mathewhe/aqua_rat huggingface dataset:
Question: 5 men 2 boys working together can do 4 times as much work as a man and a boy working capacities of a woman and boy are in ratio?
(A) 1:2
(B) 2:1
(C) 1:3
(D) 3:1
(E) 3:2
Rationale: Explanation:
1 man’s 1 day work = x
1 boy’s 1 day work = y
5x+2y = 4(x + y) => x = 2y => 2:1
Answer: Option B
Answer: (B) 2:1
Question: A boat crossed a lake from North to South at the speed of 4 km/h, entered a river and covered twice as much distance going upstream at 3 km/h. It then turned around and stopped at the south shore of the lake. If it averaged 3.5 km/h that day, what was its approximate downstream speed?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: Another way will be:
Total time for the trip = distance covered in Lake/speed in still water +distance covered upstream/upstream speed + distance covered downstream/downstream speed
If 5D is the total distance, then distance covered in lake = D, distance covered upstream = 2D and distance covered downstream = 2D
=>5D/3.5 = D/4 + 2D/3 + 2D/x (where x is the downstream speed)
=> 5/3.5 = 1/4 + 2/3 +2/x (div. both sides by D)
=> 1.42 = .25+.66 +.51/x => x=3.9 ~ 4
option A
Answer: (A) 4
Question: The following sets each have a mean of 20 and the standard deviations are given in variable form.
Set I = {10, 10, 10, 30, 30, 30}, standard deviation = P
Set II = {14, 16, 18, 22, 24, 26}, standard deviation = Q
Set III = {20, 20, 20, 20, 20, 20}, standard deviation = R
Rank these three standard deviations from greatest to least.
(A) R, P, Q
(B) P, Q, R
(C) R, Q, P
(D) Q, R, P
(E) Q, P, R
Rationale: The answer should be B as the mean is most deviated in Set I followed by Set II and then Set III.
Answer: (B) P, Q, R
Question: Because of the economic slowdown, a multinational company curtailed some of the allowances of its employees. John, the marketing manager of the company whose monthly salary has been reduced to Rs.42,000 is unable to cut more on his expenditure. He finds that there is a deficit of Rs.2,000 between his earning and expenses in the first month. This deficit, because of inflationary pressure, will keep on increasing by Rs.500 every month. John has a saving of Rs 60,000 which will be used to fill the deficit. After his savings get exhausted, John would start borrowing from his friends. How soon will he start borrowing?
(A) 3th months
(B) 5th months
(C) 8th months
(D) 11th months
(E) 13th months
Rationale: Let the Rashid 's savings will last till 'nn' months.
⇒n2[2×2000+(n−1)500]=60,000⇒n2[2×2000+(n−1)500]=60,000
[Expenditure every month increases by 500 rupees]
⇒n2+7n−200=0⇒n2+7n−200=0
n=12.38n=12.38
⇒ Rashid after Kartik's mother asked him to get the vegetables, milk and butter from the market and gave him the money in the denominator of 1 Rupee, 2 Rupee and 5 Rupee coins.
Kartik first goes to the grocery shop to buy vegetables. At the grocery shop he gives half of his 5 Rupee coins in return receives the same number of 1 Rupee coins.
Next he goes to the dairy shop to buy milk and butter and gives all 2 Rupee coins and in return get thirty 5 Rupee coins, which increase the number of five rupee coins by 75% more than the original number.
If the number of 1 rupee coins now is 50, the number of 1 rupee and 5 rupee coins originally were will start borrowing money from his friends.
E
Answer: (E) 13th months
Question: For what value of â€œkâ€ will the equation (2kx2 + 6kx +2)=0 have equal roots?
(A) 2/7
(B) 4/9
(C) 16/25
(D) 7/1
(E) 7/2
Rationale: for a 2nd degree equation ax2+bx_c=0 has equal roots the condition is b2-4ac =0
in the given equation
(6k)^2-4*2k*2=0
by solving this equation
we get k=0, k=4/9
ANSWER:B
Answer: (B) 4/9
Question: The average marks obtained by 120 candidates in a certain examinationis 35.if the average marks of passed candidate is 39 and that of the failed candidates is 15,what is the no. of candidates who passed the examination?
(A) 80
(B) 100
(C) 110
(D) 140
(E) 150
Rationale: Let No. of passed candidates are x
So, x * 39 + (120 – x) 15= 120 * 35
x = 100
B
Answer: (B) 100
Question: Elana was working to code protocols for computer processing. She did 11/18 of the job and allowed Andy to finish it. They both work at the same rate and receive the same hourly pay. If the difference between the amounts they were paid was $154, what was the total amount the two were paid for the entire coding job?
(A) $252.00
(B) $269.50
(C) $369.00
(D) $423.50
(E) $693.00
Rationale: Elena did 11/18 of The job so 7/18 was done by Andy. As 11/18+7/18=1
Now difference between work done is 11/18-7/18=4/18.
So for this 4/18 work the difference is 154.
Hence x= 154*18/4 = 693
Option - C.
Answer: (C) $369.00
Question: A cube of side one meter length is cut into small cubes of side 10 cm each. How many such small cubes can be obtained?
(A) 2997
(B) 2799
(C) 1000
(D) 2272
(E) 2702
Rationale: Along one edge, the number of small cubes that can be cut
= 100/10 = 10
Along each edge 10 cubes can be cut. (Along length, breadth and height). Total number of small cubes that can be cut = 10 * 10 * 10
=1000
Answer:C
Answer: (C) 1000
Question: Ramu rides his bike at an average speed of 45 km/hr and reaches his desitination in four hours. Somu covers the same distance in five hours. If Ramu covered his journey at an average speed which was 9 km/hr less and Somu covered his journey at an average speed which was 10 km/hr more, then the difference in their times taken to reach the destination would be (in minutes).
(A) 65 minutes
(B) 66 minutes
(C) 56 minutes
(D) 69 minutes
(E) 46 minutes
Rationale: Distance travelled by Ramu = 45 * 4 = 180 km
Somu travelled the same distance in 5 hours.
His speed = 180/5 = 36 km/hr
Hence in the conditional case, Ramu's speed = 45 - 9 = 36 km/hr and Somu's speed = 36 + 10 = 46km/hr.
Therefore travel time of Ramu and Somu would be 5 hours and 3.9 hours respectively. Hence difference in the time taken = 1.1 hours = 66 minutes.
ANSWER:B
Answer: (B) 66 minutes
Question: A batsman makes a score of 64 runs in the 16th innings and thus increased his average by 3. Find his average after the 16th inning?
(A) 22
(B) 77
(C) 26
(D) 19
(E) 88
Rationale: Let the average after the 16th inning be P.
So, the average after the 15th inning will be (P-3) Hence, 15(P-30) + 64 = 16P => P = 19.
Answer:D
Answer: (D) 19
Question: A person travelled from his house to office at 30km/hr and office to house at 50km/hr. Then find the average speed?
(A) 37.5km/hr
(B) 20km/hr
(C) 32km/hr
(D) 24km/hr
(E) 25km/hr
Rationale: Average speed = (2*30*50)/(30+50)
= 37.5km/hr
Answer is A
Answer: (A) 37.5km/hr
Question: If $600 is deposited into a savings account at an annual interest rate of 4% that compounds monthly, what is the value of the investment after 7 years?
(A) $750.00
(B) $823.50
(C) $973.25
(D) $100.25
(E) $793.49
Rationale: Using CI Formula:
A=P(1+r/n)^n*t
A=600(1+4/7)^4*7
A=793.49
Option: E
Answer: (E) $793.49
Question: A rectangle measures 8 Cm on length and its diagonal measures 17 Cm. What is the perimeter of the rectangle?
(A) 44cm
(B) 42cm
(C) 46cm
(D) 49cm
(E) 41cm
Rationale: Second side = √17power2-8power2
= √289-64
= 15 Cm
Perimeter = 2 (l+b) = 2(8+5) Cm = 2(23) = 46 Cm
Answer is C.
Answer: (C) 46cm
Question: 4% of the population of a certain country owns both a car and a boat. If 20% of those who own a boat, do not own a car, what percentage of the country's population owns a boat?
(A) 5%
(B) 7.5%
(C) 10%
(D) 12.5%
(E) 15%
Rationale: 0.04x has B+C ( x is total population)
Let # of people who own a boat = y
20% of those who own a boat, do not own a car
=> 0.2y do not have a car
=> 80% of those who own a boat own a car
=> 0.8y = 0.04x
=> y/x = 4/80
So %age = 4/80 * 100 = 5%
Answer - A
Answer: (A) 5%
Question: A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that all the four bulbs are defective
(A) 1/128
(B) 1/121
(C) 1/120
(D) 1/123
(E) 1/126
Rationale: Explanation:
Out of nine, five are good and four are defective. Required probability = 4C4/9C4 = 1/126
Answer: E
Answer: (E) 1/126
Question: A conference is to have eight presentations over the course of one day, consisting of three long presentations, and five short presentations. If the conference organizer doesn't want consecutive long presentations, and the conference is to start with a short presentation, how many schedules of presentations are possible?
(A) 1200
(B) 7200
(C) 2880
(D) 5760
(E) 11520
Rationale: S*S*S*S*S*
5 short presentations can be arranged in 5!=120 ways.
As for 3 long presentations: each can be placed instead of any of the 5 star, so in C35=10C53=10 ways, and they also can be arranged in 3!=6 ways.
Total = 120*10*6 = 7,200
Ans:B
Answer: (B) 7200
Question: The ratio, in which tea costing Rs. 192 per kg is to be mixed with tea costing Rs. 150 per kg so that the mixed tea when sold for Rs. 194.40 per kg, gives a profit of 20%.
(A) 2:5
(B) 3:5
(C) 5:3
(D) 5:2
(E) 2:3
Rationale: Solution: CP of first tea = Rs. 192 per kg.
CP of Second tea = Rs. 150 per kg.
Mixture is to be sold in Rs. 194.40 per kg, which has included 20% profit. So,
SP of Mixture = Rs. 194.40 per kg.
Let the CP of Mixture be Rs. X per kg. Therefore,
X + 20% of X = SP
6X /5 = 194.40
6X = 194.40 *5
X = Rs. 162 per kg.
Let N kg of first tea and M kg of second tea to be added.
Now, Using Alligation,
We get,
N/M = 12/30
N : M = 2 : 5.
Answer: Option A
Answer: (A) 2:5
Question: Find the area of circle whose radius is 10m?
(A) 138
(B) 154
(C) 288
(D) 280
(E) 314.3
Rationale: 22/7 * 10 * 10
= 314.3
Answer:E
Answer: (E) 314.3
Question: Solve the following quadratic equation by factoring.
X^2+15X=-50
(A) 10,4
(B) 4,-10
(C) 5,10
(D) -5,-10
(E) 6,3
Rationale: Now all we need to do is use the zero factor property to get,
X+5=0 X=-5 (OR) X+10 = 0 X=-10
ANSWER D -5,-10
Answer: (D) -5,-10
Question: A rectangular parking space is marked out by painting three of its sides. If the length of the unpainted side is 9 feet, and the sum of the lengths of the painted sides is 37 feet, then what is the area of the parking space in square feet?
(A) 46
(B) 81
(C) 126
(D) 252
(E) None of these
Rationale: Clearly, we have : l = 9 and l + 2b = 37 or b = 14.
∴ Area = (l × b) = (9 × 14) sq. ft. = 126 sq. ft.
Answer C
Answer: (C) 126
Question: To a sugar solution of 3 litres containing 40% sugar, one litre of water is added. The percentage of sugar in the new solution is
(A) 22
(B) 30
(C) 99
(D) 88
(E) 27
Rationale: Explanation:
Quantity of sugar = kg = 1.2 kg.
New percentage = = 30%.
Answer: B) 30
Answer: (B) 30
Question: A man saves Rs. 200 at the end of each year and lends the money at 5% compound interest. How much will it become at the end of 3 years?
(A) Rs. 565.25
(B) Rs. 635
(C) Rs. 662.02
(D) Rs. 666.50
(E) Rs. 686.50
Rationale: Amount = [200(1 + 5/100)3 + 200(1 + 5/100)2 + 200(1 + 5/100)]
= [200 * 21/20(21/20 * 21/20 + 21/20 + 1)] = Rs. 662.02
ANSWER:C
Answer: (C) Rs. 662.02
Question: y = x2 + bx + 256 cuts the x axis at (h, 0) and (k, 0). If h and k are integers, what is the least value of b?
(A) -32
(B) -256
(C) -255
(D) -257
(E) 0
Rationale: Explanatory Answer
The curve cuts the x axis at (h, 0) and (k, 0). So, h and k are the roots of the quadratic equation.
For a quadratic equation of the form ax2 + bx + c = 0, the sum of the roots = -b/a
The sum of the roots of this equation is -b/1 = -b.
Note: Higher the sum of the roots, lower the value of b.
For a quadratic equation of the form ax2 + bx + c = 0, the product of roots = c/a.
Therefore, the product of the roots of this equation = 256/1 = 256.
i.e., h * k = 256
h and k are both integers.
So, h and k are both integral factors of 256.
256 can be expressed as product of two numbers in the following ways:
1 * 256
2 * 128
4 * 64
8 * 32
16 * 16
The sum of the roots is maximum when the roots are 1 and 256 and the maximum sum is 1 + 256 = 257.
The least value possible for b is therefore -257.
The correct choice is (D)
Answer: (D) -257
Question: If air is called green , green is called blue, blue is called purple, sky is called yellow, yellow is called water and water is called pink, then what is the color of clear sky ?
(A) Blue
(B) Sky
(C) Water
(D) Yellow
(E) Purple
Rationale: Explanation:The colour of clear sky is 'blue' and as given, 'purple' is called 'sky'.So, the colour of clear sky is 'purple'.Answer: E
Answer: (E) Purple
Question: The salary of a worker is first increased by 30% and afterwards reduced by 30%. What is net change in his salary?
(A) 90% increase
(B) 45% increase
(C) 9% decrease
(D) Same as before
(E) NONE
Rationale: (30 * 30)/100 = 9% decrease
ANSWER:D
Answer: (D) Same as before
Question: According to the directions on a packet of smoothie mix, 1 3-ounce packet of smoothie mix is to be combined with 10 ounces of water to make a smoothie. How many 3-ounce packets of smoothie mix are required to prepare 150 12-ounce smoothies?
(A)  120
(B)  150
(C)  180
(D)  240
(E)  600
Rationale: This question wasn't particularly grueling, but I think it's the first where I had the opportunity to solve it via theory andinspectionthat many on this board suggest as strategy on the GMAT. It actually came to me by accident. Basically, if we thought that the 3 packets of powder were included in the 12 ounces of water, that would mean we would need 150 packets of smoothie mix (along with 12(150) ounces of water for a total of 150 packets. However, we know, after a more careful reading of the stimulus, that the 3 ounces are NOT included in the 12 ounces. As such, the answer has to be LESS than 150 packets, since 150 would be too much powder considering you already have 150(12) ounces of water and need less packets than water to make a smoothie. As such, the only answer less than 150 is 120, A. Does this make sense? Or am I way off base?
B
Answer: (B)  150
Question: If n is a positive integer and the greatest common divisor of n and 16 is 4, and the greatest common divisor of n and 15 is 3, which of the following is the greatest common divisor of n and 204?
(A) 34
(B) 17
(C) 48
(D) 51
(E) 102
Rationale: The greatest common divisor of n and 16 is 4 --> n is a multiple of 4 but not a multiple of 8.
The greatest common divisor of n and 15 is 3 --> n is a multiple of 3 but not a multiple of 5.
204=2*3*17*2 is divisible by 102. therefore the greatest common divisor is 102.
E
Answer: (E) 102
Question: The average of 9 observations was 9, that of the 1st of 5 being 10 and that of the last 5 being 8. What was the 5th observation?
(A) 9
(B) 12
(C) 15
(D) 17
(E) 18
Rationale: Explanation:
1 to 9 = 9 * 9 = 81
1 to 5 = 5 * 10 = 50
5 to 9 = 5 * 8 = 40
5th = 50 + 40 = 90 – 81 = 9
Option A
Answer: (A) 9
Question: The sale price sarees listed for Rs.400 after successive discount is 10% and 5% is?
(A) 338
(B) 277
(C) 342
(D) 882
(E) 212
Rationale: 400*(90/100)*(95/100) = 342
Answer: C
Answer: (C) 342
Question: Rs. 1581 is divided among A, B and C in the ratio 10 : 15 : 6. What is the share of B?
(A) 306
(B) 765
(C) 700
(D) 510
(E) 520
Rationale: 10+15+6=31
1581/31=51
so B's share=15*51
=765
A's share =10*51
=510
C's share =6*51
=306
ANSWER:A
Answer: (A) 306
Question: If P(A) = 4/5 and P (B) = 2/5, find P (A n B) if A and B are independent events.
(A) 8/25
(B) 1/25
(C) 2/25
(D) 3/14
(E) 25/8
Rationale: P (A n B) = P(A) . P(B)
P (A n B) = 4/5 . 2/5
P (A n B) = 8/25.
A
Answer: (A) 8/25
Question: A father is now three times as old as his son. Four years back, he was four times as old as his son. The age of the son (in years) is
(A) A)12
(B) B)15
(C) C)18
(D) D)20
(E) E)22
Rationale: Explanation:
Let son's age be x years. Then, father's age = (3x) years.
Four years ago, father's age = (3x - 4) years and son's age = (x - 4) years.
So, 3x - 4 = 4 (x - 4)=> 3x - 4 = 4x - 16=> x = 12.
Answer: A
Answer: (A) A)12
Question: If x/y is an integer, which of the following must also be an integer?
I. xy
II. y/x
III. x
(A) I alone
(B) II alone
(C) III alone
(D) I and III
(E) None of the above
Rationale: Let's take X = 4/3 and Y = 2/3
Then X/Y = 2 which is an integer.
But XY = 4/3 * 2/3 = 8/9 --> Not an integer.
Y/X = 2/3 divided by 4/3 = 2/4 = 1/2 Not an integer.
X alone is 4/3. Not an integer.
Hence E.
None of the above.
Answer: (E) None of the above
Question: If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance travelled by him is:
(A) 50 km
(B) 56 km
(C) 70 km
(D) 80 km
(E) 85 km
Rationale: Let the actual distance travelled be x km.
Then,	x/10	=	(x + 20)/14
=14x = 10x + 200
4x = 200
x = 50 km.
Answer :A
Answer: (A) 50 km
Question: If two numbers are in the ratio 2:3. If 10 is added to both of the numbers then the ratio becomes 3:4 then find the smallest number?
(A) 10
(B) 20
(C) 22
(D) 24
(E) 26
Rationale: 2:3
2x + 10 : 3x + 10 = 3 : 4
4[2x + 10] = 3[3x + 10]
8x + 40 = 9x + 30
9x - 8x = 40 - 30
x = 10
Then smallest number is = 2
2x = 20
B
Answer: (B) 20
Question: Rs. 6500 is divided into three parts A, B and C. How much A is more than C if their ratio is 1/2:1/3:1/4?
(A) 2000
(B) 1500
(C) 900
(D) 600
(E) 300
Rationale: 1/2:1/3:1/4
= 6:4:3
3/13*6500
= 1500
Answer: B
Answer: (B) 1500
Question: A train running at the speed of 60 km/hr crosses a pole in 3 seconds. What is the length of the train?
(A) 120 metres
(B) 180 metres
(C) 324 metres
(D) 50 metres
(E) 180 metres
Rationale: Speed=(60 x 5/18)/m/sec	=	50/3	m/sec.
Length of the train = (Speed x Time).
Length of the train =	50 x 3/3 m = 50 m.
ANSWER : OPTION D
Answer: (D) 50 metres
Question: Ravi can do a piece of work in 15 days while Prakash can do it in 6 days. In how many days will they finish it together?
(A) 5 7/9 days
(B) 6 7/9 days
(C) 5 1/9 days
(D) 5 7/2 days
(E) 4 2/7 days
Rationale: 1/15 + 1/6 = 7/30
30/7 = 4 2/7 days
ANSWER:E
Answer: (E) 4 2/7 days
Question: The Shopkeeper increased the price of a product by 25% so that customer finds it difficult to purchase the required amount. But somehow the customer managed to purchase only 60% of the required amount. What is the net difference in the expenditure on that product?
(A) 25%
(B) 13%
(C) 15%
(D) 17%
(E) 19%
Rationale: Quantity X Rate = Price
1 x 1 = 1
0.6 x 1.25 = 0.75
Decrease in price = (0.25/1) × 100 = 25%
A)
Answer: (A) 25%
Question: A bottle contains a certain solution. In the bottled solution, the ratio of water to soap is 3:4, and the ratio of soap to salt is five times this ratio. The solution is poured into an open container, and after some time, the ratio of water to soap in the open container is quartered by water evaporation. At that time, what is the ratio of water to salt in the solution?
(A) 26:64
(B) 64:9
(C) 9:64
(D) 9:60
(E) 20:64
Rationale: Water:soap = 3:4
Soap:Salt=15:20
=> For 15 soap, salt = 20
=> For 4 Soap, salt = (20/15)*4 = 80/15=16/3
So, water:soap:salt = 3:4:16/3= 9:12:16
After open container, water:soap:salt =2.25:12:16
So, water:salt = 2.25:16 = 9:64
ANSWER:C
Answer: (C) 9:64
Question: A certain car uses one gallon of gasoline every 32 miles when it travels on highway, and one gallon of gasoline every 20 miles when it travels in the city. When a car travels 4 miles on highway and 4 additional miles in the city, it uses what percent more gasoline than if it travels 8 miles on the highway?
(A) 15%
(B) 20%
(C) 22.5%
(D) 25%
(E) 30%
Rationale: 4 miles on the highway = 4/32 gallons;
4 miles in the city = 4/20 gallons;
Total = 4/32 + 4/20 = 13/40 gallons.
8 miles on the highway = 8/30 gallons .
The % change = (13/40 - 8/32)/(8/32) = 0.30.
Answer: E.
Answer: (E) 30%
Question: In an examination a pupil's average marks were 63 per paper. If he had obtained 20 more marks for his Geography paper and 2 more marks for his History paper, his average per paper would have been 64. How many papers were there in the examination?
(A) 8
(B) 9
(C) 10
(D) 22
(E) 12
Rationale: Let the number of papers be x. Then,
63x + 20 + 2 = 64x
= x = 22
ANSWER:D
Answer: (D) 22
Question: v, w, x, y, and z are five positive integers for which v≤w≤x≤y≤z. If the average (arithmetic mean) of the five numbers is 30 and their median is 25, which is the smallest possible value of z?
(A) 30
(B) 35
(C) 37
(D) 38
(E) 40
Rationale: sum=150
mid value = 25
minimize 'z'. So, 25 25 25 37 38
answer: D
Answer: (D) 38
Question: Sachin is younger than Rahul by 7 years. If the ratio of their ages is 7:9, find the age of Sachin
(A) 23.5
(B) 24.5
(C) 12.5
(D) 14.5
(E) None of these
Rationale: Explanation:
If Rahul age is x, then Sachin age is x-7,
so (x-7)/x = 7/9
=> 9x-63 = 7x
=> 2x = 63
=> x = 31.5
So Sachin age is 31.5 - 7 = 24.5
Option B
Answer: (B) 24.5
Question: Three workers have a productivity ratio of 4 to 3 to 2. All three workers are working on a job for 4 hours. At the beginning of the 5th hour, the slowest worker takes a break. The slowest worker comes back to work at the beginning of the 9th hour and begins working again. The job is done in ten hours. What was the ratio of the work performed by the fastest worker as compared to the slowest?
(A) 12 to 1
(B) 6 to 1
(C) 5 to 1
(D) 1 to 6
(E) 3 to 10
Rationale: The fastest worker who does 4 units of job worked for all 10 hours, so he did 4*10=40 units of job;
The slowest worker who does 2 unit of job worked for only 4+2=6 hours (first 4 hours and last 2 hours), so he did 2*6=12 units of job;
The ratio thus is 12 to 40, or 3 to 10.
Answer: E.
Answer: (E) 3 to 10
Question: In an examination, a student's average marks were 63. If he had obtained 20 more marks for his Geography and 2 more marks for his history, his average would have been 65. How many subjects were there in the examination?
(A) 12
(B) 11
(C) 13
(D) 14
(E) 10
Rationale: Explanation:
Let the number of subjects = x
Then, total marks he scored for all subjects = 63x
If he had obtained 20 more marks for his Geography and 2 more marks for his history, his average would have been 65
=> Total marks he would have scored for all subjects = 65x
Now we can form the equation as 65x - 63x = additional marks of the student = 20 + 2 = 22
=> 2x = 22
=> x = 22/2 = 11
Answer: Option B
Answer: (B) 11
Question: If y and g are distinct prime numbers less than 10, which of the following cannot be the product of y and g?
(A) 6
(B) 9
(C) 10
(D) 14
(E) 15
Rationale: If y and g are distinct prime numbers less than 10 prime numbers less than 10 are 2, 3, 5, 7
all except 9 is product of any two numbers picked from above set.
Ans: B
Answer: (B) 9
Question: In a partnership, A invests 1/6 of the capital for 1/6 of the time, B invests 1/3 of the capital for 1/3 of the time and C, the rest of the capital for the whole time. Out of a profit of Rs.4600, B’s share is:
(A) Rs.650
(B) Rs.800
(C) Rs.960
(D) Rs.1000
(E) Rs.1200
Rationale: Suppose A invests x/6 for y/6 months.
B invests x/3 for y/3 months.
C invests x – x/6 + x/3 i.e x/2 for y months.
Therefore, A : B : C = x/6 * y/6 : x/3 * y/3 : x/2 * y = 1/36 : 1/9 : 1/2 = 1 : 4 : 18.
Therefore, B’s share = Rs. 4600 * 4/23
= Rs.800.
ANSWER:B
Answer: (B) Rs.800
Question: if
2345 =62
6571 =73
then
8355 =?
(A) 93
(B) 94
(C) 95
(D) 96
(E) 97
Rationale: 2345
=(2*3)+(4*5)
=6+20
=26 reverse 62
6571
=(6*5)+(7*1)
=30+7
=37 reverse 73
so
8355
=(8*3)+(5*5)
=24+25
=49 reverse 94
ANSWER:B
Answer: (B) 94
Question: Loren bought a roll of cloth and sold it for a 5% profit based on the selling price. If Loren`s profit was $45.5 total on the cloth, how much did it cost her to buy the cloth?
(A) $455.
(B) $525.5.
(C) $675.
(D) $810.5.
(E) $864.5
Rationale: If the roll was sold for a 5% profit based on the cost, it means that of the total selling price, 95% was the cost, and 5% was the profit.
Selling price = 5% profit + 95% cost
5% profit = $45.5
Find: Cost - ?
Profit: 5% - $45.5
Cost: 95% - x
We cross multiply the values to find x:
x = (95∗45.5)/5(95∗45.5)/5 = $864.5
Answer: E
Answer: (E) $864.5
Question: If n is an integer, f(n) = f(n-1) - n and f(4)=12. What is the value of f(6)?
(A) 1
(B) 0
(C) -1
(D) 2
(E) 4
Rationale: Since f(n)=f(n-1)-n then: f(6)=f(5)-6 and f(5)=f(4)-5.
As given that f(4)=12 then f(5)=12-5=7 --> substitute the value of f(5) back into the first equation: f(6)=f(5)-6=7-6=1.
Answer: A.
Questions on funtions to practice:
Answer: (A) 1
Question: What should come in place of the question mark (X) in the following equation ?
60% of X + 2/3 of 39 = 44
(A) 50
(B) 60
(C) 30
(D) 20
(E) None of these
Rationale: Explanation:
60% of X + 2/3 of 39 = 44
i.e. 3/5 of X + 2/3 of 39 = 44 (60% = 3/5)
3/5 * X + 2/3 * 39 = 44
3/5 * X + 26 = 44
3/5 * X = 18
X = 18 * 5/3
X = 30
ANSWER:C
Answer: (C) 30