mathewhe/aqua_rat huggingface dataset:
Question: A young girl counted in the following way on the fingers of her left hand. She started collang the thumb 1, the index finger 2, the middle finger 3, the ring finger 4, the little finger 5, then reversed direction calling the ring finger 6, the the middle finger 7, the index finger 8, the thumb 9 then back to the index finger for 10, the middel finger for 11, and so on. She counted up to 1995. She ended on her
(A) a) thumb
(B) b) the index finger
(C) c) the middle finger
(D) d) the ring finger
(E) e) the little finger
Rationale: Notice the pattern. The thumb lansd up at numbers 1,9,17,25,33,... so every 8th number
By this patter the thumb is also at number 1993 (multiple of 8 + 1)
Hence 1995 has to be the middle finger
Answer is (C)
Answer: (C) c) the middle finger
Question: if samaira wallet have 10rs. note,50 rs. note,2000 rs.note.if 10rs. is 3/5 part of his money and 50rs. is 1/5 part of his money.if he has 8000 money consist of 2000 rs.calculate total money in samaira wallet?
(A) 18000
(B) 32000
(C) 30000
(D) 40000
(E) 35000
Rationale: if samaira have total money is x.
part of money in 2000 rs.=(1-(3/5+1/5))=1-4/5=1/5
x*1/5=8000,x=40,000rs.
answer D
Answer: (D) 40000
Question: A vessel contains 20 liters of a mixture of milk and water in the ratio 3:2. 10 liters of the mixture are removed and replaced with an equal quantity of pure milk. If the process is repeated once more, find the ratio of milk and water in the final mixture obtained?
(A) 9:1
(B) 9:6
(C) 9:2
(D) 9:9
(E) 9:3
Rationale: Milk = 3/5 * 20 = 12 liters, water = 8 liters
If 10 liters of mixture are removed, amount of milk removed = 6 liters and amount of water removed = 4 liters.
Remaining milk = 12 - 6 = 6 liters
Remaining water = 8 - 4 = 4 liters
10 liters of pure milk are added, therefore total milk = (6 + 10) = 16 liters.
The ratio of milk and water in the new mixture = 16:4 = 4:1
If the process is repeated one more time and 10 liters of the mixture are removed, then amount of milk removed = 4/5 * 10 = 8 liters.
Amount of water removed = 2 liters.
Remaining milk = (16 - 8) = 8 liters.
Remaining water = (4 -2) = 2 liters.
The required ratio of milk and water in the final mixture obtained
= (8 + 10):2 = 18:2 = 9:1.
Answer: A
Answer: (A) 9:1
Question: A five-digit number divisible by 3 is to be formed using numerical 0, 1, 2, 3, 4 and 5 without repetition. The total number Q of ways this can be done is:
(A) 122
(B) 210
(C) 216
(D) 217
(E) 225
Rationale: We should determine which 5 digits from given 6, would form the 5 digit number divisible by 3.
We have six digits: 0, 1, 2, 3, 4, 5. Their sum=15.
For a number to be divisible by 3 the sum of the digits must be divisible by 3. As the sum of the six given numbers is 15 (divisible by 3) only 5 digits good to form our 5 digit number would be 15-0={1, 2, 3, 4, 5} and 15-3={0, 1, 2, 4, 5}. Meaning that no other 5 from given six will total the number divisible by 3.
Second step:
We have two set of numbers:
1, 2, 3, 4, 5 and 0, 1, 2, 4, 5. How many 5 digit numbers can be formed using these two sets:
1, 2, 3, 4, 5 --> 5! as any combination of these digits would give us 5 digit number divisible by 3. 5!=120.
0, 1, 2, 4, 5 --> here we can not use 0 as the first digit, otherwise number won't be any more 5 digit and become 4 digit. So, desired # would be total combinations 5!, minus combinations with 0 as the first digit (combination of 4) 4! --> 5!-4!=4!(5-1)=4!*4=96
120+96=216=Q
Answer: C.
Answer: (C) 216
Question: A corporation paid $7 million in federal taxes on its first $50 million of gross profits and then $30 million in federal taxes on the next $150 million in gross profits. By approximately what percent did the ratio of federal taxes to gross profits increase from the first $50 million in profits to the next $150 million in profits?
(A) 6%
(B) 14%
(C) 20%
(D) 23%
(E) 43%
Rationale: Initial ratio of federal taxes to gross profits : 7/50 = 0.14
Final ratio : 30/150 = 0.2
Thus, the percentage change : (0.2-0.14)/0.14*100 = 6/14*100 = 3/7*100 = Just less than 50 % .
ANSWER:E
Answer: (E) 43%
Question: Two airplanes, one from Atlanta to New York and the other from New York to Atlanta, start simultaneously. After they meet, the airplanes reach their destinations after 16 hours and 4 hours respectively The ratio of their speeds is
(A) 2 : 3
(B) 4 : 3
(C) 4 : 2
(D) 1 : 2
(E) None
Rationale: Solution
Let us name the planes
as A and B.	= (A'S speed) : (B's speed)
=âˆšb : âˆša
= âˆš16 : âˆš4
= 4 : 2
Answer C
Answer: (C) 4 : 2
Question: If the roots of a quadratic equation are 20 and -7, then find the equation?
(A) x2 - x - 15 = 0
(B) x2 - 12x - 50 = 0
(C) x2 - 13x - 140 = 0
(D) x2 - 4x - 40 = 0
(E) x2 - 23x - 150 = 0
Rationale: Explanation:
Any quadratic equation is of the form
x2 - (sum of the roots)x + (product of the roots) = 0 ---- (1)
where x is a real variable. As sum of the roots is 13 and product of the roots is -140, the quadratic equation with roots as 20 and -7 is: x2 - 13x - 140 = 0.
Answer C
Answer: (C) x2 - 13x - 140 = 0
Question: Rectangle A has sides a and b, and rectangle B has sides c and d. If a/c=b/d=3/5, what is the ratio of rectangle A’s area to rectangle B’s area?
(A) 5/3
(B) 9/5
(C) 9/25
(D) 3/5
(E) 25/9
Rationale: The area of rectangle A is ab.
c=5a/3 and d=5b/3.
The area of rectangle B is cd=25ab/9.
The ratio of rectangle A's area to rectangle B's area is ab / (25ab/9) = 9/25.
The answer is C.
Answer: (C) 9/25
Question: The third proportional to 3 and 6 is?
(A) 8
(B) 7
(C) 12
(D) 5
(E) 3
Rationale: (6*6)/3 = 12
Answer:C
Answer: (C) 12
Question: At what rate percent of simple interest will a sum of money double itself in 12 years?
(A) 8 1/8
(B) 8 1/3
(C) 8 1/0
(D) 8 1/2
(E) 8 1/1
Rationale: Let sum = x. Then, S.I. = x.
Rate = (100 * S.I.) / (P * T) = (100 * x) / (x * 12)
= 25/3 = 8 1/3 %
Answer: B
Answer: (B) 8 1/3
Question: Let A be the event that a randomly selected two digit number is divisible by 10 and let B be the event that a randomly selected two digit number is divisible by 5. What is P(A and B)?
(A) 1/50
(B) 1/30
(C) 1/15
(D) 1/10
(E) 1/5
Rationale: P(A and B) = 1/10*1/5 = 1/50
The answer is A.
Answer: (A) 1/50
Question: Mr. John invested in Fund A and Fund B. The total amount he invested, in both funds combined, was $100,000. In one year, Fund A paid 23% and Fund B paid 17%. The interest earned in Fund B was exactly $200 greater than the interest earned in Fund A. How much did Mr. John invest in Fund A?
(A)  $32,000
(B)  $36,000
(C)  $40,000
(D)  $41,000
(E)  $42,000
Rationale: A+B=100,000
0.17B=0.23A+200
Take away decimals first: 17B=23A+20,000
Isolate first equation to solve for A (your goal): B=100,000-A
Plug in for B:
17(100,000-A)=23A+20,000
1,700,000-17A=23A+20,000
1,680,000=40A
1,680,000/40=A
A=42,000=Answer Choice E
Answer: (E)  $42,000
Question: Out of 15 students in a class, 9 are wearing blue shirts, 3 are wearing green shirts, and 3 are wearing red shirts. Four students are to be selected at random. What is the probability that at least one is wearing a green shirt?
(A) 28/61
(B) 38/71
(C) 48/81
(D) 58/91
(E) 68/101
Rationale: Total possible ways to choose 4 students out of 15 = 15C4 = 1365
The number of ways to choose 4 students with no green shirts = 12C4 = 495
P(no green shirts) = 495/1365 = 33/91
P(at least 1 green shirt) = 1 - 33/91 = 58/91
The answer is D.
Answer: (D) 58/91
Question: Find the simple interest on Rs. 68,000 at 16 2/3% per annum for 9 months.
(A) Rs.8500
(B) Rs.8000
(C) Rs.7500
(D) Rs.7000
(E) Rs.6500
Rationale: P = Rs.68000,R = 50/3% p.a and T = 9/12 years = 3/4years.
S.I. = (P*R*T)/100 = Rs.(68,000*(50/3)*(3/4)*(1/100))
= Rs.8500
Answer is A.
Answer: (A) Rs.8500
Question: Which of the following numbers is divisible by 8?
(A) 10021
(B) 17511
(C) 26778
(D) 18520
(E) 26711
Rationale: 18520. This is the only option with last two digits divisible by 8
Answer:D
Answer: (D) 18520
Question: At Didymus Corporation, there are just two classes of employees: silver and gold. The average salary of gold employees is $60,000 higher than that of silver employees. If there are 120 silver employees and 160 gold employees, then the average salary for the company is how much higher than the average salary for the silver employees?
(A) $24,000
(B) $28,000
(C) $32,000
(D) $36,000
(E) $40,000
Rationale: The answer should be -> D. $36,000
Answer: (D) $36,000
Question: Mike took a bus from home to market, that travels at 30 kmph. While walking back at 6 kmph,
halfway through, he suddenly realized he was getting late and he cycled back the remaining distance in 20 kmph. Find the average speed.
(A) 21.2 kmph
(B) 12.1 kmph
(C) 23.4 kmph
(D) 20.4 kmph
(E) none of these
Rationale: Let the distance be 2x(one way)
Time taken by bus = 2x/30, by walking =x/6, by cycling = x/20 hours
:. Average speed = Total Distance/Total time
= 6x / x/15 + x/6 + x/20
= 6 *60 / 4+10+3
= 21.2
ANSWER:A
Answer: (A) 21.2 kmph
Question: If the speed of X meters per hour is equivalent to the speed of Y kilometers per hour, what is Y in terms of X? (1 kilometer=1000 meters)
(A) 0.1X
(B) 0.01X
(C) 0.001X
(D) 0.0001X
(E) 0.005X
Rationale: X meters per hour -->
--> 1X meters per hour(as there are 3,600 seconds in one hour);
--> X/1,000=0.001X kilometers per hour (as there are 1,000 meters in one kilometer).
Answer: C.
Answer: (C) 0.001X
Question: A certain car increased its average speed by 5 miles per hour in each successive 5-minute interval after the first interval. If in the first 5-minute interval its average speed was 2 miles per hour, how many miles did the car travel in the third 5-minute interval?
(A) 1.0
(B) 1.5
(C) 2.0
(D) 2.5
(E) 3.0
Rationale: In the third time interval the average speed of the car was 2+5+5=12 miles per hour;
In 5 minutes (1/12 hour) at that speed car would travel 12*1/12=1 miles.
Answer: A.
Answer: (A) 1.0
Question: 150 ml of 30% sulphuric acid was added to approximate 400 ml of 12% sulphuric acid solution. Find the approximate concentration W of the acid in the mixture?
(A) 1/2
(B) 1/3
(C) 1/4
(D) 1/6
(E) 1/5
Rationale: Do not need any computation
30%-----------21%---------12%
if volume of both sol. were equal the concentration W would be 21%=1/5, but 12% is more than 3 times
only possibility is 1/6
D
Answer: (D) 1/6
Question: The slant height of a right circular cone is 10 m and its height is 8 m. Find the area of its curved surface.
(A) 30 m2
(B) 40 m2
(C) 50 m2
(D) 60 m2
(E) 80 m2
Rationale: l = 10 m,
h = 8 m.
So, r = l2 - h2 = (10)2 - 82 = 6 m.
Curved surface area = rl = ( x 6 x 10) m2 = 60 m2.
Answer: Option D
Answer: (D) 60 m2
Question: David obtained 76, 65, 82, 67 and 85 marks (out in 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks?
(A) 65
(B) 69
(C) 72
(D) 75
(E) None of these
Rationale: Solution
Average =
(76+65+82+67+85 / 5)	=(375 / 5)
= 75.
Answer D
Answer: (D) 75
Question: x and y are positive integers of V. If 1/x + 1/y < 2, which of the following must be true?
(A)  x + y > 4
(B)  xy>1
(C)  x/y + y/x < 1
(D)  (x - y)^2 > 0
(E)  None of the above
Rationale: Answer is B:
1/X + 1/Y < 2
The maximum value of 1/X is 1 because if X equals any other number greater than one it will be a fraction. The same is true with 1/Y.
So 1/X and 1/Y will always be less than 2 as long as both X and Y are not both equal to one at the same time.
Another way of putting it is:
X*Y>1.B
Answer: (B)  xy>1
Question: What is the sum of 100 consecutive integers from -49 inclusive, in a increasing order?
(A) -29
(B) 50
(C) -30
(D) 30
(E) 60
Rationale: From -49 to -1 --> 49 nos.
zero --> 1 number
from +1 to +49 --> 49 nos.
When we add up nos. from -49 to + 49 sum will be zero. Total 99 nos will be added.
100th number will be 50.
Sum of these 100 nos. = 50.
B is the answer.
Answer: (B) 50
Question: We bought 85 hats at the store. Blue hats cost $6 and green hats cost $7. The total price was $550. How many green hats did we buy?
(A) A)36
(B) B)40
(C) C)41
(D) D)42
(E) E)44
Rationale: Let B be the number of blue hats and let G be the number of green hats.
B+G=85.
B=85-G.
6B+7G=550.
6(85-G)+7G=550.
510-6G+7G=550.
G=550-510=40.
The answer is B.
Answer: (B) B)40
Question: A vessel is filled with liquid, 3 parts of which are water and 5 parts of syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?
(A) 1 / 3
(B) 1 / 4
(C) 1 / 5
(D) 1 / 7
(E) None
Rationale: Suppose the vessel initially contains 8 litres of liquid. Let x littres of this liquid be replaced with water.
Quantity of water in new mixture = (3 - 3x/8 + x) litres.
Quantity of syrup in new mixture = (5 - 5x/8) litres.
(3 - 3x/8 + x) = (5 - 5x/8) = 5x + 24 = 40 - 5x
=› 10x = 16 =› x = 8/5
So, part of the mixture replaced = (8/5 x 1/8) = 1/5.
Answer C
Answer: (C) 1 / 5
Question: A fruit seller had some apples. He sells 40% apples and still has 420 apples. Originally, he had:
(A) 700
(B) 680
(C) 720
(D) 760
(E) 660
Rationale: Apples Sold = 40%
So Remaining Apples = 60%
60% = 420
Full (100%) = (100/60) X 420
= 700
answer :A
Answer: (A) 700
Question: Suppose you want to buy three loaves of bread that cost $0.75 each
and a jar of peanut butter that costs $7. A jar of jelly is $2.75, but you
donâ€™t need any jelly. You have $17. How much money will you have left
over?
(A) $7.75
(B) $7.50
(C) $3.50
(D) $4.50
(E) $5.50
Rationale: The jelly is extra information. 17.00 â€“ 3 x 0.75 â€“ 7.00 =
17.00 â€“ 2.25 â€“ 7.00 = 7.75.
You have $7.75 left.
correct answer A
Answer: (A) $7.75
Question: For positive integers n, the integer part of the nth term of sequence F equals n, while the infinite decimal part of the nth term is constructed in order out of the consecutive positive multiples of n, beginning with 2n. For instance, F_1 = 1.2345678…, while F_2 = 2.4681012… The sum of the first seven terms of sequence F is between:
(A) 28 and 29
(B) 29 and 30
(C) 30 and 31
(D) 31 and 32
(E) 32 and 33
Rationale: First, construct the first seven terms, though only out to a few decimal places, following the given pattern.
F_1 = 1.23…
F_2 = 2.46…
F_3 = 3.69…
F_4 = 4.812…
F_5 = 5.10…
F_6 = 6.12…
F_7 = 7.14…
Now, to add up the first seven terms, you should be strategic about how many decimal places to keep. You can drop the hundredths place and get a good approximation with the tenths place—and if you find the sum too close to a boundary between choices, then you can refine your answer if necessary.
1.2 + 2.4 + 3.6 + 4.8 + 5.1 + 6.1 + 7.1 = 30.3
Including more decimal places would only add a couple of tenths to the sum—not enough to tip the sum over 31.
The correct answer is C.
Answer: (C) 30 and 31
Question: Nobel buys an old car for $1000 and spends $1000 on its repairs. If he sells the scooter for $2500, his gain percent is?
(A) 10%
(B) 15%
(C) 25%
(D) 20%
(E) 30%
Rationale: C.P. = 1000+1000 = $2000
S.P. = $2500
Gain = 2500-2000 = $500
Gain% = 500/2000 * 100 =25%
Answer is C
Answer: (C) 25%
Question: A sum of Rs. 2665 is lent into two parts so that the interest on the first part for 5 years at 3% per annum may be equal to the interest on the second part for 3 years at 5% per annum. Find the second sum?
(A) Rs.1178.55
(B) Rs.1978.25
(C) Rs.1332.5
(D) Rs.1678
(E) Rs.1675.55
Rationale: (x*5*3)/100 = ((2665 - x)*3*5)/100
15x/100 = 39975/100 - 15x/100
30x = 39975 => x = 1332.5
Second sum = 2665 – 1025 = 1332.5
ANSWER:C
Answer: (C) Rs.1332.5
Question: An employee’s annual salary was increased $25,000. If her new annual salary now equals $90,000, what was the percent increase?
(A) 15%
(B) 162⁄3%
(C) 20%
(D) 38.46%
(E) 24%
Rationale: New annual salary = $90,000
Salary increase = $25,000.
Original salary = $90,000 - $25,000.
= $75,000
%Increase = ($25,000/ $65,000 )*100
=38.46%
Hence D.
Answer: (D) 38.46%
Question: What is the smallest number which when diminished by 10, is divisible 2, 6, 12 and 24?
(A) 35
(B) 34
(C) 20
(D) 35
(E) 342
Rationale: Required Number
= (LCM of 2, 6, 12 and 24) + 12
= 24 + 10 = 34
Option B
Answer: (B) 34
Question: A train with a length of 100 meters, is traveling at a speed of 72 km/hr. The train enters a tunnel 2.3 km long. How many minutes does it take the train to pass through the tunnel from the moment the front enters to the moment the rear emerges?
(A) 2.0
(B) 2.5
(C) 3.0
(D) 3.5
(E) 4.0
Rationale: 72 km/hr = 1.2 km/min
The total distance is 2.4 km.
2.4 / 1.2 = 2 minutes
The answer is A.
Answer: (A) 2.0
Question: In a certain school, the ratio of boys to girls is 5 to 13. If there are 128 more girls than boys, how many boys are there?
(A) 27
(B) 36
(C) 45
(D) 72
(E) 80
Rationale: The ratio of b to G is 5:13 and the other data point is G are more than boys by 128...
Looking at the ratio we can say that the 8(13-5) extra parts caused this diff of 128. so 1 part corresponds to 128/8=16 and so
5 parts correspond to 5*16 = 80.
E
Answer: (E) 80
Question: How much time will a train of length 200 m moving at a speed of 72 kmph take to cross another train of length 300 m, moving at 36 kmph in the same direction?
(A) 50
(B) 88
(C) 77
(D) 55
(E) 22
Rationale: The distance to be covered = Sum of their lengths = 200 + 300 = 500 m.
Relative speed = 72 -36 = 36 kmph = 36 * 5/18 = 10 mps.
Time required = d/s = 500/10 = 50 sec.
Answer: A
Answer: (A) 50
Question: Find the largest 4 digit number which isexactly divisible by 88?
(A) 7890
(B) 8900
(C) 9944
(D) 9976
(E) 10000
Rationale: Largest 4 digit number is 9999
After doing 9999 ÷ 88 we get remainder 55
Hence largest 4 digit number exactly divisible by 88 = 9999 - 55 = 9944
C
Answer: (C) 9944
Question: Rs. 20 is the true discount on Rs. 260 due after a certain time. What will be the true discount on the same sum due after half of the former time ,the rate of interest being the same ?
(A) Rs. 10
(B) Rs. 10.40
(C) 15.20
(D) Rs. 13
(E) None of these
Rationale: Solution
S.I. on Rs. (260-20) for a given time =Rs. 7.34.
S.I. on Rs. 240 for half the time = Rs.10.
T.D. on Rs. 250 = Rs. 10.
∴ T.D. on Rs. 260 = Rs. ( 10/250x 260 ) = Rs. 10.40.
Answer B
Answer: (B) Rs. 10.40
Question: If X,Y and Z are three consecutive multiples of 5. Then which of the following will the factor of X*Y*Z
1) 125
2) 250
3) 375
4) 750
(A) only 1
(B) 1,2
(C) 1,3
(D) 1,2,3
(E) All of them
Rationale: Given choices can be re-written as multiples of 125
1. 125
2. 125*2
3. 125*3
4. 125*6
Now if, 5*a = X, then
5*(a+1) = Y & 5*(a+2) = Z
So, X*Y*Z = 125* a(a+1)(a+2)
Now, among any 3 consecutive positive integers, we will either have (a number that is divisible by both 2 & 3) or (a number divisible by 2 and another number divisible by 3).
Ex:
17, 18, 19 -> 18 divisible by 2 & 3.
14, 15,16 -> 14, 16 divisible by 2 & 15 divisible by 3.
Hence 'E'
Answer: (E) All of them
Question: 2056 x 987 = ?
(A) 1936372
(B) 2029272
(C) 1896172
(D) 1926172
(E) 1956231
Rationale: Answer: Option B
2056 x 987	= 2056 x (1000 - 13)
= 2056 x 1000 - 2056 x 13
= 2056000 - 26728
= 2029272.
Answer: (B) 2029272
Question: A watch was sold at a loss of 46%. If it was sold for Rs.140 more, there would have been a gain of 4%. What is the cost price?
(A) 280
(B) 288
(C) 279
(D) 277
(E) 290
Rationale: 54%
104%
--------
50% ---- 140
100% ---- ? => Rs.280
Answer: A
Answer: (A) 280
Question: ABCD is a square where AB =√2016. Let X be a point on AB and Y be a point on CD such
that AX = CY . Compute the area of trapezoid AXYD.
(A) 3008
(B) 2002
(C) 1008
(D) 2016
(E) 3000
Rationale: Note that trapezoids AXY D and BXY C are congruent, so the area of AXY D is
always
2016/2= 1008 .
correct answer C
Answer: (C) 1008
Question: What sum of money put at C.I amounts in 2 years to Rs.8820 and in 3 years to Rs.9261?
(A) 8000
(B) 8020
(C) 2879
(D) 2686
(E) 2996
Rationale: 8820 ---- 441
100 ---- ? => 5%
x *105/100 * 105/100 = 8820
x*1.1025=8820
x=8820/1.1025 => 8000
Answer: A
Answer: (A) 8000
Question: Two taps A and B can fill a tank in 5 hours and 20hours respectively. If both the taps are open then due to a leakage, it took 30 minutes more to fill the tank. If the tank is full, how long will it take for the leakage alone to empty the tank?
(A) 24 hr
(B) 36 hr
(C) 18 hr
(D) 42 hr
(E) 30 hr
Rationale: Part filled by A+B in 1 hour = 1/5 + 1/20 = 1/4
A and B together can fill the tank in 4 hour
Work done by the leak in 1 hour = 1/4 - 2/9 = 1/36
leak will empty the tank in 36 hours.
Answer is B
Answer: (B) 36 hr
Question: A car dealer sold x used cars and y new cars during May. If the number of used cars sold was 10 greater than the number of new cars sold. Which of the following expresses this relationship ?
(A)  x > 10y
(B)  x > y + 10
(C)  x > y – 10
(D)  x = y + 10
(E)  x = y – 10
Rationale: Let number of used cars sold in May = x
number of new cars sold in May = y
x= y + 10
Answer D
Answer: (D)  x = y + 10
Question: Peter will arrange 6 people of 6 different heights for photograph by placing them in two rows of three so that each person in the first row is standing is standing in front of someone in the second row. The heights of the people within each row must increase from left to right, and each person in the second row must be taller than the person standing in front of him or her. How many such arrangements of the 6 people are possible?
(A) 5
(B) 6
(C) 9
(D) 24
(E) 26
Rationale: Peter will arrange 6 people of 6 different heights for photograph by placing them in two rows of three so that each person in the first row is standing is standing in front of someone in the second row.person with max height is in the second row, person with min height is in the first row. We need to select 1 person in the middle of each row... In the middle of the first row we can put only 2, 3 or 4. In the middle of the second row we can put only 3, 4, 5. If we select {3 in the sec. row, 2 in the first}, {4,2}, {5,2}, {4,3}, {5,3}, {5,4}. So, there are 0*1 + 1*1 + 2*1 + 1*1 + 1*1 + 0*1 = 5 cases...A
Answer: (A) 5
Question: If k > 0, x + 2k = y, and y + 3k = z, what is the ratio between z - x and y - x ?
(A) 3 to 1
(B) 3 to 2
(C) 4 to 1
(D) 5 to 1
(E) 5 to 2
Rationale: y-x = 2k
z-y = 3k
Let's add the two equations together:
z-x = 5k
The ratio of z-x to y-x is 5:2.
The answer is E.
Answer: (E) 5 to 2
Question: A man can row with a speed of 5 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is?
(A) A)63kmph
(B) B)63kmph
(C) C)10kmph
(D) D)62kmph
(E) E)74kmph
Rationale: Explanation:
M = 5
S = 5
DS = 5 + 5 = 10
Answer: Option C
Answer: (C) C)10kmph
Question: A train 640 meters long is running with a speed of 64 kmph. The time taken by it to cross a tunnel 140 meters long is?
(A) 44 sec
(B) 49 sec
(C) 48 sec
(D) 16 sec
(E) 17 sec
Rationale: D = 640 + 140 = 780
S = 64 * 5/18 = 17.7 mps
T = 780/17.7 = 44 sec
Answer: A
Answer: (A) 44 sec
Question: For every order, a certain mail-order company charges a shipping fee of $3 plus an additional $2 if the value of the order is over $50 but not over $100 or an additional $3 if the value of the order is over $100. How much greater are the total shipping fees for 2 orders of $75 each than the total shipping fee for 1 order of $120 ?
(A)  $1
(B)  $2
(C)  $3
(D)  $4
(E)  $5
Rationale: Total cost involved for each 75 $ shipment: 3+2 = 5 $. Thus, for two such orders = 10$
Total cost involved for a 120$ shipment: 3+3 = 6$.
The difference = 4$.
D.
Answer: (D)  $4
Question: Two trains of equal length, running with the speeds of 60 and 40 kmph, take 50 seconds to cross each other while they are running in the same direction. What time will they take to cross each other if they are running in opposite directions?
(A) 10 sec
(B) 17 sec
(C) 18 sec
(D) 16 sec
(E) 12 sec
Rationale: RS = 60 -40 = 20 * 5/18 = 100/18
T = 50
D = 50 * 100/18 = 2500/9
RS = 60 + 40 = 100 * 5/18
T = 2500/9 * 18/500
= 10 sec
Answer: A
Answer: (A) 10 sec
Question: r=2^(n+1), then in terms of r, 9^n=
(A) r^2/81
(B) r^2/9
(C) r^2/4
(D) r/3
(E) r
Rationale: Questions in terms of variables can be easily solved by plugging in some values: Say n = 0
r = 2^1 = 2
and you need the value of 2^n which is 2^0 = 1
So when you put r = 2 in the options, you should get 1. Only option (C) satisfies.
Answer (C)
Answer: (C) r^2/4