mathewhe/aqua_rat huggingface dataset:
Question: Fred and Sam are standing 50 miles apart and they start walking in a straight line toward each other at the same time. If Fred walks at a constant speed of 5 miles per hour and Sam walks at a constant speed of 5 miles per hour, how many miles has Sam walked when they meet?
(A) 5
(B) 9
(C) 25
(D) 30
(E) 45
Rationale: relative distance =50 miles
relative speed =5+5 =10 miles per hour
time taken =50/10=5 hours
distance travelled by sam =5*5=25 miles= C
Answer: (C) 25
Question: If -1 < x < 0, which of the following must be true?
I. x^7 < x^3
II. x^3 < 1 – x
III. x^5 < x^3
(A) II,III only
(B) I,II,III only
(C) I only
(D) II only
(E) III only
Rationale: Answer : B
Answer: (B) I,II,III only
Question: On a trip, a cyclist averaged 8 miles per hour for the first 12 miles and 12 miles per hour for the remaining 24 miles. If the cyclist returned immediately via the same route and took a total of 7.5 hours for the round trip, what was the average speed (in miles per hour) for the return trip?
(A) 9
(B) 10
(C) 11
(D) 12
(E) 13
Rationale: The time to go 36 miles was 12/8+24/12=1.5+2=3.5 hours.
The average speed for the return trip was 36 miles/4 hours= 9 mph.
The answer is A.
Answer: (A) 9
Question: A man can do a piece of work in 5 days, but with the help of his son he can do it in 3 days. In what time can the son do it alone ?
(A) 13/2
(B) 19/2
(C) 21/2
(D) 15/2
(E) None
Rationale: Son's one day work = (1/3âˆ’1/5)=2/15
So son will do whole work in = 15/2 days
Answer: C
Answer: (C) 21/2
Question: At present, the ratio between the ages of Arun and Deepak is 4:3. After 6 years, Arun's age will be 30 years. What is the age of Deepak at present?
(A) 77 years
(B) 15 years
(C) 66 years
(D) 18 years
(E) 55 years
Rationale: Let the present ages of Arun and Deepak be 4x and 3x years respectively.
Then, 4x + 6 = 30 => x = 6
Deepak's age = 3x = 18 years.
Answer: D
Answer: (D) 18 years
Question: Calculate the amount that an investor needs to be invest to earn $441 in interest in 12 months if the investor plans to invest x dollars in a savings account that pays interest at an annual rate of 7% compounded semi-annually?
(A) 6209
(B) 6200
(C) 6799
(D) 6199
(E) 6685
Rationale: the approach is substitution,
our interest requirement is $441 after 12 months, 2 compounding period.
calculate the compound interest on each option and find out the one that yields $441 in 12 months
6200 yielded $441
using the formula
A = P(1 + r/n)nt
hence answer is B
Answer: (B) 6200
Question: What least number should be added to 1052, so that the sum is completely divisible by 23
(A) A)4
(B) B)1
(C) C)6
(D) D)3
(E) E)5
Rationale: Explanation:
(1052 / 23) gives remainder 17
17 + 6 = 23, So we need to add 6
Answer: Option C
Answer: (C) C)6
Question: The population of a bacteria colony doubles every day. If it was started 9 days ago with 2 bacteria and each bacteria lives for 11 days, how large is the colony today?
(A) 512
(B) 768
(C) 4096
(D) 2048
(E) 1024
Rationale: 9 days ago- 2
8 days ago- 4
7 days ago- 8
6 days ago- 16
5 days ago- 32
4 days ago- 64
3 days ago- 128
2 days ago- 256
Yesterday- 512
Today- 1024
Ans:E
Answer: (E) 1024
Question: Given 2x + y + z = 3 and 5x + 3y + z = 15, what is the value of x + y - z?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: (1) 5x + 3y + z = 15
If 2x + y + z = 3, then (2) 4x + 2y + 2z = 6
Let's subtract equation (2) for equation (1).
x + y - z = 9
The answer is E.
Answer: (E) 9
Question: A woman takes 5hr 45min in walking to certain place and riding back. She would have gained 2hrs by riding both ways. The time she would take to walk both ways is?
(A) 6 hr 45 min
(B) 3 hr 45 min
(C) 8 hr 55 min
(D) 7 hr 45 min
(E) 4 hr 60 min
Rationale: D
7 hr 45 min
Let x be the speed of walked
Let y be the speed of ride
Let D be the distance
Then D/x + D/y = 23/4 hr -------------------(1)
D/y + D/y = 23/4 – 2 hr
D/y = 15/8 ----------------------------------(2)
substitute 2 in 1
D/x + 15/8 = 23/4
D/x = 23/4 -15/8 =46-15/8 =31/8
Time taken for walk one way is 31/8 hr
time taken to walk to and fro is 2*31/8 = 31/4 hr
=7 hr 45 min
Answer: (D) 7 hr 45 min
Question: If x > 0.7, which of the following could be the value of x?
(A) √0.06
(B) √0.07
(C) √0.7
(D) √0.05
(E) √0.04
Rationale: Answer : C
Answer: (C) √0.7
Question: (64 - 12)^2 + 4 x 64 x 12 = ?
(A) 5246
(B) 4406
(C) 5776
(D) 5126
(E) 5128
Rationale: Explanation :
(a + b)^2 = a^2 + 2ab + b^2
(a - b)^2 = a^2 - 2ab + b^2
Here, the given statement is like (a - b)^2 + 4ab where a= 64 and b = 12
(a - b)^2 + 4ab = (a^2 - 2ab + b^2) + 4ab = a^2 + 2ab + b^2 = (a + b)^2
Hence (64 - 12)^2 + 4 x 64 x 12 = (64 + 12)^2 = 76^2 = 5776
Answer is C
Answer: (C) 5776
Question: There is a sequence ni such, in which i is a positive integer, ni+1=2ni.
If n1=1, n2=2, n3=4, n4=8, what is the scope including n11?
(A) 10~100
(B) 1,000~10,000
(C) 10,000~100,000
(D) 100,000~1,000,000
(E) 1,000,000~
Rationale: -> ni=2^(i-1) -> 2^10=1,024>1,000=10^3 -> n11=2^10=(2^10)>(10^3)=10^3
Thus, the answer is B.
Answer: (B) 1,000~10,000
Question: A and B can do a job in 15 days and 10 days, respectively. They began the work together but A leaves after some days and B finished the remaining job in 5 days. After how many days did A leave?
(A) 2 days
(B) 3 days
(C) 1 day
(D) 4 days
(E) None of these
Rationale: A’s one day’s work = 1⁄15 th work.
B’s one day’s work = 1⁄10 th work.
(A + B)’s one day’s work = 1⁄15 + 1⁄10 = 1⁄6 th work.
Let A left after x days.
∴ (A + B)’s x days’ work = x⁄6 th work.
Remaining work = 1 - x⁄6 = (6 - x)⁄6 th work.
Now, in 5 days, work done by B = (6 - x)⁄6 th work.
∴ in 1 day work done by B = (6 - x)⁄30 th work.
and (6 - x)⁄30 = 1⁄10
∴ x = 3 days
Answer B
Answer: (B) 3 days
Question: If Q = x% of y and B = y% of x, then which of the following is true?
(A) 1) Q is smaller than B.
(B) 2) A is greater than B
(C) 3) Relationship between A and B cannot be determined.
(D) 4) If x is smaller than y, then Q is greater than B.
(E) 5) None of the above
Rationale: Basically Q = B = xy/100
None of the options mentions this; hence E.
Answer: (E) 5) None of the above
Question: A and B undertake to do a piece of work for Rs. 600. A alone can do it in 6 days while B alone can do it in 8 days. With the help of C, they finish it in 3 days. !find the share of each.
(A) 25
(B) 50
(C) 75
(D) 80
(E) None of them
Rationale: C's 1 day's work = 1/3-(1/6+1/8)=24
A : B : C = Ratio of their 1 day's work = 1/6:1/8:1/24= 4 : 3 : 1.
A’s share = Rs. (600 *4/8) = Rs.300, B's share = Rs. (600 *3/8) = Rs. 225.
C's share = Rs. [600 - (300 + 225») = Rs. 75.
Answer is C
Answer: (C) 75
Question: A grocer is storing soap boxes in cartons that measure 25 inches by 42 inches by 60 inches. If the measurement of each soap box is 7 inches by 12 inches by 5 inches, then what is the maximum number of soap boxes that can be placed in each carton?
(A) 210
(B) 150
(C) 280
(D) 300
(E) 420
Rationale: however the process of dividing the volume of box by the volume of a soap seems flawed but it does work in this case due to the numbers
Dimensions of the box =25*42*60
Dimensions of the soap = 5*12*7
placing the 7 inch side along 42 inch side we get 6 soaps in a line and in a similar way 5 along 25 and 6 along 60
we get = 5x6x5 = 150
so the question is why this particular arrangement, in order to maximize number of soaps we need to minimize the space wasted and this is the only config where we dont waste any space so we can expect the maximum number
the answer is (B)
Answer: (B) 150
Question: Find the value of 72515 x 9999 = m?
(A) 456578972
(B) 725077485
(C) 653658791
(D) 725117481
(E) 357889964
Rationale: 72515 x 9999 = 72515 x (10000 - 1)
= 72515 x 10000 - 72515 x 1
= 725150000 - 72515
= 725077485
B
Answer: (B) 725077485
Question: The rate of a certain chemical reaction is directly proportional to the square of the concentration of chemical A present and inversely proportional to the concentration of chemical T present. If the concentration of chemical T is increased by 100 percent, which of the following is closest to the percent change in the concentration of chemical A required to keep the reaction rate unchanged?
(A) 100% decrease
(B) 50% decrease
(C) 40% decrease
(D) 40% increase
(E) 50% increase
Rationale: Let A and T be the concentratrations of the individual chemicals.
Rate of chemical reaction = A^2/T
Since new T is increased by 100%
Rate = A^2/(2T)
For the rate to be constant, new value of A should be square root(2)
So new value of A = 1.414A
That means A is increased by 41.4%
Nearest solution is D
Answer: (D) 40% increase
Question: How many of the following numbers are divisible by 132?
264, 396, 462, 792, 968, 2178, 5184, 6336,528,1320
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: Explanation:
A number is divisible by 132, if it is divisible by each one of 11, 3 and 4.
Clearly, 968 is not divisible by 3. None of 462 and 2178 is divisible by 4.
Also, 5184 is not divisible by 11.
Each one of remaining 6 is divisible by each one of 11, 3 and 4 and therefore, by 132.
Answer: C
Answer: (C) 6
Question: Rs.160 contained in a box consists of one rupee, 50 paisa and 25 paisa coins in the ratio 4:5:6. What is the number of 25 paisa coins?
(A) 120
(B) 130
(C) 140
(D) 150
(E) 200
Rationale: 4x 5x 6x
100 50 25
400x + 350x + 150x = 16000
x = 20
6x = 120
ANSWER A
Answer: (A) 120
Question: If x is an integer and 2.134 × 10^x is less than 2,200,000, what is the greatest possible value for x?
(A) 7
(B) 6
(C) 5
(D) 4
(E) 3
Rationale: x is an integer and 2.134 × 10x is less than 2,200,000, what is the greatest possible value for x?
for 2.134 × 10x is less than 2,200,000 to remain true, the greatest number is 2,134,000, which makes x=6
B. 6
Answer: (B) 6
Question: Population of a city in 20004 was 1000000. If in 2005 there isan increment of 15% , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45%, then find the population of city atthe end of the year 2007
(A) 986431
(B) 964347
(C) 946778
(D) 934656
(E) 1083875
Rationale: Required population = P (1 + R1/100)(1 - R2/100)(1 + R3/100)
= P (1 + 15/100)(1 - 35/100)(1 + 45/100)
= 1083875
E
Answer: (E) 1083875
Question: A jar holds 10 pink candies and 30 yellow candies. One candy is drawn at random. What is the probability that the candy drawn is yellow?
(A) 1
(B) 1/2
(C) 3/5
(D) 3/4
(E) None of these
Rationale: Explanation:
Total cases = 10 + 30 = 40
Favourable cases = 30
So probability = 30/40 = 3/4
Answer: D
Answer: (D) 3/4
Question: The annual interest rate earned by an investment increased by 10 percent from last year to this year. If the annual interest rate earned by the investment this year was 12 percent, what was the annual interest rate last year?
(A) 1%
(B) 1.1%
(C) 9.1%
(D) 10%
(E) 10.9%
Rationale: 12=1.1*x
X=10.90%
Answer E)
Answer: (E) 10.9%
Question: If square-root of 15 is 3.87. Then find the value of square-root of (5/3)
(A) 1.29
(B) 1.39
(C) 1.49
(D) 1.59
(E) 1.69
Rationale: => root 5/ root 3 = (root 5/ root 3)*(root 3/ root 3)
= root 15/ root 9
= 3.87/3
= 1.29
ANSWER:A
Answer: (A) 1.29
Question: A boat covers a certain distance downstream in 1 hour, while it comes back in 1½ hours. If the speed of the stream be 3 kmph, what is the speed of the boat in still water?
(A) 12 kmph
(B) 13 kmph
(C) 14 kmph
(D) 15 kmph
(E) None
Rationale: Sol.
Let the speed of the boat in still water be x kmph. Then,
Speed downstream = (x + 3) kmph, Speed upstream = (x - 3)kmph.
∴ (x + 3) * 1 = (x -3) * 3/2 ⇔ 2x + 6 = 3x - 9 ⇔ x = 15 kmph.
Answer D
Answer: (D) 15 kmph
Question: What is the product of the greatest 2 digit multiple of 9 and the greatest 2 digit prime number?
(A) 9,312
(B) 9,408
(C) 9,603
(D) 9,603
(E) 9,702
Rationale: the greatest 2 digit multiple of 9: 99
the greatest 2 digit prime numebr: 97
97*99.
9603
C
Answer: (C) 9,603
Question: a,b,c,d,e,f,g sitting in a row what is the probability that a & c sitting adjacent.
(A) 6/7
(B) 5/7
(C) 4/7
(D) 3/7
(E) 2/7
Rationale: total number of arrangement is= 7!= 5040
Favorable event i.e a and b can be arranged in 2! and the remaining can be arranged in 6! since ab can be in any of the four positions.
so 6!*2!/7! = 2/7
ANSWER:E
Answer: (E) 2/7
Question: The least number which when divided by 5, 6 , 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder, is:
(A) 1677
(B) 2523
(C) 1683
(D) 3363
(E) 3567
Rationale: L.C.M. of 5, 6, 7, 8 = 840.
Required number is of the form 840k + 3
Least value of k for which (840k + 3) is divisible by 9 is k = 2.
Required number = (840 x 2 + 3) = 1683. Answer: Option 'C'
Answer: (C) 1683
Question: Joe’s average (arithmetic mean) test score across 4 equally weighted tests was 90. He was allowed to drop his lowest score. After doing so, his average test score improved to 95. What is the lowest test score that was dropped?
(A) 20
(B) 25
(C) 55
(D) 75
(E) 80
Rationale: The arithmetic mean of 4 equally weighted tests was 90. So what we can assume is that we have 4 test scores, each 90.
He dropped his lowest score and the avg went to 95. This means that the lowest score was not 90 and other three scores had given the lowest score 5 each to make it up to 90 too. When the lowest score was removed, the other 3 scores got their 5 back. So the lowest score was 3 *5 = 15 less than 90.
So the lowest score = 90 - 15 = 75
Answer (D)
Answer: (D) 75
Question: What is the units digit of 28! + 50! + 3! + 4!?
(A) 0
(B) 2
(C) 4
(D) 6
(E) 8
Rationale: For all N greater than 4, the units digit of N! is 0.
The sum of the four units digits is 0 + 0 + 6 + 4 = 10
The units digit is 0.
The answer is A.
Answer: (A) 0
Question: On a certain baseball team, 1 out of 5 batters hit the ball. If 2 out of every 10 batters who hit the ball score a home-run, and there are 20 batters who've hit home-runs, how many players have been up to bat?
(A) 500
(B) 50
(C) 100
(D) 5,0000
(E) 2,000
Rationale: Proportions: Let B = batters, and Bh = batters hit the ball, and Bhr = batters hit the ball and home-run.
20Bhr/xBh = 2Bhr/10Bh
xBh = 100Bh
1Bh/5B = 100Bh/yB
yB = 500B
Answer: A
Answer: (A) 500
Question: The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 2000 resolutions?
(A) 1187 m
(B) 1704 m
(C) 2816 m
(D) 2827 m
(E) 2897 m
Rationale: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 2000 resolutions.
= 2000 * 2 * 22/7 * 22.4
= 281600 cm
= 2816 m
Answer:C
Answer: (C) 2816 m
Question: In the county of Veenapaniville, there are a total of 50 high schools, of three kinds: 25 public schools, 16 parochial schools, and 9 private independent schools. These 50 schools are divided between three districts: A, B, and C. District A has 18 high schools total. District B has 17 high schools total, and only two of those are private independent schools. If District C has an equal number of each of the three kinds of schools, how many private independent schools are there in District A?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: “In the county of Veenapaniville, there are a total of 50 high schools, of three kinds: 25 public schools, 16 parochial schools, and 9 private independent schools.”
“District A has 18 high schools total.”
“District B has 17 high schools total, and only two of those are private independent schools.”
“District C has an equal number of each of the three kinds of schools.” Hmm. That’s not a simple number. Let’s put that on hold for a moment. So far, from the matrix it looks like we could figure out the missing number in the “totals” row. That number must be 15, because 18 + 17 + 15 = 50.
Now, go back to that last fact: “District C has an equal number of each of the three kinds of schools.” Now that makes sense. District C has 15 schools, so it must have 5 of each kind:
The question is asking: “how many private independent schools are there in District A?” Well, now that’s just a matter of adding across the “private independent” row. We know 2 + 2 + 5 = 9, so the missing number must be 2.
There’s still a good deal of information we can’t figure out from the information given in the question, but we are able to answer the specific question asked here. There are 2 private independent schools in District A, so the answer = (A).
Answer: (A) 2
Question: A sum was put at simple interest at certain rate for 3 years. Had it been put at 1% higher rate it would have fetched Rs. 75 more. The sum is: A. Rs. 2,400 B. Rs. 2,100 C. Rs. 2,200 D.Rs. 2,480
(A) 2500
(B) 2100
(C) 2200
(D) 2300
(E) 2400
Rationale: 1 percent for 3 years= 75
1 percent for 1 year = 25
=> 100 percent = 2500
ANSWER:A
Answer: (A) 2500
Question: The unit digit in the product (611 * 704 * 912 * 261) is:
(A) 2
(B) 5
(C) 6
(D) 8
(E) 10
Rationale: Explanation:
Unit digit in the given product = Unit Digit in (1*4*2*1) = 2
ANSWER: A
Answer: (A) 2
Question: The perimeter of one square is 48 cm and that of another is 20 cm. Find the perimeter and the diagonal of a square which is equal in area to these two combined?
(A) 13√7
(B) 13√2
(C) 13√8
(D) 13√9
(E) 12√2
Rationale: 4a = 48 4a = 20
a = 12 a = 5
a2 = 144 a2 = 25
Combined area = a2 = 169 => a = 13
d = 13√2
Answer:B
Answer: (B) 13√2
Question: Ratio of ages of three persons is 4:7:9, Eight years ago, the sum of their ages was 56. Find their present ages.
(A) 16,35,36
(B) 12,28,36
(C) 16,28,27
(D) 16,28,36
(E) None of these
Rationale: Explanation:
Let the present ages are 4x, 7x, 9x.
=> (4x-8) + (7x-8) + (9x-8) = 56
=> 20x = 80
=> x = 4
So their present ages are: 16,28,36
Option D
Answer: (D) 16,28,36
Question: An error 2% in excess is made while measuring the sideofa square. The % of error in the calculated area of the square is?
(A) 4%
(B) 4.04%
(C) 4.15%
(D) 5%
(E) 5.24%
Rationale: 100 cm is read as 102 cm.
A1 = (100 x 100) cm2 and A2 (102 x 102) cm2.
(A2 - A1) = [(102)2 - (100)2]
= (102 + 100) x (102 - 100)
= 404 cm2.
Percentage error = 404	x 100	%	= 4.04%
100 x 100
B
Answer: (B) 4.04%
Question: Which of the following describes all the values of x for which 8−4x < 18x−18?
(A) x > 5/7
(B) x < 5/11
(C) 5/11 < x
(D) x > 13/11
(E) 13/11 > x
Rationale: 8−4x < 18x−18
i.e. 8+18 < 18x+4x
i.e. 26 < 22x
i.e. x>26/22
i.e. x>13/11
Answer: Option D
Answer: (D) x > 13/11
Question: How much does a watch lose per day, if its hands coincide ever 64 minutes?
(A) 32 8/11
(B) 32 8/12
(C) 32 8/18
(D) 32 8/17
(E) 32 8/14
Rationale: 55min spaces are covered in 60min
60 min. spaces are covered in (60/55 x 60) min= 65+5/11 min.
loss in 64min=(65+5/11)- 64 =16/11
Loss in 24 hrs (16/11 x 1/64 x 24 x 60) min= 32 8/11.
Answer: A
Answer: (A) 32 8/11
Question: An athlete runs 200 metres race in 24 seconds. What is his speed?
(A) 23
(B) 38
(C) 37
(D) 30
(E) 28
Rationale: Speed=DistanceTime=20024 m/s=20024×185 km/hr=40×34 km/hr=10×3 km/hr=30 km/hr
Answer :D
Answer: (D) 30
Question: A dishonest dealer professes to sell goods at the cost price but uses a weight of 800 grams per kg, what is his percent?
(A) 65%
(B) 67%
(C) 45%
(D) 78%
(E) 25%
Rationale: E
800 --- 200
100 --- ? => 25%
Answer: (E) 25%
Question: What is the diffference between the place value and face value of 7 in the numeral 9751?
(A) 691
(B) 692
(C) 693
(D) 694
(E) 695
Rationale: place value of 7 = 7 * 100 = 700
face value of 7 = 7
700 - 7 = 693
C
Answer: (C) 693
Question: A rectangular-shaped carpet that measures x feet by y feet is priced at $40. What is the cost of the carpet, in dollars per square yard? (1 square yard = 9 square feet)
(A) xy/360
(B) 9xy/40
(C) 40xy/9
(D) 360xy
(E) 360/(xy)
Rationale: The area of the carpet in feet is xy.
The area in square yards is xy / 9.
The price per square yard is 40 / (xy/9) = 360/(xy).
The answer is E.
Answer: (E) 360/(xy)
Question: A sum of money is to be distributed among A, B, C, D in the proportion of 5:2:4:3. If C gets Rs. 1000 more than D, what is B's share?
(A) Rs.2029
(B) Rs.2028
(C) Rs.2000
(D) Rs.2022
(E) Rs.2021
Rationale: Let the shares of A, B, C and D be 5x, 2x, 4x and 3x Rs. respectively.
Then, 4x - 3x = 1000 => x = 1000.
B's share = Rs. 2x = 2 * 1000
= Rs.2000.
Answer: C
Answer: (C) Rs.2000
Question: A woman swims downstream 45 km and upstream 15 km taking 3 hours each time, what is the speed of the woman in still water?
(A) 10
(B) 12
(C) 14
(D) 16
(E) 18
Rationale: 45 --- 3 DS = 15
? ---- 1
15 ---- 3 US = 5
? ---- 1 M = ?
M = (15 + 5)/2 = 10
Answer:A
Answer: (A) 10
Question: If 2 cards are selected at random from the deck of 52 cards then What is the probability of one of the selected cards will be King and other will be Jack?
A deck of cards has a total of 52 cards, consisting of 4 suits; (spades(Black), hearts(Red), diamond(Red)s, and clubs(Black)); and 13 cards including 1 king, 1 queen and 1 jack in each suit
(A) 8/2652
(B) 1/2652
(C) 18/2652
(D) 12/2652
(E) 6/2652
Rationale: 2 possible cases:
King - Jack or Jack -King (4 kings and 4 Jacks).
Either way,
the total probability = 2( King -Jack) = 2 (4/52 * 4/51) = 18/2652. C is the correct answer.
Answer: (C) 18/2652
Question: 1,3,5,7,9,..50 find term of sequnce for this.
(A) 1200
(B) 1345
(C) 1456
(D) 1478
(E) 2500
Rationale: This is an arithmetic progression, and we can write down
a=1a=1 ,d=2d=2 , n=50n=50 .
We now use the formula, so that
Sn=12n(2a+(n−1)l)Sn=12n(2a+(n−1)l)
S50=12×50×(2×1+(50−1)×2)S50=12×50×(2×1+(50−1)×2)
=25×(2+49×2)=25×(2+49×2)
=25×(2+98)=25×(2+98)
=2500=2500 .
E
Answer: (E) 2500
Question: Compute the probability that two random integers, independently chosen and both taking on
an integer value between 1 and 10 with equal probability, have a prime product.
(A) 1/25
(B) 2/25
(C) 3/25
(D) 4/25
(E) 5/25
Rationale: There are 4 primes between 1 and 10. In order for the product of the integers to be
prime, one of them must be one of these primes (2, 3, 5, or 7) and the other must be the number
There are therefore 8 possible pairs of generated integers that will yield a prime product.
Since there are 100 possible pairs overall, the desired probability is
2/25
correct answer B
Answer: (B) 2/25
Question: Audrey 4 hours to complete a certain job. Ferris can do the same job in 3hours. Audrey and Ferris decided to collaborate on the job, working at their respective rates. While Audrey worked continuously, Ferris took 1 breaks of equal length. If the two completed the job together in 2 hours, how many minutes long was each of Ferris’ breaks ?
(A) 5
(B) 30
(C) 15
(D) 20
(E) 25
Rationale: Audery and Ferris collective Work rate:
1/4 + 1/3 = 7/12
Collective work Time = 12/7 = 1.7 Hrs
Job Was actually done in = 2 (Includes breaks)
Breaks = Actual time taken - Collective work time
= 2 - 1.7
= .3 Hrs = 1/2
so ferrais took 1 breaks
=.3/1=.3 hrs = 30 m
so Answer is B) 30 mins
Answer: (B) 30
Question: If r is even and t is odd, which of the following is odd?
(A) rt
(B) 5rt
(C) 6(r^2)t
(D) 5r + 6t
(E) 6r + 5t
Rationale: R is even, A B and C are out a even number multiplied by any number is even.
D is out because 5r = even, 6t =even so even + even = even
E is correct because: 6r = even, 5t = odd as any number of the form odd x integer... the integer value determines the even/odd nature.
so, even + odd = odd ;Answer: E
Answer: (E) 6r + 5t
Question: If x and y are prime numbers such that x > y > 3, then x^2 − y^2 must be divisible by which one of the following numbers?
(A)  3
(B)  7
(C)  5
(D)  9
(E)  12
Rationale: If x=6 and y=4, then x^2-y^2=20and 20 is divisible only by 5 from the options, thus it must be correct.
Answer: C.
Answer: (C)  5
Question: If M = N/O, -1 < O < 0 and 4 < N, which of the following is correct?
(A) M > 4.
(B) 0 < M <4.
(C) -4 < M < 0.
(D) M < -4.
(E) M < -20.
Rationale: N is +veO is -ve
Eliminate AB
For min. value max. numerator and minimize dinominator
take N=4.1M=-0.9
M=4.1/-0.9
M<-4
Ans D
Answer: (D) M < -4.
Question: there are 4 consonants 3 vowels how many 6 letter strings can u form with atleast one vowels in each?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: 6 letter strings with atleast one vowel means possibilities are
1) 4 Constants and 2 Vowels = 4c4*3c2 = 3
2) 3 Constants and 3 Vowels = 4c3*3c3 = 4
So the answer is 3+4 = 7
ANSWER:C
Answer: (C) 7