mathewhe/aqua_rat huggingface dataset:
Question: 3 letters have to be put into their 3 respective envelopes. If the letters are inserted randomly into the envelopes, what is the probability that all the letters go into their respective envelopes?
(A) 1/30
(B) 1/6
(C) 1/120
(D) 1/240
(E) 3/5
Rationale: A-B-C-D-E (envelopes)
a-b-c-d-e (letters)
3 letters (a, b, c, d, and e) can be assigned to 3 envelopes (arranged) in 3! ways, out of which only one will be correct, thus the probability is 1/3! = 1/6.
Answer: B.
Answer: (B) 1/6
Question: A number is said to be prime saturated if the product of all the different positive prime factors of a is less than the square root of a. What is the greatest two digit prime saturated integer ?
(A) 99
(B) 98
(C) 97
(D) 96
(E) 95
Rationale: Clearly D A number is said to be prime saturated if the product of all the different positive prime factors of a is less than the square root of a.
96 has more number of smaller prime factor thats the clue !!=D
Answer: (D) 96
Question: If x-1 – 1 is divided by x - 1 the quotient is:
(A) 1
(B) 1/(x-1)
(C) - 1/(x-1)
(D) 1/x,
(E) – 1/x
Rationale: Solution:
x-1 – 1 is divided by (x – 1)
= x-1 – 1 × 1/(x-1)
= 1/x – 1 × 1/(x-1)
= (1 – x/x) × 1/(x-1)
= - (1 – x)/x × 1/(x-1)
= – 1/x [cancel x – 1 from the numerator and denominator].
Answer: E
Answer: (E) – 1/x
Question: Two trains of equal are running on parallel lines in the same direction at 44 km/hr and 36 km/hr. The faster train passes the slower train in 36 sec. The length of each train is?
(A) 40 m
(B) 72 m
(C) 80 m
(D) 82 m
(E) 84 m
Rationale: Let the length of each train be x m.
Then, distance covered = 2x m.
Relative speed = 44 - 36 = 8 km/hr.
= 8 * 5/18 = 20/9 m/sec.
2x/36 = 20/9 => x = 40.
ANSWER:A
Answer: (A) 40 m
Question: If two sides of a triangle are 5 and 12, respectively, which of the following could NOT be the area of this triangle?
(A) 1
(B) 6
(C) 38
(D) 29
(E) 17
Rationale: For this question it would be helpful to know the largest area that this triangle could be, given the two sides of 5 and 12.
We know that the area of a triangle will be maximized when two sides are perpendicular to each other (consult Bunuel's drawing above). Thus we have a max area being equal to one half the base times the height, either (.5)12 * 5 -or- (.5)5 * 12 will result in a maximum area of 30 for the triangle; therefore, the triangle could never have an area of 38.
C
Answer: (C) 38
Question: You and your friend spent a total of $11 for lunch. Your friend spent $3 more than you. How much did your friend spend on their lunch?
(A) $9
(B) $3
(C) $7
(D) $6
(E) $5
Rationale: My lunch = l, my friends lunch = l+1
(l)+(l+3)=11
l+l+3-3=11-3
2l=8
l=4
My friends lunch l+3 = 4+3=$7, the answer is C
Answer: (C) $7
Question: The ratio between the sale price and the cost price of an article is 9:7. What is the ratio between the profit and the cost price of that article?
(A) 2:9
(B) 2:7
(C) 3:6
(D) 2:0
(E) 2:1
Rationale: Let C.P. = Rs. 7x and S.P. = Rs. 9x.
Then, Gain = Rs. 2x
Required ratio = 2x : 7x = 2:7
Answer:B
Answer: (B) 2:7
Question: In what time will a train 100 m long cross an electric pole, it its speed be 144 km/hr?
(A) 2.5 sec
(B) 2.8 sec
(C) 8.5 sec
(D) 2.2 sec
(E) 4.5 sec
Rationale: Speed = 144 * 5/18
= 40 m/sec
Time taken = 100/40
= 2.5 sec.
Answer:A
Answer: (A) 2.5 sec
Question: If A lends Rs.3500 to B at 10% per annum and B lends the same sum to C at 11.5% per annum then the gain of B in a period of 3 years is?
(A) 157.78
(B) 157.98
(C) 157.5
(D) 157.19
(E) 157.12
Rationale: (3500*1.5*3)/100
=> 157.50
Answer: C
Answer: (C) 157.5
Question: In how many different number of ways 3 boys and 1 girls can sit on a bench?
(A) 24
(B) 40
(C) 60
(D) 78
(E) 80
Rationale: npn = n!
4p4= 4 × 3 × 2 × 1 = 24
A)
Answer: (A) 24
Question: On my sister’s 15th birthday, she was 159 cm in height, having grown 6% since the year before. How tall was she the previous year?
(A) 150 cm
(B) 140 cm
(C) 142 cm
(D) 154 cm
(E) 160 cm
Rationale: Explanation :
Given that height on 15th birthday = 159 cm and growth = 6%
Let the previous year height = x
Then height on 15th birthday = x ×100+6100=x×106100
⇒159 = x × (106/100)
⇒x=159×100106=1.5×100=150;cm
ANSWER IS A
Answer: (A) 150 cm
Question: Average of all prime numbers between 25 to 50
(A) 37
(B) 38
(C) 39
(D) 39.8
(E) 40
Rationale: Explanation:
Prime numbers between 25 and 50 are:
29, 31, 37, 41, 43, 47
Average of prime numbers between 25 to 50 will be
(29+31+37+41+43+47 / 6)=228 / 6=38
Option B
Answer: (B) 38
Question: Weights of two friends Ram and Shyam are in the ratio 6:5. If Ram's weight is increased by 10% and total weight of Ram and Shyam become 82.8 kg, with an increases of 15%. By what percent did the weight of Shyam has to be increased?
(A) 19%
(B) 10%
(C) 21%
(D) 16%
(E) None
Rationale: Solution:
given ratio of Ram and Shayam's weight = 6:5
Hence, (x-15)/(15-10) = 6/5
Or, x = 21%.
Answer: Option C
Answer: (C) 21%
Question: The telephone company wants to add an area code composed of 2 letters to every phone number. In order to do so, the company chose a special sign language containing 324 different signs. If the company used 322 of the signs fully and two remained unused, how many additional area codes can be created if the company uses all 324 signs?
(A) 246
(B) 248
(C) 1292
(D) 15,128
(E) 30,256
Rationale: # of 2-letter codes possible from 324 different signs = 324*324.
# of 2-letter codes possible from 322 different signs = 322*322.
The difference = 324^2 - 322^2 = (324 - 322)(324 + 322) = 1292.
Answer: C.
Answer: (C) 1292
Question: If 5 cats can kill 5 rats in 5 minutes, how long will it take 100 cats to kill 100 rats?
(A) 1 minutes
(B) 2 minutes
(C) 3 minutes
(D) 4 minutes
(E) 5 minutes
Rationale: It will take 5 minutes for 100 cats to kill 100 rats.
1 cat can kill 1 rat in 5 minutes, so 100 cats can kill 100 rats in 5 minutes
Answer E
Answer: (E) 5 minutes
Question: Vijay bought 160 shirts at the rate of Rs. 225 per shirt. The transport expenditure was Rs. 1400. He paid an octroi at the rate of Rs. 1.75 per shirt and labour charges were Rs. 320. What should be the selling price of one shirt, if he wants a profit of 20%?
(A) Rs.225
(B) Rs.288
(C) Rs.485
(D) Rs.285
(E) Rs.282
Rationale: Total CP per shirt = 225 + 1400/160 + 1.75 + 320/160 = Rs. 237.5
SP = CP[(100 + profit%)/100]
= 237.5 * [(100 + 20)/100] = Rs.285.
Answer:D
Answer: (D) Rs.285
Question: If 6x^2 + x - 12 = (qx + b)(cx + d), then |q| + |b| + |c| + |d| =
For a complete solution and more practice problems, see this blog:
http://magoosh.com/gmat/2012/algebra-on ... to-factor/
(A)  10
(B)  12
(C)  15
(D)  18
(E)  20
Rationale: 6x^2+x-12 = 6x^2 + 9x -8x -12
=> 3x(2x+3) -4(2x+3)
=> (2x+3)(3x-4) = (qx+b)(cx+d)
Hence q=2, b=c=3, d=-4
So, 2+3+3+ |-4| = 2+3+3+4 = 12
Answer B.
Answer: (B)  12
Question: A person travels 12 km in the southward direction and then travels 5km to the right and then travels 15 km toward the right and finally travels 5km towards the east, how far is he from his starting place?
(A) 2
(B) 3
(C) 4
(D) 6
(E) 7
Rationale: To solve these type of questions, first draw the direction diagram and assume the person is at the intersection point.
From the diagram it is clear that he is 3 km from where he started.
Answer:B
Answer: (B) 3
Question: If n = 20! + 15, then n is divisible by which of the following?
I. 15
II. 17
III. 19
(A) I only
(B) II only
(C) III only
(D) I and II
(E) II and III
Rationale: 15 divides 20! so 15 also divides 20! + 15.
17 and 19 divide 20! so they do not divide 20! + 15.
The answer is A.
Answer: (A) I only
Question: Jack has three more cards than Bill. Together they have 47 cards. If x represents the number of cards Bill has, then an equation that can be used to determine the number of cards each one has is
(A) x + 3 = 47
(B) 2x + 3 = 47
(C) x - 3 = 47
(D) 2x - 3 = 47
(E) 3x + 3 = 47
Rationale: Explanatory Answer
Bill has x cards.
Jack has 3 more cards than Bill. So, Jack has x + 3 cards.
So, together Bill and Jack have x + x + 3 = 2x + 3 cards.
The question states that they have 47 cards between them.
So, 2x + 3 = 47.
Answer B
Answer: (B) 2x + 3 = 47
Question: A key ring has 7 keys. How many different ways can they be arranged?
(A) 6
(B) 7
(C) 5!
(D) 6!
(E) 7!
Rationale: I would like to argue against OA. 7 => 6! circular permutations. Therefore, for a keyring - arrangements = 6!/2
ANS:A
Answer: (A) 6
Question: If a class of 10 students has three men, how many ways can the men and women be arranged in a circle so that no two men sit next to each other?
(A) 3!2!
(B) 5!5!
(C) 4!4!
(D) 10!
(E) 10!/5!
Rationale: for no two men to sit together, either all are in even or odd position
fix one at any one position then rest four can be fixed in 2! ways...
also rest five position of women can be fixed in 3!..
total ways 3!2!
A
Answer: (A) 3!2!
Question: A trader bought a car at 20% discount on its original price. He sold it at a 50% increase on the price he bought it. What percent of profit did he make on the original price?
(A) 17%
(B) 72%
(C) 20%
(D) 82%
(E) 16%
Rationale: Original price = 100
CP = 80
S = 80*(150/100) = 120
100 - 120 = 20%
Answer:C
Answer: (C) 20%
Question: The number of positive integer solutions for the equation x +y +z + t = 15 is
(A) 654
(B) 584
(C) 384
(D) 364
(E) 394
Rationale: The number of positive integer solutions for the equatio fx1+x2+⋯+xn=k
(k-1)C(n-1)- where k is the number and n is number of variable in the equation.
15-1 C 4-1 = 14C3 = 364
Answer : D
Answer: (D) 364
Question: A watch passes through three hands and each gains 25%. If the 3rd sells it for Rs250, what did the 1st pay for it?
(A) 112
(B) 116
(C) 128
(D) 175
(E) 256
Rationale: First Purchased = 250 Wes= 128
C
Answer: (C) 128
Question: A father said to his son, "I was as old as you are at present at the time of your birth." If the father's age is 40 years now, the son's age 10 years back was?
(A) 12yr
(B) 15yr
(C) 14yr
(D) 10yr
(E) 20yr
Rationale: Let the son's present age be x years
Then, 40-x = x
x = 20
Son's age 10 years back = 20-10 = 10years
Answer is D
Answer: (D) 10yr
Question: A collection of 16 coins, each with a face value of either 10 cents or 25 cents, has a total face value of $2.35. How many of the coins have a face value of 10 cents?
(A) 2
(B) 5
(C) 8
(D) 9
(E) 11
Rationale: 0.10(x)+0.25(16-x)=2.35
0.10x+4-0.25x=2.35
so x=11
ans is E
Answer: (E) 11
Question: John and Mary were each paid x dollars in advance to do a certain job together. John worked on the job for 10 hours and Mary worked 5 hours less than John. If Mary gave John y dollars of her payment so that they would have received the same hourly wage, what was the dollar amount, in terms of y, that John was paid in advance?
(A)  4y
(B)  5y
(C)  3y
(D)  8y
(E)  9y
Rationale: Let $x be the advance that both receive = 5x
Amount earned per hour by John and Mary = x/10 and x/5
Mary gives $y to John to make the wages earned equal
Hence John wage per hr = (x+y)10 which is now equal to Mary's wage (x-y)/5
Solve (x+y)10 = (x-y)/5
5x + 5y = 10x -10y
5x = 15y
x = 3y
Ans. C
Answer: (C)  3y
Question: From a pack of 52 cards, one card is drawn. What is the probability that the card drawn is a queen of club or a king of heart?
(A) 1/26
(B) 25/26
(C) 3/26
(D) 1/52
(E) 4/52
Rationale: Solution
Let S be the sample space. Then,
n(S) = 52C1	= 52.
Let E = event of getting a queen of club or a king of heart.
n(E) = 2C1	= 2.
P(E) = n(E) / n(S)	= 2 / 52
= 1/26.
Answer A
Answer: (A) 1/26
Question: Divide $100 among W,X in the ratio 3:7. How many $ that X get?
(A) $40
(B) $50
(C) $60
(D) $70
(E) $80
Rationale: Sum of ratio terms = 3+7 = 10
X = 100*7/10 = $70
Answer is D
Answer: (D) $70
Question: 3, 12, 7, 26, 15, ?
(A) 34
(B) 44
(C) 54
(D) 64
(E) 74
Rationale: 3, ,7, ,15
(3*2)+1=7
(7*2)+1=15
12, ,26, ,?
(12*2)+2=26
(26*2)+2=54
ANSWER:C
Answer: (C) 54
Question: A box contains 12 marbles of three different colours green, yellow and blue---4 each.
If you were to close your eyes and pick them at random, how many marbles must you take out to be sure that there are at least two of one colour among the marbles picked out?
(A) 1
(B) 4
(C) 6
(D) 3
(E) 7
Rationale: B
4
In the first three pickings you may get 1 of each colour, on the 4th pick there will be at least two of one colour.
Therefore, the answer is 4.
Answer: (B) 4
Question: Two taps can separately fill a cistern 10 minutes and 15 minutes respectively and when the waste pipe is open, they can together fill it in 18 minutes. The waste pipe can empty the full cistern in?
(A) 6
(B) 8
(C) 1
(D) 9
(E) 2
Rationale: 1/10 + 1/15 - 1/x = 1/18
x = 9
Answer:D
Answer: (D) 9
Question: Jim drove 642 miles of a 1200 miles journey. How many more miles does he need to drive to finish his journey?
(A) 113 miles
(B) 432 miles
(C) 558miles
(D) 887 miles
(E) 767 miles
Rationale: The number of miles to drive to finish his journey is given by
1200 - 642 = 558 miles
correct answer C
Answer: (C) 558miles
Question: How many boxes do you need if you have to pack 1080 apples into cases that each hold one dozen apples ?
(A) 40
(B) 60
(C) 70
(D) 80
(E) 90
Rationale: E
90
1080 apples = 90 dozens
The required number of boxes = 90.
Answer : E
Answer: (E) 90
Question: A train running at the speed of 60 km/hr crosses a pole in 15 sec. What is the length of the train?
(A) 287
(B) 699
(C) 250
(D) 168
(E) 150
Rationale: Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 12 = 250 m
Answer: C
Answer: (C) 250
Question: Barbara, Becky and Beth dressed up as princesses for Halloween. One was Snow White. One was Sleeping Beauty. One was Cinderella. Becky is not Sleeping Beauty and she went trick-or-treating with Snow White. Beth and Sleeping Beauty are sisters. Who is Snow White?
(A) Becky
(B) Beth
(C) Barbara
(D) none
(E) Mary
Rationale: Becky is neither Sleeping Beauty nor Snow White (since Becky went trick-or-treating with Snow White). Therefore, Becky has to be Cinderella.
Beth is neither Sleeping Beauty nor Cinderella (since Becky is Cinderella). Therefore, Beth has to be Snow White.
correct answer B
Answer: (B) Beth
Question: If y is an integer, then the least possible value of |32 - 7y| is
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: We know that 5y is a multiple of 7, so let’s first look at the multiples of 7 closest to 32. We have “28” and “35”. Let’s subtract both of these from 32 and see which one produces the smallest result. When 7y = 28, y is 4 and when 7y = 35, y is 5. Let’s start with letting y = 4.
|32-7(4)|
|32-28|
|4| = 4
Next, let’s let y equal 5.
|32-7(5)|
|32-35|
|-3| = 3
We see that the smallest possible value of |32-7y| is 3.
Answer C.
Answer: (C) 3
Question: A can do a piece of work in 4hours. B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it?
(A) 8 hours
(B) 10 hours
(C) 12 hours
(D) 24 hours
(E) 30 hours
Rationale: A's 1 hour work= 1/4
(B+C)'s 1 hour work= 1/3
(A+C)'s 1 hour work= 1/2
(A+B+C)'s 1 hour work= (1/4+1/3)=7/12
B's 1hour's work= (7/12-1/2)= 1/12
B alone will take 12 hours to do the work.
correct option is C
Answer: (C) 12 hours
Question: On dividing 17698 by a certain number, we get 89 as quotient and 14 as remainder. What is the divisor?
(A) 199
(B) 154
(C) 852
(D) 741
(E) 785
Rationale: Divisor *quotient+remainder=dividend
divisor=(dividend)-(remainder)/quotient
(17698-14)/89=199
Answer(A)
Answer: (A) 199
Question: In a bag, there are two 6-sided dice (numbered 1 to 6), three 12-sided dice (numbered 1 to 12), and two 20-sided dice (numbered 1 to 20). If four of these dice are selected at random from the bag, and then the four are rolled and we find the sum of numbers showing on the four dice, how many different possible totals are there for this sum?
(A) 60
(B) 50
(C) 42
(D) 84
(E) 61
Rationale: As 'complex-looking' as this question might appear, it's actually rather simple. Pay careful attention to what the specific questions asks for - the number of DIFFERENT possible SUMS from 4 dice. Since we're dealing with some 'special' dice (some 12-sided and 20-sided dice), we have to adjust out math accordingly, but the possibilities are rather limited:
1) The minimum number on any given die is 1
2) The maximum possible sum would only occur if we took the 4 biggest possible dice and rolled the highest possible number on each.
With 4 dice, we could end up with any SUM between:
4 (if we rolled 1s on all 4 dice)
to
64 (if we rolled two 20s on the 20-sided dice and two 12s on the 12-sided dice).
Thus, there are only 61 possible sums.
E
Answer: (E) 61
Question: A lends Rs. 2500 to B and a certain to C at the same time at 7% p.a. simple interest. If after 4 years, A altogether receives Rs. 1120 as interest from B and C, then the sum lent to C is?
(A) 3377
(B) 1500
(C) 2887
(D) 1778
(E) 1221
Rationale: Let the sum lent to C be Rs. x. Then,
(2500 * 7 * 4) / 100 + (x * 7 * 4) / 100 = 1120
7/25 x = (1120 - 700) => x = 1500
Answer: B
Answer: (B) 1500
Question: At present, the ratio between the ages of Arun and Deepak is 4:3. After 6 years, Arun's age will be 22 years. What is the age of Deepak at present?
(A) 12 years
(B) 15 years
(C) 66 years
(D) 88 years
(E) 55 years
Rationale: Let the present ages of Arun and Deepak be 4x and 3x years respectively.
Then, 4x + 6 = 22 => x = 4
Deepak's age = 3x = 12 years.
Answer: A
Answer: (A) 12 years
Question: How many numbers from 29 to 79 are exactly divisible by 11?
(A) 5
(B) 7
(C) 9
(D) 11
(E) 12
Rationale: Option 'A'
29/11 = 2 and 79/11 = 7 ==> 7 - 2 = 5 Numbers
Answer: (A) 5
Question: In the equation 2x â€“ cy = 18, c is a constant. If the value of y is 2 when x is 6, what is the value of x when y is 5 ?
(A) âˆ’9/2
(B) -1
(C) -3
(D) 4
(E) 9/2
Rationale: 2x - cy = 18
x=6, y=2;
12-2c=18
c=-3
2x-cy=18
when y=5, c=-3, x=
x=9/2
ANSWER:B
Answer: (B) -1
Question: the age of a and b are in the ratio 4:5 and of b and c in the ratio 3:2.the youngedt of three is
(A) a
(B) b
(C) c
(D) can't say
(E) none
Rationale: a:b => 4:5 3*(a:b)=> 12:15
b:c=>3:2 5*(b:c)=> 15:10
a:b:c =>12:15:10
Therefore youngest is c.
ANSWER:C
Answer: (C) c
Question: Average of first five multiples of 5 is
(A) 9
(B) 11
(C) 13
(D) 15
(E) 17
Rationale: Explanation:
Average=5(1+2+3+4+5) / 5=75 / 5=15
Option D
Answer: (D) 15
Question: 5 blue marbles, 3 red marbles and 4 purple marbles are placed in a bag. If 4 marbles are drawn without replacement, what is the probability that the resu lt will not be 2 blue and 2 purple marbles?
(A) 4/33
(B) (5/36)^2
(C) 1/2
(D) (31/36)^2
(E) 29/33
Rationale: Answer is 29/33.
The probability of 2 blue and 2 purple marbles selected is 5C2.4C2/12C4 =4/33.
Subtracting the above from 1 we get 29/33 E
Answer: (E) 29/33
Question: Number of prime numbers between 15 and 45 is
(A) 4
(B) 8
(C) 6
(D) 7
(E) 9
Rationale: total 8=17, 19, 23, 29, 31, 37, 41, 43
ANSWER:B
Answer: (B) 8
Question: A, B, C together started a business. A invested Rs.2000 for 5 months B invested Rs.2500 for 6 months and C Rs.3000 for 3 months. If they get a total profit of Rs.3400. Find the share of A?
(A) 2999
(B) 3000
(C) 1000
(D) 2999
(E) 17212
Rationale: 4*5:5*6:6*3
20 : 30 : 18
20/68 * 3400 = 1000
Answer:C
Answer: (C) 1000
Question: A goods train runs at the speed of 72 km/hr and crosses a 250 m long platform in 30 sec. What is the length of the goods train?
(A) 299
(B) 277
(C) 350
(D) 270
(E) 281
Rationale: Speed = 72 * 5/18 = 20 m/sec.
Time = 30 sec.
Let the length of the train be x meters.
Then, (x + 250)/30 = 20
x = 350m.
Answer: C
Answer: (C) 350
Question: The seating chart of an airplane shows 30 rows of seats. Each row has 3 seats on each side of the center aisle, and one of the seats on each side is a window saet. The view from the window seats in 15 of the rows is obscured by the wings of the airplane. If the first person to be assigned a seat is assigned a window seat and thw window seat is assigned randomly, what is the probability that the person will get a seat with an unobscured view?
(A) 1/6
(B) 1/2
(C) 2/3
(D) 5/6
(E) 17/18
Rationale: priyalr
6 seats per row, think of a boeing 737. We have 30 rows, therefore window 30 seats one one side and 30 window seats on the other, totaling 60 window seats on the whole plane.
the view of the window of 15 rows is blocked. two wings, therefore 30 window seats are blocked.
Total window seats = 60
Total blocked window seats = 30
Total unblocked seats = 30
We know that a window seat was given, therefore probability for not window seat is 30/60 =1/2
ANS B
Answer: (B) 1/2
Question: A and B can do a piece of work in 10 days. With the help of C they finish the work in 5 days. C alone can do that piece of work in?
(A) 33
(B) 878
(C) 30
(D) 10
(E) 11
Rationale: C = 1/5 â€“ 1/10 = 1/10 => 10 days
Answer: D
Answer: (D) 10
Question: What is the square root of 16?
(A) 8
(B) 4
(C) 35
(D) 42
(E) 86
Rationale: 4X4= 16
ANSWER B
Answer: (B) 4
Question: Six points are marked on a straight line and five points are marked on another line which is parallel to the first line. How many straight lines, including the first two, can be formed with these points?
(A) 11
(B) 17
(C) 16
(D) 32
(E) 10
Rationale: We know that, the number of straight lines that can be formed by the 11 points in which 6 points are collinear and no other set of three points, except those that can be selected out of these 6 points are collinear.
Hence, the required number of straight lines
= 11C2 - 6C2 - 5C2 + 1 + 1
= 55 - 15 - 10 + 2 = 32
Answer: D
Answer: (D) 32
Question: In how many ways can 7 boys and 4 girls sit around a table in such a way that no two girls sit together?
(A) 695400
(B) 625800
(C) 685000
(D) 615000
(E) 604800
Rationale: The 7 boys can be seated around a table in 6! Ways. In between them there are 7 places.
The 4 girls can be placed in the 7 places in 7P4 ways.
Therefore, Required number of ways= 6!* 7P4
=720 * 840 =604800
ANSWER:E
Answer: (E) 604800
Question: A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 240 m long?
(A) 40 sec
(B) 42 sec
(C) 45 sec
(D) 48 sec
(E) 50 sec
Rationale: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 360 + 240 = 600 m
Required time = 600 * 2/25 = 48 sec
ANSWER:D
Answer: (D) 48 sec
Question: If r and s are even integers, which of the following is an odd integer?
(A) rs + 2
(B) r(s − 1)
(C) r(r + 5)
(D) 3r + 4s
(E) (r + 3)(s − 1)
Rationale: If r and s are even integers, then:
A. rs + 2: even + even = even
B. r(s − 1): even(odd) = even
C. r(r + 5): even(odd) = even
D. 3r + 4s: even + even = even
E. (r + 3)(s − 1): (odd)(odd) = odd.
Answer is E.
Answer: (E) (r + 3)(s − 1)
Question: By selling 110 mangoes, a fruit-seller gains the selling price of 20 mangoes. Find the gain percent?
(A) 28.28%
(B) 32.32%
(C) 17.71%
(D) 22.22%
(E) 33.33%
Rationale: SP = CP + g
110 SP = 110 CP + 20 SP
90 SP = 110 CP
90 --- 20 CP
100 --- ? => 22.22%
Answer: D
Answer: (D) 22.22%
Question: On three consecutive flips of a coin, what is the probability that all three produce the same result?
(A) 1/16
(B) 1/8
(C) 1/4
(D) 3/8
(E) 1/2
Rationale: TTT case --> P = (1/2)^3 = 1/8.
HHH case --> P = (1/2)^3 = 1/8.
P(TTT or HHH) = 1/8 + 1/8 = 1/4.
Answer: C.
Answer: (C) 1/4
Question: Alex takes a loan of $4,000 to buy a used truck at the rate of 6 % simple Interest.Calculate the annual interest to be paid for the loan amount.
(A) 680
(B) 700
(C) 240
(D) 620
(E) 260
Rationale: From the details given in the problem Principle = P = $4,000 and R = 6% or 0.06 expressed as a decimal.
As the annual Interest is to be calculated, the time period T =1.
Plugging these values in the simple Interest formula,
I = P x T x R
= 4,000 x 1 x 0.06
= 240.00
Annual Interest to be paid = $240
answer :C
Answer: (C) 240
Question: The area of a square is subtracted from one of its sides, and the perimeter is then added to this total, the result is 4. What is the length of one side?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: The equation is; side - Area + Perimeter = s - A + P = s - s^2 + 4s = s(1 - s + 4).
By plugging in the answers we can test the answers quickly; then, 4 is the only possible answer.
Answer: A
Answer: (A) 1