divelab/Sys2Bench huggingface dataset:
Question: A man took loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay Rs. 2520 interest only for the period. The principal amount borrowed by him was:
Options:
A)s. 2,000
B)s. 1,000
C)s. 5,000
D)s. 8,000
E)s. 7,000
Rationale: Principal = Rs. (100 x 2520)/(12X3) = Rs. 7000. Answer: Option E
Answer: E
Question: Nitin borrowed some money at the rate of 6% p.a. for the first three years, 9% p.a. for the next five years and 13% p.a. for the period beyond eight years. If the total interest paid by him at the end of eleven years is Rs. 12240, how much money did he borrow?
Options:
A)12000
B)80288
C)2668
D)2600
E)2781
Rationale: Let the sum be Rs. x. Then,
[(x * 6 * 3)/100] + [(x * 9 * 5)/100] + [(x * 13 * 3)/100] = 12240
18x + 45x + 39x = (12240 * 100)
102x = 1224000 => x = 12000.
Answer:A
Answer: A
Question: A basket contains 5 apples, of which 1 is spoiled and the rest are good. If Henry is to select 2 apples from the basket simultaneously and at random, what is the probability W that the 2 apples selected will include the spoiled one?
Options:
A)a. 1/5
B)b. 3/10
C)c. 2/5
D)d. 1/2
E)e. 3/5
Rationale: there can be two ways in which one can select a spoiled apple and a good apple.
1. you pick the spoiled one first and the good one later..
Prob of picking bad one = 1/5 (one bad apple)
Prob of picking a good one from the remaining 4 good apples (4/4 =1)
therefore the total prob for case 1 = i/5 * 1 = 1/5
Total prob W= porb1 + prob2 = 1/5+1/5 = 2/5.C
Answer: C
Question: The average of a set of five distinct integers is 370. If each number is less than 2,000, and the median of the set is the greatest possible value, what is the sum of the two smallest numbers?
Options:
A)-4,494
B)-3,997
C)-3,494
D)-4,144
E)The answer cannot be determined from the information given
Rationale: Sum of the set = 370*5=1850 Each number is less than 2000 and median of the set is the greatest possible value.
Therefore last 3 numbers can be 1999,1998 and 1997. Their sum=5994.
Therefore sum of two smallest numbers= 1850-5994= -4144
Answer=D
Answer: D
Question: A crate measures 7 feet by 8 feet by 12 feet on the inside. A stone pillar in the shape of a right circular cylinder must fit into the crate for shipping so that it rests upright when the crate sits on at least one of its six sides. What is the radius, in feet, of the pillar with the largest volume that could still fit in the crate?
Options:
A)2
B)4
C)6
D)7
E)12
Rationale: We can find the radius of all the three cases of cylinders.
The only crux to find the answer faster is that:
Voulme is pi*r^2*h. The volume is a function of r^2. so r has to be the highest to find the largest volume.
So r=7 for the surface 8*12 face.
Volume = 343pi
Answer D
Answer: D
Question: A car dealer has only red and yellow cars in his show room. He currently has 20% more yellow cars then red. IF he has 20 red cars, how many yellow cars does he have?
Options:
A)25
B)30
C)35
D)40
E)45
Rationale: Since we know the dealer only has yellow and red cars in their showroom we can conclude that red and yellow cars make up 100% of the cars. Since we know the difference between the amount of cars is 20% we can assume that the red cars make up 40% of the cars.
20/x=40/100 using cross multiplication we can find that 100x20=2000 and 2000/40=50
So now we know that there are 50 cars total. We can subtract the number of red cars from the total to find the number of yellow cars. 50-20=30
there are a total of 30 yellow cars. The answer is B
Answer: B
Question: If 4 men working 10 hours a day earn Rs. 1000 per week, then 9 men working 6 hours a day will earn how much per week?
Options:
A)Rs 840
B)Rs 1350
C)Rs 1620
D)Rs 1680
E)None of these
Rationale: Explanation :
(Men 4:9) : (Hrs/Day 10:6) :: 1000 : x
hence 4 * 10 *x = 9 * 6 * 1000
or x = 9*6*1000/ 4*10 = 1350
Answer : B
Answer: B
Question: Working together, 7 identical pumps can empty a pool in 6 hours. How many hours will it take 6 pumps to empty the same pool?
Options:
A)6
B)5
C)4
D)8
E)7
Rationale: The answer is E
7 pumps take 6 hours. 1 Pump will take 6*7 hours . Hence 6 pumps will take (6*7)/6 = 7 hours
Answer: E
Question: Mr. Ram is on tour and he has Rs 360 for his expenses. If he exceeds his tour by 4 days he must cut down daily expenses by Rs 3. The number of days of Mr. Ram's tour programme is
Options:
A)28 Days
B)24 Days
C)22 Days
D)20 Days
E)None of these
Rationale: Solution:
Let Ram under takes a tour of x days.
Then, expenses for each day = 360/x
360/x+4=360/x−3
x=20x=20 and −24−24
Hence, x= 20 days.
Option(D)
Answer: D
Question: If x is an even integer, which of the following is an even integer?
Options:
A)3x-3
B)x+x^2
C)5x-3
D)2x+1
E)9x-5
Rationale: Plug in an even integer; in this case 2
(3*2)-3 = 6-3 = 3 Odd
2+2^2 = 6 Even
(5*2)-3 = 10 - 3 = 7 Odd
(2*2)+1 = 4 + 1 = 5 Odd
(9*2)-5 = 18 - 5 = 13 Odd
Answer: B
Answer: B
Question: Two pipes A and B can fill a tank in 6 hours and 4 hours respectively. If they are opened on alternate hours and if pipe A is opened first, in how many hours, the tank shall be full ?
Options:
A)4 hrs
B)5 hrs
C)7 hrs
D)9 hrs
E)None
Rationale: Solution
A's work in 1 hour	= 1/6.
B's work in 1 hour	= 1/4.
(A+B)'s 2 hour's work when opened alternately	= (1/6 + 1/4)
= 5/12.
(A+B)'s 4 hour's work when opened alternately	= 10/12
= 5/6.
Remaining part	= (1 - 5/6)
= 1/6.
Therefore, total tank to fill the tank	(4+1)hrs = 5 hrs.
Answer B
Answer: B
Question: A certain amount earns simple interest of Rs. 1750 after 7 years. Had the interest been 2% more, how much more interest would it have earned?
Options:
A)Rs. 35
B)Rs. 245
C)Rs. 350
D)Cannot be determined
E)None of these
Rationale: EXPLANATION
We need to know the S.I., principal and time to find the rate.
Since the principal is not given, so data is inadequate.
Answer D
Answer: D
Question: Carl bought 16 gumballs, Lewis bought 12 gumballs, and Carey bought X gumballs. The average (arithmetic mean) number of gumballs the three bought is between 19 and 25, inclusive. What is the difference between the greatest number and the smallest number of gumballs Carey could have bought?
Options:
A)20
B)16
C)22
D)18
E)24
Rationale: Smallest gumballs = (19-16) + (19-12) +19= 29
Largest gumballs = (25-16) + (25-12) +25= 47
Difference = 47 - 29 = 18
D
Answer: D
Question: The sum of three numbers is 98. If the ratio of the first to second is 2 :3 and that of the second to the third is 5 : 8, then the second number is:
Options:
A)10
B)50
C)20
D)30
E)40
Rationale: Let the three parts be A, B, C. Then,
A : B = 2 : 3 and B : C = 5 : 8
= (5 x (3/5)):(8 x (3/5))
= 3 : 24/5
A : B : C = 2 : 3 : 24/5
= 10 : 15 : 24
B = (98 x 15/49)= 30.
Answer is D.
Answer: D
Question: Shekhar started a business investing Rs. 25,000 in 1999. In 2000, he invested an additional amount of Rs. 10,000 and Rajeev joined him with an amount of Rs. 35,000. In 2001, Shekhar invested another additional amount of Rs. 10,000 and Jatin joined them with an amount of Rs. 35,000. What will be Rajeev’s share in the profit of Rs. 1,50,000 earned at the end of 3 years from the start of the business in 1999?.
Options:
A)Rs. 10000
B)Rs. 20000
C)Rs. 30000
D)Rs. 40000
E)Rs. 50000
Rationale: Shekhar : Rajeev : Jatin = (25000 X 12 + 35000 X 12 + 45000 X 12) : (35000 X 24) : (35000 X 12)
= 1260000 : 840000 : 420000 = 3 : 2 : 1.
Rajeev’s share = Rs.(150000×2/6) = Rs. 50000
Answer E
Answer: E
Question: Maximum no of unsuccessful attempts, a thief can do in order to break a number locking system of 4 digits.
Options:
A)9988
B)9999
C)9799
D)9685
E)6545
Rationale: From 0 to 9999 there are 10000 four digit numbers
So maximum number of unsuccessful attempts = 10000 - 1 = 9999
ANSWER:B
Answer: B
Question: If a coin has an equal probability of landing heads up or tails up each time it is flipped , what is the probability that the coin will land Tails up exactly twice in 2 consecutive flips ?
Options:
A)0.125
B)0.25
C)0.375
D)0.5
E)0.666
Rationale: Total number of ways in which H or T can appear in 3 tosses of coin is
= 2 * 2 = 4 ways
For 2 H
TT,
Thus probability is
= P(TT)
= 1/4
= .25
Answer : B
Answer: B
Question: A woman took some money for borrowed, for 3 years the total will be Rs.4000 and 5 years it will be Rs.5000/-. Then how much amount she borrowed?
Options:
A)Rs.2500/-
B)Rs.2550/-
C)Rs.2590/-
D)Rs.2600/-
E)Rs.2650/-
Rationale: 3 years --------> Rs.4000/-
5 years --------> Rs.5000/-
~ ~
------------------------------
2 years ---------> Rs.1000/-
1 year ----------> Rs.500/-
3years * Rs.500/- = Rs.1500/-
P = Rs.4000/- - Rs.1500/- = Rs.2500/-
P = Rs.2500/-
A
Answer: A
Question: If we have 5 people in a meeting, in how many ways they can sit around a table?
Options:
A)10*9!
B)9*8!
C)8*7!
D)7*6!
E)4*3!
Rationale: If there arenpeople sitting around a table, there are(n-1)!possible arrangements:
Here, n=5
(n-1)!=4!=4*3!
Ans:E
Answer: E
Question: How many seconds will a 500 meter 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?
Options:
A)878 meters
B)154 meters
C)500 meters
D)184 meters
E)157 meters
Rationale: Let length of tunnel is x meter
Distance = 800+x meter
Time = 1 minute = 60 seconds
Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s
Distance = Speed*Time
800+x = (65/3) * 60
800+x = 20 * 65 = 1300
x = 1300 - 800
=500 meters
Answer:C
Answer: C
Question: Approximately how many revolutions will be made by a car tire with a 12-inch diameter if the car travels 1 mile?
Options:
A)1,205
B)1,800
C)1,356
D)1,672
E)1,440
Rationale: Diameter of car tire = 12 inches
Radius of car tire = 6 inches = 6*2.54 cm = 15.24 cm
Circumference of the car tire = 2*pi * 15.24 = 2 *3.14 *15.24= 95.71 cm
Distance traveled by car =1 mile = 1 *1.6 km = 1.6 km = 1600 m = 1.6 * 10^5 cm
Number of revolutions =Distance traveled / Circumference of tire = 1.6 * 10^5 / 95.71 = 1671.72
Since the answer choices are far apart we should use estimation in this question .
Ideally ,in the GMAT the conversion between units would be provided .
Answer D
Answer: D
Question: The present ages of Lewis and Brown are in the ratio 1:2. Three years from now, the ages will be in the ratio 3:5. Find the present age of Brown.
Options:
A)8
B)9
C)10
D)11
E)12
Rationale: l:b=1:2 & (l+3):(b+3)=3:5
then 2l=b & 5l+15=3b+9
by solving above we get
b=12
ANSWER:E
Answer: E
Question: A crew can row a certain course up the stream in 84 minutes; they can row the same course down stream in 6 minutes less than they can row it in still water. How long would they take to row down with the stream
Options:
A)45 or 23 minutes
B)63 or 12 minutes
C)78 minutes
D)19 minutes
E)25 minutes
Rationale: A method has been discussed here to nullify the calculations though.
All I can input here is,
speed of a crew in still water = 1/2 ( speed upstream + speed downstream)
approximating this for time,
t = 1/2(84+ (t-6))
giving t = 78
C.
Answer: C
Question: If k and y are integers, and 10k + y is odd, which of the following must be true?
Options:
A)k is odd
B)k is even
C)y is odd integer
D)y is even
E)both k and y are odd
Rationale: 10k will be always even as 10 has 2 as one of its factors
if 10k+y is odd, then the only possible explanation is that y is odd
correct answer C
Answer: C
Question: what is the minimum possible range in scores of the three test-takers?Three people each took 5 tests. If the ranges of their scores in the 5 practice tests were 17, 25 and 36.
Options:
A)36
B)17
C)25
D)40
E)35
Rationale: I simply looked at the 3 different possible scores for each individual test: 17,36,25
We have to find the minimum range:
36-17=9
36-25=11
25-17=8
The find the minimum range, you have to make the set of the 5 scores as small as possible.
Which means that 4 of the 5 scores of each individual person is zero.
8*5 = 40
Answer:D
Answer: D
Question: At a supermarket, John spent 1/2 of his money on fresh fruits and vegetables, 1/3 on meat products, and 1/10 on bakery products. If he spent the remaining $10 on candy, how much did John spend at the supermarket?
Options:
A) $60
B) $80
C) $90
D) $120
E) $150
Rationale: Let's let T = total number of dollars spent at the supermarket. With this variable we can set up an equation and determine T.
We are given that John spent 1/2 of his money on fresh fruits and vegetables, or (1/2)T, 1/3 on meat products, or (1/3)T, and 1/10 on bakery products, or (1/10)T. We are also given that he spent the remaining $10 on candy. Since we know where all his money was allocated, we can sum these values together and set the sum to T. So we have:
(1/2)T + (1/3)T + (1/10)T + 10 = T
To get rid of the fractions we can multiply the entire equation by 30, and we obtain:
15T + 10T + 3T + 300 = 30T
28T + 300 = 30T
300 = 2T
T = 150
John spent $90 at the supermarket.
Answer: E
Answer: E
Question: If A : B = 4 : 5 and B : C = 6 : 7 then A : B : C is :
Options:
A)20 : 35 : 63
B)35 : 36 : 63
C)30 : 35 : 65
D)25 :34: 68
E)None of these
Rationale: Expl : A : B = 4 : 5
B : C = 6 :7 = 6*5/6 : 7 *5/6 = 5 : 35/6
A : B : C = 4 : 5 : 36/6 = 24 : 30 : 36 = 4 : 5 : 6
Answer: E
Answer: E
Question: What is the probability that a two digit number selected at random will be a multiple of '3' and not a multiple of '5'?
Options:
A)2/15
B)4/15
C)1/15
D)4/90
E)5/60
Rationale: Solution:
There are a total of 90 two digit numbers. Every third number will be divisible by '3'. Therefore, there are 30 of those numbers that are divisible by '3'.
Of these 30 numbers, the numbers that are divisible by '5' are those that are multiples of '15'. i.e. numbers that are divisible by both '3' and '5'.
There are 6 such numbers -- 15,30,45,60,75 and 90.
We need to find out numbers that are divisible by '3' and not by '5', which will be:
30âˆ’6=24
24 out of the 90 numbers are divisible by '3' and not by '5'.
The required probability is therefore,
=24/90
=4/15
ANSWER IS B
Answer: B
Question: In a maths test, students were asked to find 5/16 of a certain number. One of the students by mistake found 5/6th of that number and his answer was 50 more than the correct answer. Find the number.
Options:
A)96
B)280
C)384
D)400
E)500
Rationale: Explanation:
Let the number be x.
5*x/6 = 5*x/16 +50
25*x/48 = 50
x = 96
ANSWER A
Answer: A
Question: man is 20 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:
Options:
A)14years
B)26 years
C)17 years
D)18 years
E)22 years
Rationale: Let the son's present age be x years. Then, man's present age = (x + 20) years.
(x + 20) + 2 = 2(x + 2)
x + 22 = 2x + 4
x = 18.
answer :D
Answer: D
Question: A company consists of 6 senior and 5 junior staff officers. If a committee is created with 3 senior and 3 junior staff officers, in how many ways can the committee be formed?
Options:
A) 12
B) 30
C) 45
D) 80
E) 200
Rationale: Choose 3 senior from 6 senior and choose 3 junior from 5 junior:
6C3 * 5C3 = 20*10 = 200
Ans: E
Answer: E
Question: From the word 'LAPAROSCOPY' how many independent meaningful words can be made without changing the order of the letters and using each letter only once ?
Options:
A)8
B)7
C)6
D)2
E)3
Rationale: Explanation:
The words are LAP and COPY.
Answer: D) 2
Answer: D
Question: Find (7x + 5y ) / (x-2y) if x/2y = 3/2 ?
Options:
A)24
B)25
C)26
D)27
E)29
Rationale: x/2y=3/2
=>x=6y/2=3y
=>(7x+5y)/(x-2y)=((7*(3y))+5y)/(3y-2y)
=>26y/y=26
ANSWER:C
Answer: C
Question: When positive integer n is divided by 4, the remainder is 2. When n is divided by 7, the remainder is 5. How many values less than 100 can n take?
Options:
A) 0
B) 2
C) 3
D) 4
E) 5
Rationale: a quick approac to this Q is..
the equation we can form is.. 3x+2=7y+5..
3x-3=7y... 3(x-1)=7y...
so (x-1) has to be a multiple of 7 as y then will take values of multiple of 3..
here we can see x can be 1,8,15,22,29 so 5 values till 100 is reached
as (29-1)*3=84 and next multiple of 7 will be 84+21>100..
ans 3.. C
Answer: C
Question: The number of cars present at a particular time was measured at 3,999 different locations on Tuesday and on Wednesday. The number of locations that had more cars on Wednesday was 10% higher than the number of locations that had more cars on Tuesday. How many of the locations had more cars on Tuesday?
Options:
A)1,159
B)1,333
C)1,860
D)1,904
E)2,829
Rationale: The question states that all these 3,999 locations were measured twice, once on each day.
It also breaks the 3,999 into two groups, the higher-on-Tuesday locations and the higher-on-Wednesday locations, which we can call T and W.
Therefore, we can write two equations:
For each of the first and second day count of locations, T + W = 3999
But, for the second day count, W = 1.10 T
i.e. for Second day count, T + 1.10T = 3999
i.e. 2.10 T = 3999
i.e. T = 1904
D
Answer: D
Question: A train 360 m long runs with a speed of 45 km/hr. What time will it take to pass a platform of 340 m long?
Options:
A)38 sec
B)35 sec
C)44 sec
D)40 sec
E)56 sec
Rationale: Explanation:
Speed = 45 km/hr = 45×(10/36) m/s
= 150/12 = 50/4 = 25/2 m/s
Total distance = length of the train + length of the platform
= 360 + 340 = 700 meter
Time taken to cross the platform = 700/(25/2) = 700×2/25 = 56 seconds
Answer: Option E
Answer: E
Question: Mixture of milk & water has been kept in two separate bowl. Ratio of milk to water in one of the bowls is 5 : 1 and that in the other bowl 7 : 2. In what ratio the mixtures of these 2 bowl should be added together so that the quantity of milk in the new mixture may become 80%?
Options:
A)2:3
B)1:3
C)2:5
D)2:7
E)3:8
Rationale: Lett. mixtures of the two containers be added together in the ratio of x
= = [ixoox l00%
Since the percentage quantity ofmilk in the new mixture is SO% — so% (45x + 42y) x 5 4 x 54(x y) 225x 210y 216.3E+216y
9x=6y
x:y=2:3
A
Answer: A
Question: Find the value of y from (12)^3 x 6^4 ÷ 432 = y?
Options:
A)2234
B)4350
C)4560
D)5132
E)y=5184
Rationale: Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184
432 12 x 62
E
Answer: E
Question: Numbers from 1 to 10^2012 are given, there are 'm' no of 1's and 'n' no of 2's.
Then what is (m-n).
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: let us consider 1-100 here no of 1's m =21 and no.of 2's n = 20 there by m-n=1 similary from 1 to (10^2012-1) no.of 1's=no.of 2's but in last term 10^2012 a one is added there by the ans is 1.
ANSWER:B
Answer: B
Question: In a fuel station the service costs $1.75 per car, every liter of fuel costs 0.65$. Assuming that a company owns 12 cars and that every fuel tank contains 57 liters and they are all empty, how much money total will it cost to fuel all cars?
Options:
A)320.50$
B)380.50$
C)425.50$
D)450.50$
E)465.60$
Rationale: Total Cost = ( 1.75*12 ) + ( 0.65 * 12 * 57 ) = 465.60
Hence answer will be (E)
Answer: E
Question: If z2 + 4y2 = 4zy, then z : y is :
Options:
A)2 : 1
B)1 : 2
C)1 : 1
D)1 : 4
E)1 : 5
Rationale: as the coefficient of z is 1 and coefficient of y is 4
ANSWER:D
Answer: D
Question: A sells a bicycle to B at a profit of 50% and B sells it to C at a loss of 40%. Find the resultant profit or loss.
Options:
A)-4%
B)5%
C)-5%
D)6%
E)-10%
Rationale: The resultant profit or loss = 50 - 40 - (50*40)/100 = -10%
loss = 10%
Answer is E
Answer: E
Question: The sum of three consecutive even numbers is 42. Find the middle number of the three?
Options:
A)14
B)86
C)16
D)28
E)23
Rationale: Three consecutive even numbers (2P - 2), 2P, (2P + 2).
(2P - 2) + 2P + (2P + 2) = 42
6P = 42 => P = 7.
The middle number is: 2P
= 14.
Answer:A
Answer: A
Question: Arabica coffee costs $0.5 per ounce while Robusta coffee costs $0.3 per ounce. If the blend of Arabica and Robusta costs $0.33 per ounce, what is the share of Arabica in this blend?
Options:
A)15%
B)24%
C)30%
D)33%
E)40%
Rationale: a= amount of arabica coffee
1-a = amount of robusta coffee. because if you subtract a from the 1 ounce, the remaining amount is robusta
therefore:
.5a + .3(1-a) = .33
.5a + .3 - .3a = .33
a= .3/2
therefore: .3/2/1 ounce = 15%. Therefore, the answer should be A
Answer: A
Question: A shopkeeper sold an article offering a discount of 4% and earned a profit of 44%. What would have been the percentage of profit earned if no discount was offered?
Options:
A)24
B)28
C)30
D)32
E)50
Rationale: Let C.P. be Rs. 100.
Then, S.P. = Rs. 144
Let marked price be Rs. x. Then, 96/100 x = 144
x = 14400/96 = Rs. 150
Now, S.P. = Rs. 150, C.P. = Rs. 100
Profit % = 50%.
ANSWER:E
Answer: E
Question: What is the least number of squares tiles required to pave the floor of a room 15 m 17 cm long and 9 m 2 cm broad
Options:
A)814
B)256
C)3258
D)896
E)745
Rationale: Explanation:
Length of largest tile = H.C.F. of 1517 cm and 902 cm = 41 cm.
Area of each tile = (41 x 41) cm^2.
Required number of tiles =(1517 x 902/41*41)= 814.
Answer : A
Answer: A
Question: Jerry’s average (arithmetic mean) score on the first 3 of 4 tests is 81. If Jerry wants to raise his average by 2 points, what score must he earn on the fourth test?
Options:
A)87
B)89
C)90
D)93
E)95
Rationale: Total score on 3 tests = 81*3 = 243
Jerry wants the average to be = 83
Hence total score on 4 tests should be = 83*4 = 332
Score required on the fourth test = 332 - 243 = 89
Option B
Answer: B
Question: What is remainder of the division (1625*1627*1629)/12?
Options:
A)3
B)2
C)1
D)0
E)4
Rationale: remainder will be number/ 100 here as the divisor is two digit number = 12.
hence checking for the last two digits = 5*7*9 = 15
Thus remainder = 3.
Answer : A
Answer: A
Question: Machine X takes 60 hours longer than machine Y to produce 1080 Widgets. Machine Y produces 20 percent more widgets in an hour than machine x does in an hour. How many widgets per hour does machine X produce
Options:
A)100
B)65
C)25
D)11
E)3
Rationale: Machine Y produces 20 percent more widgets in an hour than machine x does in an hour.
So if machine X produces 100 widgets, then machine Y produces 120 widgets.
Ratio of 120/100 = 6/5.
This is their speed of work (Y:X).
i.e. speed of their work (X:Y) = 5/6
Now, time is inversely proportional to speed.
Hence the ratio of the time spent (X:Y)= 6/5
Let us assume that they spend 6x and 5x hours.
Given that 6x-5x = 60
So, x = 60.
Hence 6x = 6*60 = 360 hours.
Hence X takes 120 hours to produce 1080 widgets.
So, in 1 hour, it can produce (1 * 1080)/360
= 3
Hence option (E).
Answer: E
Question: There are 12 balls in a bag; 8 are blue balls and the other 4 are yellow balls. If 3 balls are to be selected at random from the 12 balls, what is the probability that at least one of the yellow ball will be selected?
Options:
A)57/55
B)56/55
C)54/55
D)53/55
E)52/55
Rationale: Total probability=12C3=220
8C3 +8C2*4C1+8C1*4C2=56+112+48=216
therefore the probability that at least one of the yellow ball will be selected= 216/220=54/55
answer is C
Answer: C
Question: A certain quantity of 40% concentration solution is replaced with 25% concentration solution such that the concentration of the combined amount is 35%.
What's the ratio of the amount of solution that was replaced to the amount of solution that was not replaced?
Options:
A)1:3
B)1:2
C)2:3
D)2:1
E)3:1
Rationale: From the wording in the prompt, we're essentially mixing two liquids:
Liquid X is 40% concentrate
Liquid Y is 25% concentrate
We're supposed to mix some of each and end up with a solution that is 35% concentrate. The prompt doesn't give us specific amounts of liquids to work with and the question itself asks for the ratio of the two liquids, so we could even TEST VALUES if doing it that way made it easier for you. For now though, here's the Algebra:
X = # of ounces of liquid X
Y = # of ounces of liquid Y
(.4X + .25Y) / (X + Y) = .35
.4X + .25Y = .35X + .35Y
.05X = .1Y
5X = 10Y
From here, you have to be CAREFUL to answer the question that is ASKED.
5X = 10Y
Y/X = 5/10 = 1/2
ANSWER:B
Answer: B
Question: A company has 16 equally qualified applicants for 4 open positions. How many different groups of 4 applicants can be chosen by the company to fill the positions if the order of selection does not matter?
Options:
A)1780
B)1820
C)1860
D)1900
E)1940
Rationale: 16C4=1820
The answer is B.
Answer: B
Question: Tough and Tricky questions: Exponents.
If 6^(3x+4)*2^(2y+1) = 36^x*16^y, then x + y =
Options:
A)-7/2
B)-1/7
C)3/7
D)7/2
E)-3/7
Rationale: Here is my solution.
6^(3x+4)*2^(2y+1) = 36^x*16^y
Here RHS 36^x*16^y= 6^(2x)*2^(4y)
Equating powers on both sides-->
3x+4=2x , thus x=-4 and
2y+1=4y giving y=1/2
So, x+y=-7/2
Option: A
Answer: A