are red?
A.2/13
B.3/17
C.5/26
D.5/21
Answer: C.5/26
Explanation: P(Both are red),
=6C213C2=6C213C2
=5/26
C
Question: How many words, with or without meaning, can be formed using all letters of the word SHARP using each letter exactly once?
A.90
B.100
C.110
D.120
Answer: D.120
Explanation: The Word SHARP has exactly 5 letters which are all different.
Therefore the number of words that can be formed = Number of permutations of 5 letters taken all at a time.
= P (5, 5) = 5!
= 5 x 4 x 3 x 2 × 1
= 120
ANSWER:D