mathewhe/aqua_rat huggingface dataset:
Question: What is the sum of the prime factors of 27 and the prime factors of 121?
(A) 14
(B) 20
(C) 22
(D) 26
(E) 31
Rationale: The prime factors of 27 are 3*3*3
The prime factors of 121 are 11*11
3+3+3+11+11 = 31. E is the correct answer
Answer: (E) 31
Question: Fill in the blank with the correct number in this number series: 5, 15, 7, 12, __, 9, 11,... ?
(A) 6
(B) 9
(C) 8
(D) 7
(E) 5
Rationale: In this simple alternating subtraction and addition series; The first series begins with 5 and adds 2; the second begins with 15 and subtracts 3, and so on.
Answer: B
Answer: (B) 9
Question: A contractor undertakes to do a job within 100 days and hires 10 people to do it. After 20 days, he realizes that one fourth of the work is done so he fires 2 people. In how many more days G will the work get over?
(A) 60
(B) 70
(C) G=75
(D) G=80
(E) 100
Rationale: We can also use the concept of man-days here
100 days -->10men so the job includes 100*10=1000 man-days
After 20 days
1/4 of Job is completed so 1/4 X 1000 man-days=250 man-days Job is done
Now the Balance Job=1000-250=750 man-days worth of Job
Since 2 men are fired so B/L men=8
Therefore Total no. of days of Job=750 man-day/8 days = 375/4=94 days (approx.)
Now since this is total and Ques. is asking for additional no. of days,
So 94-20=74 days
The nearest approx. to answer is 75
Ans: C (75 days)
Answer: (C) G=75
Question: P,Q and R together earn Rs.1620 in 9 days. P and R can earn Rs.600 in 5 days. Q and R in 7 days can earn Rs.910. How much amount does R can earn per day?
(A) 40
(B) 35
(C) 55
(D) 60
(E) 70
Rationale: Amount Earned by P,Q and R in 1 day = 1620/9 = 180 ---(1)
Amount Earned by P and R in 1 day = 600/5 = 120 ---(2)
Amount Earned by Q and R in 1 day = 910/7 = 130 ---(3)
(2)+(3)-(1) => Amount Earned by P , Q and 2R in 1 day
- Amount Earned by P,Q and R in 1 day = 120+130-180 = 70
=>Amount Earned by R in 1 day = 70
Answer is E.
Answer: (E) 70
Question: At a certain zoo, the ratio of zebras to penguins is 6 to 11. If there are 85 more penguins than zebras at the zoo, how many zebras are there?
(A) 24
(B) 36
(C) 48
(D) 72
(E) 102
Rationale: 6/11 = x / x+85
6*85 = 5x
x=102
E. 102
Answer: (E) 102
Question: In a rare coin collection, all coins are either pure gold or pure silver, and there is initially one gold coin for every three silver coins. With the addition of 16 more gold coins to the collection, the ratio of gold coins to silver coins is 1 to 2. Based on this information, how many total coins are there now in this collection (after the acquisition)?
(A) 144
(B) 150
(C) 156
(D) 162
(E) 168
Rationale: Initially the number of gold coins and silver coins is 2k and 6k.
After adding gold coins, the number of coins is 3k and 6k.
Thus k = 16 and the total number of coins is 9k = 144.
The answer is A.
Answer: (A) 144
Question: How many seconds will a 300 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
(A) 11 sec
(B) 18 sec
(C) 77 sec
(D) 14 sec
(E) 12
Rationale: Speed of train relative to man = 63 - 3 = 60 km/hr.
= 60 * 5/18 = 50/3 m/sec.
Time taken to pass the man = 300 * 3/50
= 18 sec.
Answer: B
Answer: (B) 18 sec
Question: 800 men have provisions for 15 days. If 200 more men join them, for how many days will the provisions last now?
(A) 11.5
(B) 12.5
(C) 10.5
(D) 11
(E) 12
Rationale: 800*15 = 1000*x
x = 12
ANSWER:E
Answer: (E) 12
Question: On a Monday in a certain restaurant, 20 percent of the 180 customers ordered the daily special. On Tuesday, only 20 percent of the 120 customers ordered the special. For the two days combined, what percent of the customers ordered the daily special?
(A) 15%
(B) 16%
(C) 18%
(D) 23%
(E) 20%
Rationale: 20% of 180= 36
20% of 120=24
Total =60
percent for 2 days combined =60/300 =0.2. so it should be less than 0.2 so it is 20%
Answer:E
Answer: (E) 20%
Question: If a(a + 7) = 18 and b(b + 7) = 18, where a ≠ b, then a + b =
(A)  −48
(B)  −2
(C)  2
(D)  −7
(E)  48
Rationale: a(a + 7) = 18 and b(b + 7) = 18
=> a, b must be integers and if a is -9 or 2, b will be 2 and -9 respectively
=> a+b = -7
Ans: D
Answer: (D)  −7
Question: Five years ago, the average age of A, B, C and D was 45 yr. with E joining them now, the average of all the five is 48 yr. How old is E?
(A) 25 yr
(B) 40 yr
(C) 45yr
(D) 64 yr
(E) NOne
Rationale: Solution:
Total present age of A, B, C and D,
= (45*4)+(4*5) = 200 yr;
Total age present age of A, B, C, D and E,
= 48*5 = 240 yr.
So, age of E = 40 yr.
Answer: Option B
Answer: (B) 40 yr
Question: Anmol can eat 27 pastries in a hour.
Aakriti can eat 2 pastries in 10 minutes.
Divya can eat 7 pastries in 20 minutes.
How long will it take them to eat a 300 pastries ?
(A) 2 hours.
(B) 1 hours.
(C) 5 hours.
(D) 4 hours.
(E) 3 hours.
Rationale: In one hour, Anmol eats 27 pastries, Aakriti eats 12, and Divya eats 21. A total of 60 pastries. Therefore 300 pastries would take 300 ÷ 60 = 5 hours.
ANSWER C
Answer: (C) 5 hours.
Question: Three consecutive even numbers are such that thrice the first number exceeds double the third number by seven. What is the third number?
(A) 19
(B) 21
(C) 23
(D) 25
(E) 27
Rationale: Let the three numbers be x, x+2, and x+4.
3x = 2(x+4) + 7
x = 15 and then the third number is x+4 = 19.
The answer is A.
Answer: (A) 19
Question: A tour group of 25 people paid a total of $1155 for entrance to a museum. If this price included a 5% sales tax, and all the tickets cost the same amount, what was the face value of each ticket price without the sales tax?
Choices
(A) $22
(B) $23.94
(C) $44
(D) $25.20
(E) $30
Rationale: Soln:-
1155/25=x+0.05x
1155/25=1.05x
x=44
ANSWER:C
Answer: (C) $44
Question: Find the compound interest on $1200 for 4 years at 20% p.a. if CI is component yearly?
(A) $120
(B) $150
(C) $1288
(D) $250
(E) $300
Rationale: A = P(1 + R/100)^T
= 1200(1 + 20/100)^4
=$2488
CI = $1288
Answer is C
Answer: (C) $1288
Question: Share Rs.4320 among John, Jose & Binoy in the ration 2 : 4 : 6.Find the amount received by John?
(A) 900
(B) 980
(C) 1200
(D) 1240
(E) 1440
Rationale: Amount received by sanjay.
4 / 12 X 4320 = 1440= ( related ratio / sum of ratio ) x Total amount
So, the Amount received by sanjay is 1440.
E
Answer: (E) 1440
Question: A man is 26 years older than his son. In two years, his age will be twice the age of his son. The
present age of his son is
(A) 20 years
(B) 21 years
(C) 22 years
(D) 24 years
(E) 26 years
Rationale: Explanation:
Let the son's present age be x years. Then, man's present age = (x + 26) years
=> (x + 26) + 2 = 2(x + 2)
=> x + 28 = 2x + 4
So, x = 24
Answer: Option D
Answer: (D) 24 years
Question: 3-6*6+2=
(A) A)-31
(B) B)-13
(C) C)-18
(D) D)-17
(E) of the above
Rationale: 3-6*6+2 = 5-36 = -31...
so the answer is -31... A
Answer: (A) A)-31
Question: Susan, John, Daisy, Tim, Matt,Rose,Lily and Kim need to be seated in 8 identical chairs in straight line so that Susan is seated always left to Tim. How many such arrangements are possible ?
(A) A)20160
(B) B)120
(C) C)80
(D) D)240
(E) E)60
Rationale: Total number of arrangements = 8! = 40320
In exactly half, Susan will be to the left of Tim, which gives us 20160 arrangements
Option (A)
Answer: (A) A)20160
Question: Will must choose a 3-character computer password, consisting of 2 letter from the alphabet and 1 distinct digits, in any order.From how many different passwords can Will choose?
(A) 390
(B) 2,340
(C) 4,680
(D) 39,000
(E) 14,040
Rationale: 10C1*26C1*25C1 =6500
=>6500 * 3 ! = 39000.
Option E is correct answer...but OA is D.
Answer: (D) 39,000
Question: What will come in place of the question mark (?) in the following questions?
7777/35 =?
(A) 333.2
(B) 222.2
(C) 242.1
(D) 553.1
(E) 567.6
Rationale: B
7777/35 = 222.2
Answer: (B) 222.2
Question: If |x| < x^2, which of the following must be true ?
(A) x² >- 1.
(B) x² > -2.
(C) x² > 0.
(D) x² > 1.
(E) x² > 2.
Rationale: |x| < x² implies that x is NONZERO.
Since x is nonzero, |x| > 0 and x² > 0.
Implication:
Both sides of the inequality are positive, allowing us to SQUARE the inequality.
(|x|)² < (x²)²
x² < x⁴.
Since x² > 0, we can safely DIVIDE both sides by x²:
x²/x² < x⁴/x²
1 < x²
x² > 1.
Answer D
Answer: (D) x² > 1.
Question: From a container having pure milk, 20% is replaced by water and the process is repeated thrice. At the end of the third operation, the milk is?
(A) 45%
(B) 49.6%
(C) 51.2%
(D) 55%
(E) 60.3%
Rationale: Let the total quantity of original milk = 1000gm
Milk after 1st operation = 80% of 1000 = 800gm
Milk after second operation = 80% of 800 = 640gm
Milk after third operation = 80% of 640 = 512gm
Strength of final mixture = 51.2%
Answer is C
Answer: (C) 51.2%
Question: A large box contains 15 small boxes and each small box contains 20 chocolate bars. How many chocolate bars are in the large box?
(A) A)220
(B) B)490
(C) C)380
(D) D)300
(E) E)690
Rationale: the only thing you have to do is a simple multiply
we have:
15*20
=300
correct answer is:
D) 300
Answer: (D) D)300
Question: Out of 460 students of a school, 325 play football, 175 play cricket and 50 neither play football nor cricket. How many students play both football and cricket ?
(A) 120
(B) 150
(C) 100
(D) 180
(E) 90
Rationale: n(A)=325,n(B)=175,n(AuB)=460-50=410.
Required number = n(AnB)=n (A)+n (B)-n(AuB)=325+175-410=90.
Answer is E
Answer: (E) 90
Question: a, b, c, d, and e are positive consecutive integers and a < b < c < d < e.
If the sum of a + b is one less than e, and the product of ab is one more than d, then what is the value of c?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Since the integers are consecutive, we can write each as the previous integer +1. For example, b = a+1, and c = b+1. We can also reverse this: a+1 = b, and b+1 = c.
Since ab = d+1, we can also write this ab = e.
Since a+b = e-1, then a+b = ab-1.
Find the pair of consecutive integers whose sum is one less than its product. These numbers are 2 and 3 (sum: 5; product: 6).
Now that we know how the series starts, we can find the value of c. If the first two numbers are 2 and 3, the third number is 4 (option B).
Answer: (B) 4
Question: Product of two natural numbers is 11. Then, the sum of reciprocals of their squares is
(A) 290/289
(B) 122/121
(C) 290/90
(D) 290/19
(E) None of these
Rationale: Explanation:
If the numbers are a, b, then ab = 17,
as 17 is a prime number, so a = 1, b = 17.
1/a2+1/b2=1/1(2)+1/11(2)
=122/121
Option B
Answer: (B) 122/121
Question: If x is a positive integer, which of the following must be odd?
(A) x+1
(B) x^2+x
(C) x^2+x+3
(D) x^2−1
(E) 3x^2−3
Rationale: A. X+1 = can be odd or even. Since O + O =E or E + O = O
B. X^2 + X = X(X+1). Since from the above derivation we already know the term X+1 can be Odd or Even, directly substitute here. X(ODD) = Even (When X is Even) or X(EVEN) = EVEN [When X is ODD]
C. Here's the answer. Since we know the term x^2 + X can always take a EVEN number, EVEN + 3 = ODD
Hence C.
Answer: (C) x^2+x+3
Question: A mixture of 150 liters of wine and water contains 20% water. How much more water should be added so that water becomes 25% of the new mixture?
(A) 18 liters
(B) 17 liters
(C) 10 liters
(D) 19 liters
(E) 11 liters
Rationale: Explanation:
Number of liters of water in150 liters of the mixture = 20% of 150 = 20/100 * 150 = 30 liters.
P liters of water added to the mixture to make water 25% of the new mixture.
Total amount of water becomes (30 + P) and total volume of mixture is (150 + P).
(30 + P) = 25/100 * (150 + P)
120 + 4P = 150 + P => P = 10 liters.
Answer: C
Answer: (C) 10 liters
Question: Sam the Squirrel found a basket
of pine cones one morning. He
decided that every day he would
double the number of pine cones in the basket in
the morning and eat 2 pine cones out of the
basket in the afternoon. At the end of the third
day, there were 34 pine cones in the basket.
How many pine cones were in the basket when
Sam the Squirrel found it?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
Rationale: We will work backwards to find how many pinecones there were initially.
3rd day:
At the end of the afternoon, Sam had 34.
At the beginning of the afternoon, he had 34 + 2 =36.
At the beginning of the morning, he had 36 ÷ 2 =18.
2nd day:
At the end of the afternoon, he had 18.
At the beginning of the afternoon, he had 18 + 2 = 20.
At the beginning of the morning, Sam had 20 ÷ 2 =10.
1st day:
At the end of the afternoon, Sam had 10.
At the beginning of the afternoon, he had 10 + 2=12.
At the beginning of the morning, he had 12 ÷ 2 = 6
correct answer C
Answer: (C) 6
Question: The average amount with a group of seven numbers is Rs. 20. If the newly joined member has Rs. 50 with him, what was the average amount with the group before his joining the group?
(A) Rs.17
(B) Rs.76
(C) Rs.15
(D) Rs.72
(E) Rs.71
Rationale: Total members in the group = 7
Average amount = Rs. 20
Total amount with them = 7 * 20 = Rs. 140
One number has Rs. 50. So, the amount with remaining 6 people = 140 - 50 = Rs. 90
The average amount with them = 90/6 = Rs. 15.
Answer:C
Answer: (C) Rs.15
Question: How many years will it take my savings account initial deposit to double given that I receive just 2% per annum simple interest on the deposited money.
(A) 50
(B) 45
(C) 55
(D) 35
(E) 40
Rationale: P = (P*2*R)/100
100P = P*2*R
100 = 2R
Therefore R = 50 Years
A= 50
Answer: (A) 50
Question: The current of a stream at 1 kmph. A motor boat goes 35 km upstream and back to the starting point in 12 hours. The speed of the motor boat in still water is?
(A) 6
(B) 5
(C) 4
(D) 2
(E) 9
Rationale: S = 1
M = x
DS = x + 1
US = x - 1
35/(x + 1) + 35/(x - 1) = 12
x = 6
Answer: A
Answer: (A) 6
Question: Speed of boat in still water is 9km/hr . if boat moves upstream A to B in 2 hrs. &
B to A in 1 hrs. Then find distance between A&B
(A) 10km
(B) 11km
(C) 12km
(D) 13km
(E) 14km
Rationale: Let speed of stream = s kmph
distance be x
for upstream
(9-s)*2=x (speed*time=distance)
for downstream
(9+s)*1=x
On solving we get x=12km
ANSWER:C
Answer: (C) 12km
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) 7 1/2days
(B) 6 1/2days
(C) 5 1/2days
(D) 4 1/2days
(E) 3 1/2days
Rationale: Explanation:
In this type of question, where we have one person work and together work done. Then we can easily get the other person work just by subtracting them. As,
Son's one day work =
(1/3−1/5)=(5−3/15)=2/15
So son will do whole work in 15/2 days
which is =
7 1/2days
Option A
Answer: (A) 7 1/2days
Question: If the product of the integers a, b, c, and d is 1,155 and if a > b > c > d > 1, then what is the value of a – d?
(A) 2
(B) 8
(C) 10
(D) 11
(E) 14
Rationale: 1155 = 3 * 5 * 7 * 11
a = 11
d = 3
a - d = 8
Answer is B
Answer: (B) 8
Question: Ravi can do a piece of work in 11 days while Prakash can do it in 22 days. In how many days will they finish it together?
(A) 5 7/3 days
(B) 7 1/3days
(C) 5 1/9 days
(D) 5 7/3 days
(E) 4 7/9 days
Rationale: 1/11 + 1/22 = 3/22
22/3 = 7 1/3 days
ANSWER:B
Answer: (B) 7 1/3days
Question: What is 3/5 of 5/7 of 2/3?
(A) 2/7
(B) 3/8
(C) 9/16
(D) 5/8
(E) 16/9
Rationale: 3/5 * 5/7 * 2/3= 2/7
Answer: A
Answer: (A) 2/7
Question: A boat running downstream covers a distance of 10km in 3hr while for covering the same distance upstream, it takes 6hr.
What is the speed of the boat?
(A) 2.5 kmph
(B) 3.5 kmph
(C) 4.5 kmph
(D) 1.5 kmph
(E) 9.5 kmph
Rationale: speed upstream = 10/3
speed of boat down stream = 10/6
speed of boat = 1/2(10/3 + 10 /6 ) = 2.5 kmph
ANSWER:A
Answer: (A) 2.5 kmph
Question: Over a ten-year period Pat's income rose from $15,000 to $35,000. What was the percent increase in her income?
(A) 33 [1][/3]%
(B) 42.8%
(C) 133 [1][/3]%
(D) 142.8%
(E) 233 [1][/3] %
Rationale: % Increase(+)/Decrease(-) = (Final Value−InitialValue)/InitialValue∗100
Final Value = $35,000
Initial Value = $15,000
% Increase(+)/Decrease(-) = (35000−15000)/15000∗100
% Increase(+)/Decrease(-) = (20000)/15000∗100=133.33
Answer: Option C
Answer: (C) 133 [1][/3]%
Question: 11
a3
+4b
___
65
If a and b represent positive single digits in the correctly worked computation above, what is the value of the two digit integer ab?
(A) 12
(B) 11
(C) 34
(D) 544
(E) 546
Rationale: 1+3+b=5
b=1
1+a+4=6
a=1
ab=11
ans=B
Answer: (B) 11
Question: If Greg buys 5 shirts, 4 trousers and 2 ties, the total cost is $80. If Greg buys 7 shirts, 4 trousers and 2 ties, the total cost is $70. How much will it cost him to buy 2 trousers, 3 shirts and 1 ties?
(A) $37.5
(B) $64
(C) $75
(D) $96
(E) Cannot be determined
Rationale: Solution: 5x+4y+2z=80 7x+4y+2z=70
adding both the equations= 12x+8y+4z=150
3x+2y+1z=37.5
ans A
Answer: (A) $37.5
Question: Population is 23000. Population increases by 10% every year, then the population after 3 years is?
(A) 26630
(B) 26640
(C) 36623
(D) 30613
(E) 26820
Rationale: population after 1st year = 23000*10/100 = 2300 ===> 23000+2000 = 25300
population after 2nd year = 25300*10/100 = 2530 ===> 25300+2530= 27830
population after 3rd year = 27830*10/100 = 2783 ===> 27830+2783 = 30613
ANSWER:D
Answer: (D) 30613
Question: If the L.C.M of two numbers is 720 and their product is 38880, find the H.C.F of the numbers.
(A) 50
(B) 30
(C) 125
(D) 54
(E) None of these
Rationale: H.C.F = (Product of the numbers) / (Their L.C.M) = 38880/720 = 54.
ANSWER:D
Answer: (D) 54
Question: In a T.V. factory, an average of 65TVs are produced per day for the fist 25days of the months. A few workers fellill for the next five daysreducing the daily avg for the month to58 sets/day . The average production per day for day last 5days is ?
(A) 35
(B) 39
(C) 48
(D) 50
(E) 23
Rationale: Production during these 5 days = Total production in a month - production in first 25 days.
= 30 x 58 - 25 x 65
= 115
âˆ´ Average for last 5 days = 115/5= 23
= 23
E
Answer: (E) 23
Question: The sale price sarees listed for Rs.400 after successive discount is 10% and 5% is?
(A) 298
(B) 237
(C) 342
(D) 876
(E) 291
Rationale: 400*(90/100)*(95/100)
= 342
Answer: C
Answer: (C) 342
Question: In a certain pet shop, the ratio of dogs to cats to bunnies in stock is 3 : 5 : 9. If the shop carries 204 dogs and bunnies total in stock, how many dogs are there?
(A) 51
(B) 66
(C) 98
(D) 112
(E) 154
Rationale: Let us assume the number of dogs, cats and bunnies to be 3x, 5x and 9x
Total dogs and bunnies = 12x.
And we are given that 12x = 204.
Hence x = 17.
Dogs = 3x = 3*17 = 51 (Option A)
Answer: (A) 51
Question: A boy has nine trousers and 10 shirts. In how many different ways can he select a trouser and a shirt?
(A) 50ways
(B) 90ways
(C) 100ways
(D) 108ways
(E) 56ways
Rationale: The boy can select one trouser in nine ways.
The boy can select one shirt in 10 ways.
The number of ways in which he can select one trouser and one shirt is 9 * 10
= 90 ways.
Answer: B
Answer: (B) 90ways
Question: The probability that A speaks truth is 3/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact?
(A) 18/35
(B) 18/34
(C) 18/30
(D) 18/37
(E) 18/31
Rationale: If both agree stating the same fact, either both of them speak truth of both speak false.
Probability = 3/5 * 4/7 + 2/5 * 3/7
= 12/35 + 6/35 = 18/35
Answer:A
Answer: (A) 18/35
Question: In what time will a train 100 metres long cross an electic pole, if its speed be 144 km/hr?
(A) 2.5 sec
(B) 4.25 sec
(C) 5 sec
(D) 12.5 sec
(E) None
Rationale: Sol.
Speed = [144x5/18] m/sec = 40 m / sec.
Time taken = (100/40)sec = 2.5 sec.
Answer A
Answer: (A) 2.5 sec
Question: If the positive integer x is a multiple of 4 and the positive integer y is a multiple of 8, then xy must be a multiple of which of the following?
I. 8
II. 12
III 18
(A) II only
(B) I and II only
(C) I and III only
(D) II and III only
(E) I, II and III
Rationale: Ans D
From question x/4 is an integer.
x/4 = 2*2*q/4 ---> where q is the integer
Also y/6 = p => y/6 = 2*3*p/6
So, xy = 2*2*2*3 *pq
Thus 2*2*2 = 8 and 2*3*2 = 12 satisfy
D
Answer: (D) II and III only
Question: Look at this series: F2, __, D8, C16, B32, ... What number should fill the blank?
(A) A16
(B) G4
(C) E4
(D) E3
(E) None
Rationale: Explanation: The letters decrease by 1; the numbers are multiplied by 2.
Answer: Option C
Answer: (C) E4
Question: A company wants to spend equal amounts of money for the purchase of two types of computer printers costing $375 and $150 per unit, respectively. What is the fewest number of computer printers that the company can purchase?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: The smallest amount that the company can spend is the LCM of 375 and 150, which is 750 for each, which is total 1500.
The number of 1st type of computers which costing $375 = 750/375 = 2.
The number of 2nd type of computers which costing $150 = 750/150 = 5.
Total = 2+5 = 7
Answer is E.
Answer: (E) 7
Question: If an integer n is to be chosen at random from the integers 1 to 94, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 8?
(A) 1/4
(B) 3/8
(C) 1/2
(D) 5/8
(E) 59/94
Rationale: n(n+1)(n+2) will be divisible by 8 when n is a multiple of 2 or when (n+1) is a multiple of 8.
Thus when n is even, this whole expression will be divisible by 8.
from 1 to 96, there are 47 even integers.
Now when (n+1) is multiple by 8, we have 12 such values for (n+1)
probability that n(n+1)(n+2) will be divisible by 8
= (47 + 12)/94
= 59/94
= 5/8
Ans is E
Answer: (E) 59/94
Question: Due to construction, the speed limit along an 9-mile section of highway is reduced from 55 miles per hour to 35 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
(A)  5.61
(B)  8
(C)  10
(D)  15
(E)  24
Rationale: Old time in minutes to cross 9 miles stretch = 9*60/55 = 9*12/11 = 9.81
New time in minutes to cross 9 miles stretch = 9*60/35 = 9*12/7 = 15.42
Time difference = 5.61
Ans:A
Answer: (A)  5.61
Question: A salesperson receives a base salary of $1000 per month and a commission of 7.5% of the selling price of each item sold above the first 50 item. If this month she sold 210 items for $150 each, what will her monthly salary be?
(A) $1,500
(B) $1,800
(C) $2,100
(D) $2,500
(E) $2,800
Rationale: Ans : 1000+ 7.5 % * 150 * (210-50) = $ 2800
ANSWER:E
Answer: (E) $2,800
Question: It takes 3 tons of copper ore and 5 tons of iron ore to make one ton of alloy A. How many tons of alloy A can be made from 30 tons of copper ore and 80 tons of iron ore?
(A)  18
(B)  18 3/4
(C)  17
(D)  16
(E)  14
Rationale: Yes, you need copper ore:iron ore in the ratio 3:5. Total 8 tons of the mix in this ratio will give 1 ton of alloy A.
If you have 30 tons of copper ore, it is enough for 30/3 = 10 tons of alloy A.
If you have 80 tons of iron ore, it is enough for 80/5 = 16 tons of alloy A.
Since iron ore is available for only 16 tons of alloy A, you can make only 16 tons of alloy A.
The leftover copper ore alone cannot make any alloy A and hence will be leftover only.
Answer must be 16.
(D)
Answer: (D)  16
Question: The base of a parallelogram is twice its height. If the area of the parallelogram
is 72 sq. cm, find its height.
(A) 5cm
(B) 6cm
(C) 7cm
(D) 8cm
(E) 9cm
Rationale: Let the height of the parallelogram be x. cm. Then, base = (2x) cm.
2x X x =72  2x^2 = 72  X ^2=36  x=6
Hence, height of the parallelogram = 6 cm
ANSWER B 6cm
Answer: (B) 6cm
Question: When positive integer N is divided by positive integer J, the remainder is 18. If N/J = 134.08, what is value of J?
(A) 22
(B) 56
(C) 78
(D) 112
(E) 225
Rationale: When a number is divided by another number, we can represent it as : Dividend = Quotient * Divisor + Remainder
So, Dividend/Divisor = Quotient + Remainder/Divisor
Given that N/J = 134.08
Here 134 is the quotient.
Given that Remainder = 18
So, 134.08 = 134 + 18/J
So, J = 225 ANS E
Answer: (E) 225
Question: If 25% of x is 15 less than 12% of 1500, then x is?
(A) 660
(B) 738
(C) 837
(D) 840
(E) 83
Rationale: 25% of x = x/4 ; 12% of 1500
= 12/100 * 1500 = 180
Given that, x/4 = 180 - 15
=> x/4 = 165 => x = 660.
Answer:A
Answer: (A) 660
Question: If 20% of a = b, then b% of 20 is the same as:
(A) 4% of a
(B) 25% of a
(C) 20% of a
(D) 5% of a
(E) 13% of a
Rationale: 20% of a = b
=> b = 20/100a
b% of 20 = (b/100)20 = [(20/100a)/100]20
= (20 × 20 × a)/(100 × 100)
= 4a/100 = 4% of a
A
Answer: (A) 4% of a