mathewhe/aqua_rat huggingface dataset:
Question: In a 500 m race,the ratio of the speeds of two contestants A and B is 3 : 4. A has a start of 140 m.Then,A wins by
(A) 60 m
(B) 40 m
(C) 20 m
(D) 10 m
(E) 50 m
Rationale: Solution
To reach the winning post A will have to cover a distance of ( 500 -140)m, i.e,360m.
While A covers 3 m, B covers 4 m.
While A covers 360 m, B covers (4/3 x 360)m =480m
Thus,when A reaches the winning post, B covers 480 m and therefore remains 20 m behind.
∴ A wins by 20 m.
Answer C
Answer: (C) 20 m
Question: Two pipes A and B can separately fill a cistern in 45 minutes and 60 minutes respectively. There is a third pipe in the bottom of the cistern to empty it. If all the three pipes are simultaneously opened, then the cistern is full in 40 minutes. In how much time, the third pipe alone can empty the cistern?
(A) 90 min
(B) 100 min
(C) 72 min
(D) 75 min
(E) 130 min
Rationale: 1/40-(1/45+1/60)=-1/72
third pipe can empty in 72 minutes
ANSWER:C
Answer: (C) 72 min
Question: Which of the following CANNOT be the median W of the four consecutive positive integers w, x, y, and z, where w < x < y < z ?
(A) (w+x)/2 - 1
(B) (w+z)/2
(C) (x+y)/2
(D) (y+z)/2 -1
(E) (w+x+y+z)/4
Rationale: Using the properties of consecutive positive integers we could right away eliminate B,C and E.
(B) - The average of first and last terms is the median
(C) - For even number of integers, the median is the average of middle terms
(E) - The average is equal to median if the integers are consecutive
Remaining answer choices are A and D.
For A, the average of first two consecutive numbers (w,x) will definitely be less than x making it impossible to be a median W.
Answer (A)
Answer: (A) (w+x)/2 - 1
Question: The time it took car P to travel 600 miles was 2 hours less than the time it took car R to travel the same distance. If car P’s average speed was 10 miles per hour greater than that of car R, what was car R’s average speed, in miles per hour?
(A) 40
(B) 50
(C) 60
(D) 70
(E) 80
Rationale: Let speed of car R be=x
Then speed of car P= x+10
A/Q,
(600/x)-(600/(x+10))=2
Solving for x=50 miles\hr
ANSWER:B
Answer: (B) 50
Question: Carrie likes to buy t-shirts at the local clothing store. They cost $8.75 each. One day, she bought 18 t-shirts. How much money did she spend?
(A) $150
(B) $70
(C) $200
(D) $171.6
(E) $190
Rationale: $8.75*18=$70. Answer is B.
Answer: (B) $70
Question: Sides of a rectangular park are in the ratio 3: 2 and its area is 3750 sq m, the cost of fencing it at 50 ps per meter is?
(A) Rs.122
(B) Rs.129
(C) Rs.125
(D) Rs.120
(E) Rs.121
Rationale: 3x * 2x = 3750 => x = 25
2(75 + 50) = 250 m
250 * 1/2 = Rs.125
Answer:C
Answer: (C) Rs.125
Question: The compound and the simple interests on a certain sum at the same rate of interest for two years are Rs.11730 and Rs.10200 respectively. Find the sum.
(A) Rs.17277
(B) Rs.17000
(C) Rs.17287
(D) Rs.172827
(E) Rs.172711
Rationale: Explanation:
The simple interest for the first year is 10200/2 is Rs.5100 and compound interest for first year also is Rs.5100. The compound interest for second year on Rs.5100 for one year
So rate of the interest = (100 * 1530)/ (5100 * 1) = 30% p.a.
So P = (100 * 10200)/ (30 * 2) = Rs.17000
Answer: B
Answer: (B) Rs.17000
Question: A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, the how old is B?
(A) 1 years
(B) 20 years
(C) 10 years
(D) 15 years
(E) 25 years
Rationale: Explanation:
Let C's age be x years. Then, B's age = 2x years. A's age = (2x + 2) years.
(2x + 2) + 2x + x = 27
5x = 25
x = 5.
Hence, B's age = 2x = 10 years.
Answer: C
Answer: (C) 10 years
Question: There are 40 students in a certain geometry class. If two thirds of the students are boys and three fourths of the boys are under six feet tall, how many boys in the class are under six feet tall?
(A) 6
(B) 12
(C) 20
(D) 24
(E) 27
Rationale: 40*2/3 *3/4= 20
Answer: C
Answer: (C) 20
Question: A dishonest dealer professes to sell goods at the cost price but uses a weight of 900 grams per kg, what is his percent?
(A) 28%
(B) 25%
(C) 11.11%
(D) 28%
(E) 55%
Rationale: 900 --- 100
100 --- ? => 11.11%
Answer: C
Answer: (C) 11.11%
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 6 inches by 6 inches, then what is the maximum number of soap boxes that can be placed in each carton?
(A) 210
(B) 252
(C) 250
(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 = 6*6*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 = 5x5x10 = 250
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 (C)
Answer: (C) 250
Question: If x is an odd negative integer and y is an even integer, which of the following statements must be true?
I. (3x - 4y) is odd
II. xy^2 is an even negative integer
III. (y^2 - x) is an odd negative integer
(A) (3X-4Y) IS ODD TRUE
(B) II only
(C) I and II
(D) I and III
(E) II and III
Rationale: If x is an odd negative integer and y is an even integer, which of the following statements must be true?
I. (3x - 4y) is odd
3x - is always negative and odd
2y - can be 0, when y=0, or always even integer (positivie or negative)
odd integer +/- even integer = always odd
I statement is always true
II. xy^2 is an even negative integer
y can be 0 => xy^2 = 0 (non-negative even) => II statement is not true
III. (y^2 - x) is an odd negative integer
y can be 0 => -x will be positive => III statement is not true
basing on above, only I statement will always be true
answer is A
Answer: (A) (3X-4Y) IS ODD TRUE
Question: A train speeds past a pole in 15 sec and a platform 100 m long in 25 sec, its length is?
(A) 100
(B) 150
(C) 140
(D) 130
(E) 123
Rationale: Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 15 => y = x/15
(x + 100)/25 = x/15 => x = 150 m.
Answer: Option B
Answer: (B) 150
Question: Two trains are moving at 50 kmph and 70 kmph in opposite directions. Their lengths are 150 m and 100 m respectively. The time they will take to pass each other completely is?
(A) 7 1/2 sec
(B) 2 sec
(C) 3 sec
(D) 5 sec
(E) 7 sec
Rationale: 70 + 50 = 120 * 5/18 = 100/3 mps
D = 150 + 100 = 250 m
T = 250 * 3/100 = 15/2 = 7 Â½ sec
ANSWER A
Answer: (A) 7 1/2 sec
Question: The jogging track in a sports complex is 900 m in circumference. Sunil and Sachin start from the same point and walk in opposite directions at 5.4 km/hr and 3.6km/hr respectively. They will meet for the first time in?
(A) 2.98 min
(B) 5.7 min
(C) 6.0 min
(D) 6.3 min
(E) 7.2 min
Rationale: Clearly, the two will meet when they are 900m apart.
To be (5.4+ 3.6) = 9.0 km apart, they take 1 hour.
To be 900 m apart, they take
= (900/9000 * 60) min
= 6.00 min.
Answer: C
Answer: (C) 6.0 min
Question: Which of the following is an integer?
I. 11! / 6!
II. 11! / 8!
III. 11! / 7!5!
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I, II and III
Rationale: 11!/6! = 11*10*9*8*7 which is an integer.
11!/8! = 11*10*9 which is an integer.
11!/7!5! = 11*10*9*8 / 5*4*3*2 = 11*3*2 which is an integer.
The answer is E.
Answer: (E) I, II and III
Question: A trainer is standing in one corner of a square ground of side 25m. His voice can be heard upto 140m. Find the area of the ground in which his voice can be heard?
(A) 12300
(B) 14500
(C) 15400
(D) 16700
(E) 18200
Rationale: Area covered by goat = Pi*r^2/4 ( here we divide by 4 because the trainer is standing in a corner of the ground and only in 1/4 part , the voice can be heard)
where r= 14 m = length reaching the voice
So area = (22/7)*140*140/4 = 15400 sq m
answer :C
Answer: (C) 15400
Question: Pipe A can fill a tank in 6 hours. Due to a leak at the bottom, it takes 9 hours for the pipe A to fill the tank. In what time can the leak alone empty the full tank?
(A) 17
(B) 16
(C) 18
(D) 77
(E) 11
Rationale: Explanation:
Let the leak can empty the full tank in x hours 1/6 - 1/x = 1/9
=> 1/x = 1/6 - 1/9 = (3 - 2)/18 = 1/18
=> x = 18.
Answer: C
Answer: (C) 18
Question: What is the difference between the compound interests on Rs. 5000 for 11â„2 years at 4% per annum compounded yearly and half-yearly?
(A) 2.04
(B) 4.8
(C) 3.06
(D) 8.3
(E) 3.5
Rationale: compunded yearly
= 5000*(1+4/100)*(1+1/2*4/100)
=5304
compound interest for 1 1/2 years when interest=>(5304-5000)
=>P(1+(R/2)/100)^2T = 5000(1+(4/2)/100)2*3/2 = 5000(1+2/100)^3
=5000(102/100)^3 = 5306.04
1 1/2 Years half yearly = (5306.04 - 5000)=> 2.04
ANSWER A
Answer: (A) 2.04
Question: A water tank is four-fifth full.Pipe A can fill a tank in 10 minutes and pipe B can empty it in 6 minutes.If both the pipes are open,how long will it take to empty or fill the tank completely?
(A) 12 min.to empty
(B) 9 min.to empty
(C) 5 min.to empty
(D) 4 min.to empty
(E) 7 min.to empty
Rationale: Explanation:
Clearly,pipe B is faster than pipe A and so,the tank will be emptied.
part to be emptied = 4/5
part emptied by (A+B) in 1 minute=(1/6-1/10)=1/15
so, the tank will be emptied in 12 min
Answer: A
Answer: (A) 12 min.to empty
Question: Which of these lines in the xy-plane does not contain any point with two negative coordinates?
(A) y = 5x
(B) y = x + 6
(C) y = x^2 - 7
(D) y = x^3 + 2x
(E) y = 3x^6
Rationale: 3x^6 is 0 when x is 0 and positive for all other values of x.
The answer is E.
Answer: (E) y = 3x^6
Question: A garrison of 2000 men has provisions for 54 days. At the end of 15 days, a reinforcement arrives, and it is now found that the provisions will last only for 20 days more. What is the reinforcement?
(A) 1977
(B) 1893
(C) 1979
(D) 1900
(E) 1278
Rationale: 2000 ---- 54
2000 ---- 39
x ----- 20
x*20 = 2000*39
x = 3900
2000
-------
1900
Answer: D
Answer: (D) 1900
Question: There are 4 books on a shelf, of which 3 are paperbacks and 6 are hardbacks. How many possible selections of 4 books from this shelf include at least one paperback?
(A) a) 40
(B) b) 45
(C) c) 50
(D) d) 55
(E) e) 111
Rationale: approach 1
at-least 1 paper back = total - no paper back
9c4-6c4 = 111
approach 2
at-least 1 paper back = 1 paper back , 3 hard back or 2 paper back 2 hard back
= 3c1*6c3+3c2*6c2 + 3c3*6c1 = 111
Answer is E
Answer: (E) e) 111
Question: For one toss of a certain coin, the probability that the outcome is heads is 0.8. If this coin is tossed 5 times, which of the following is the probability that the outcome will be heads at least 4 times?
(A) (0.8)^5
(B) 2(0.8)^4
(C) 3(0.8)^4
(D) 4(0.8)^4(0.2) + (0.8)^5
(E) 5(0.8)^4(0.2) + (0.8)^5
Rationale: P(5 heads) = (0.8)^5
There are 5 ways to get 4 heads: HHHHT, HHHTH, HHTHH, HTHHH, THHHH
P(4 heads) = 5*(0.8)^4(0.2)
The answer is E.
Answer: (E) 5(0.8)^4(0.2) + (0.8)^5
Question: If 2^k = 4, then 2^(2K+2) =
(A) 29
(B) 45
(C) 81
(D) 64
(E) 18
Rationale: 2^k=4
2^2k=4^2
2^2k=16
2^(2k+2)
=2^2k*2^2
=16*4
=64
Answer: D
Answer: (D) 64
Question: The true discount on Rs.2562 due 4 months hence is Rs.122.The rate % is?
(A) 12%
(B) 13 (1/3)%
(C) 15%
(D) 14%
(E) 13%
Rationale: Explanation:
P.W = Rs.( 2562 - 122) = Rs.2440
S.I on Rs.2440 for 4 months is Rs.122
Rate = [100X 122/2440X1/3 ] % = 15%
Answer: A
Answer: (A) 12%
Question: Find the compound interest on $1200 for 5 years at 20% p.a. if CI is component yearly?
(A) $120
(B) $150
(C) $1786
(D) $250
(E) $300
Rationale: A = P(1 + R/100)^T
= 1200(1 + 20/100)^5
=$2986
CI = $1786
Answer is C
Answer: (C) $1786
Question: The S.I. on a certain sum of money for 3 years at 10% per annum is half the C.I. on Rs. 4000 for 2 years at 10% per annum. The sum placed on S.I. is?
(A) 2197
(B) 1267
(C) 1750
(D) 2267
(E) 1400
Rationale: Explanation:
C.I. = [4000 * (1 + 10/100)2 - 4000]
= (4000 * 11/10 * 11/10 - 4000) = Rs. 840.
Sum = (420 * 100)/(3 * 10) = Rs. 1400
Answer:E
Answer: (E) 1400
Question: An article is bought for Rs.675 and sold for Rs.700, find the gain percent?
(A) 2%
(B) 3%
(C) 4%
(D) 5%
(E) 6%
Rationale: 675 ---- 25
100 ---- ? =>
=4%
Answer:C
Answer: (C) 4%
Question: 0, 180, 12, 50, 100, 200, ?, 3, 50, 4, 25, 2, 6, 30, 3
(A) 150
(B) 175
(C) 225
(D) 250
(E) 275
Rationale: 90, 180, 12, 50, 100, 200, ?, 3, 50, 4, 25, 2, 6, 30, 3
I think 1st term will be 90
two series
90, 180, 12, 50, 100, 200, ?,
and 3, 50, 4, 25, 2, 6, 30, 3
3*50=150
50*4=200
4*25=100
25*2=100
2*6=12
6*30=180
30*3=90
so ans is 150
ANSWER:A
Answer: (A) 150
Question: At a particular graduation party with 220 guests, 70% of the guests brought gifts, and 40% of the female guests brought gifts. If 12 males did not bring gifts to the party, how many females did bring gifts?
(A) 18
(B) 36
(C) 42
(D) 68
(E) 70
Rationale: the correct method
total = 220..
70% of 220= 154 got gifts..
66 did not get gift, out of which 12 are males, so remaining 60-12=54 are females..
But 40% females brought gift, so 60% did not get it..
so 60% = 54, 100%= 54*100/60= 90..
ans 40% of 90 =36
B
Answer: (B) 36
Question: A car traveled 480 miles per tankful of gasoline on the highway and 336 miles per tankful of gasoline in the city. If the car traveled 6 fewer miles per gallon in the city than on the highway, how many miles per gallon did the car travel in the city?
(A) 14
(B) 16
(C) 21
(D) 22
(E) 27
Rationale: Let the speed in highway be h mpg and in city be c mpg.
h = c+6
h miles are covered in 1 gallon
462 miles will be covered in 462/h.
Similarly c miles are covered in 1 gallon
336 miles will be covered in 336/c.
Both should be same (as car's fuel capacity does not change with speed)
=> 336/c = 480/h
=> 336/c = 480/(c+6)
=> 336c+336*6=480c
=>c=336*6/144 =14
Answer A.
Answer: (A) 14
Question: Ramesh has solved 108 questions in an examination. If he
got only ‘0’ marks, then how many questions were wrong
when one mark is given for each one correct answer and 1/3
mark is subtracted on each wrong answer.
(A) 78
(B) 79
(C) 80
(D) 81
(E) 82
Rationale: If Ramesh attempts 'x' questions correct and 'y' questions wrong, then
x + y=108 ---(i) &
x - (1/3)y=0 ---(ii)
On solving x=27, y=81
ANSWER:D
Answer: (D) 81
Question: Sara bought both German chocolate and Swiss chocolate for some cakes she was baking. The Swiss chocolate cost $2.5 per pound, and German chocolate cost $1.5 per pound. if the total the she spent on chocolate was $30 and both types of chocolate were purchased in whole number of pounds, how many total pounds of chocolate she purchased?
(A) 7
(B) 18
(C) 10
(D) 12
(E) 11
Rationale: If there were all the expensive ones 2.5....
There would be 30/2.5 or 12 of them but since 1.5$ ones are also there, answer has to be >12....
If all were 1.5$ ones, there will be 30/1.5 or 20...
So ONLY 18 is left
Ans B..
Answer: (B) 18
Question: A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec. What is the length of the platform?
(A) 340
(B) 350
(C) 360
(D) 370
(E) 380
Rationale: Speed = 300/18 = 50/3 m/sec.
Let the length of the platform be x meters.
Then, (x + 300)/39 = 50/3
3x + 900 = 1950 => x = 350 m.
Answer: Option B
Answer: (B) 350
Question: In a river flowing at 2 km/hr, a boat travels 72 km upstream and then returns downstream to the starting point. If its speed in still water be 6 km/hr, find the total journey time.
(A) 10 hours
(B) 12 hours
(C) 14 hours
(D) 27 hours
(E) None of these
Rationale: Explanation :
speed of the boat = 6 km/hr
Speed downstream = (6+2) = 8 km/hr
Speed upstream = (6-2) = 4 km/hr
Distance travelled downstream = Distance travelled upstream = 72 km
Total time taken = Time taken downstream + Time taken upstream
= (72/8) + (72/4) = 27 hr. Answer : Option D
Answer: (D) 27 hours
Question: Each week a restaurant serving Mexican food uses the same volume of chili paste, which comes in either 25-ounce cans or 15-ounce cans of chili paste. If the restaurant must order 30 more of the smaller cans than the larger cans to fulfill its weekly needs, then how manysmallercans are required to fulfill its weekly needs?
(A) 60
(B) 70
(C) 75
(D) 100
(E) 120
Rationale: let x be the number of 25 ounce cans. Therefore (x+30) is the number of 15 ounce cans.
Total volume is same, therefore
25x=15(x+30)
10x=450
x=45
Therefore, number of 15 ounce cans=45+30=75
Ans - C
Answer: (C) 75
Question: If x^2 + y^2 = 2xy, then (x+y)^2 =
(A) x^2
(B) 3x^2
(C) 4xy
(D) 2y^2
(E) -y^2
Rationale: Its B
x^2 +y^2 = 2xy
Add 2xy on both sides we get
x^2 +y^2+2xy = 2xy+2xy
(x+y)^2=4xy
Correct Option : C
Answer: (C) 4xy
Question: A company D has 30 percent of the employees are secretaries and 20 percent are salespeople. If there are 60 other employees of Company D, how many employees does Company D have?
(A) 120
(B) 162
(C) 180
(D) 152
(E) 250
Rationale: Let the total number of employees in the company be x
% of secretaries = 30%
% of salespeople = 20%
% of of employees other than secretaries and salespeople = 100 - 50 = 50%
But this number is given as 60
so 50% of x = 60
x = 120
Therefore there a total of 120 employees in the company D
Correct answer - A
Answer: (A) 120
Question: A tradesman by means of his false balance defrauds to the extent of 20%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?
(A) 74%
(B) 49%
(C) 44%
(D) 74%
(E) 34%
Rationale: g% = 20 + 20 + (20*20)/100
= 44%
Answer:C
Answer: (C) 44%
Question: The editor of an anthology of short stories will select authors from a pool of 10 authors, of which 3 are female. If the anthology is to include the work of 7 authors of which at least 2 are female, in how many ways can the editor select the authors?
(A) 58
(B) 68
(C) 78
(D) 88
(E) 98
Rationale: 10C7 = 120
The number of ways to select 7 males is 7C7 = 1
The number of ways to select 6 males and 1 female is 7C6*3C1 = 21
120 - 1 - 21 = 98
The answer is E.
Answer: (E) 98
Question: Find the value of p: 5p^2-12p+1 = 20.25
(A) 4.5
(B) 3.5
(C) 20.25
(D) 6.2
(E) 2.1
Rationale: Using the elimination method substitute options for x and find the correct option.
Answer: B
Answer: (B) 3.5
Question: A can do a job in 15days and B in 20days. If they work on it together for 8 days, then the fraction of the work that is left is?
(A) 2/15
(B) 8/15
(C) 3/11
(D) 1/12
(E) 1/15
Rationale: A's 1 day work = 1/15
B's 1day work = 1/20
A+B 1day work = 1/15 + 1/20 = 7/60
A+B 8days work = 7/60*8 = 14/15
Remaining work = 1 - 14/15 = 1/15
Answer is E
Answer: (E) 1/15
Question: The price of a shirt is increased by 15% and then reduced by 15%. The final price of the shirt is?
(A) $97.75
(B) $90
(C) $91.56
(D) $95.62
(E) $93.45
Rationale: Let the original price be $100
New final price = 85% of (115% of $100) = 85/100 * 115/100 * 100 = $97.75
Answer is A
Answer: (A) $97.75
Question: The average marks in mathematics scored by the pupils of a school at the public examination were 39. If four of these pupils who actually scored 5, 12, 15 and 19 marks at the examination had not been sent up, the average marks for the school would have been 44. Find the number of pupils sent up for examination from the school?
(A) 33
(B) 25
(C) 66
(D) 72
(E) 81
Rationale: 39x = 5 + 12 + 15 + 19 + (x – 4)44
x = 25
Answer: B
Answer: (B) 25
Question: The average of first 13 even numbers is?
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
Rationale: Sum of 13 even numbers = 13 * 14 = 110
Average = 182/13 = 14
ANSWER:E
Answer: (E) 14
Question: A man whose speed is 4.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey?
(A) 3
(B) 4
(C) 8
(D) 9
(E) 2
Rationale: M = 45
S = 1.5
DS = 6
US = 3
AS = (2 * 6 * 3) /9 = 4
Answer:B
Answer: (B) 4
Question: How many integers between 324,700 and 468,600 have tens digit 1 and units digit 3?
(A) 10,300
(B) 10,030
(C) 1,353
(D) 1,352
(E) 1,439
Rationale: There is one number in hundred with 1 in the tens digit and 3 in the units digit:13, 113, 213, 313, ...
The difference between 324,700 and 468,600 is 468,600-324,700=133,900 - one number per each hundred gives 143,900/100=1,439 numbers.
Answer: E.
Answer: (E) 1,439
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) 2.9 sec
(C) 3.5 sec
(D) 7.5 sec
(E) 2.4 sec
Rationale: Speed = 144 * 5/18 = 40 m/sec
Time taken = 100/40
= 2.5 sec.
Answer: A
Answer: (A) 2.5 sec
Question: A man bought 20 shares of Rs. 50 at 5 discount, the rate of dividend being 13. The rate of interest obtained is:
(A) 12	1/2%
(B) 13	1/2%
(C) 15%
(D) 16	2/3%
(E) 18	2/3%
Rationale: there is a small correction in this question. the rate of dividend is 13 1/2.
replace 13 in the solution by 13 1/2.
the ans is 15%
ANSWER:C
Answer: (C) 15%
Question: The ratio of the present age of Sandy to that of Molly is 9:2. Sixteen years from now, the ratio of the ages of Sandy to Molly will be 5:2. What was Sandy's age 6 years ago?
(A) 30
(B) 36
(C) 42
(D) 48
(E) 54
Rationale: Let the present age of Sandy be 9x years and that of Molly be 2x years.
(9x + 16) / (2x + 16) = 5 / 2
8x = 48
x = 6
Six years ago, Sandy's age was 9(6) - 6 = 48
The answer is D.
Answer: (D) 48
Question: One out of every 200 light bulbs are defected. If 2 out of every 10 defected light bulbs have a broken glass and there are 20 broken glass light bulbs in the shipment, how many light bulbs total are there in the shipment?
(A) 2,000
(B) 5,000
(C) 10,000
(D) 50,000
(E) 20,000
Rationale: 20 broken glasses indicates that 10*10= 100 defected bulbs are present.
100 defected bulbs indicates that 100*200= 20,000 light bulbs are present.
E is the answer
Answer: (E) 20,000
Question: What is the tens digit of 7^1213?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: 7^1 = 7
7^2 = 49
7^3 = 343
7^4 = 2401
7^5 = 16807
7^6 = 117649
We should see this as pattern recognition . We have a cycle of 4 . (We can multiply the last 2 digits only as we care about ten's digit )
0 , 4 , 4 , 0 .
1213= 4*304 + 1
The ten's digit will be 0 .
Answer A
Answer: (A) 0
Question: A car engine is half filled and holds 15 litres of petrol.what fraction of the engine is full if it contains 18 litres of petrol?
(A) 1/4
(B) 2/3
(C) 2/5
(D) 3/5
(E) 4/5
Rationale: half of the car engine filed with 15 ltrs means full engine filed with 30 ltrs so the fraction will be=18/30=6/10=3/5
ANSWER:D
Answer: (D) 3/5
Question: A no. when divided by the sum of 555 and 445 gives 2times their difference as quotient & 40 as remainder. Find the no. is?
(A) 145646
(B) 236578
(C) 645353
(D) 456546
(E) 220040
Rationale: (555 + 445) * 2 * 110 + 40 = 220000 + 40 = 220040
E
Answer: (E) 220040
Question: How many pairs of letters in the word 'CHAIRS' have as many letters between them in the word as in the alphabet?
(A) 2
(B) 1
(C) 3
(D) 5
(E) 4
Rationale: Letters in the word Letters in the alphabet
C H A C B A
R S R S
ANSWER A
Answer: (A) 2
Question: For integers x and y if x^2+x/y is always an odd integer then which of the following must be true?
(A) x is even ; y is odd
(B) x is even ; y is even
(C) x is odd ; y is odd
(D) x is odd ; y is even
(E) cannot be determined
Rationale: Given x and y are integers...NOTE : While taking values, x/y must be properly divisible and the result has to integer itself..
x^2+x/y = odd always...
lets take x even (2) and y even (2)
4 + 2/2 = odd...
lets take x odd(3) and y odd(3)
9+3/3 = even...
So only x even and y even satisfies the equation..
If we take one even and other odd then we get x/y as non integer..which shouldn't be the case as per our question stem.
Option B is correct...
Answer: (B) x is even ; y is even