divelab/Sys2Bench huggingface dataset:
Question: A man swims downstream 36 km and upstream 18 km taking 6 hours each time, what is the speed of the man in still water?
Options:
A)4.5
B)5.5
C)6.5
D)4.8
E)2
Rationale: 36 --- 6 DS = 6
? ---- 1
18 ---- 6 US = 3
? ---- 1 M = ?
M = (6 + 3)/2 = 4.5
Answer: A
Answer: A
Question: The product of 4 consecutive even numbers is always divisible by:
Options:
A)600
B)768
C)864
D)384
E)356
Rationale: To solve this question, we need to know two facts.
Fact 1:
The product of 4 consecutive numbers is always divisible by 4!.
Fact 2:
Since, we have 4 even numbers, we have an additional 2 available with each number.
Now, using both the facts, we can say that the product of 4 consecutive even numbers is always divisible by,
=(24)×4!=(24)×4!
=16×24=16×24
=384
Option(D)
Answer: D
Question: If 4d^4 − 41d^2 + 100 = 0, then what is the sum of the two greatest possible values of d ?
Options:
A)4
B)9/2
C)7
D)41/4
E)25
Rationale: just forget about the value of d^4 for the moment and let d^2= X. (its better to work with power of 2 than 4)
now we have equation as 4x^2 -41x +100 =0, factoring them gives us 4X^2 -16x -25x +100 =0. which can be solved as (4x-25)(x-4) , so x= 4 and 25/4.
so d^2 = 4 and 25/4
so d= +2 and minus 2 and +5/2 and minus 5/2
The two greatest values are +2 and +5/2. so their sum 2+5/2 =9/2 = B
Answer: B
Question: According to the directions on the can of frozen orange juice concentrate, 1 can of concentrate is to be mixed with 3 cans of water to make orange juice. How many 12 ounces cans of the concentrate are required to prepare 320 6 ounces servings of orange juice?
Options:
A)a) 25
B)b) 34
C)c) 50
D)d) 40
E)e) 100
Rationale: Its D.
Total juice rquired = 320*6 = 1920 ounce
12 ounce concentate makes = 12 * 4 = 48 ounce juice
Total cans required = 1920/48 = 40.
Answer D
Answer: D
Question: A circular ground whose diameter is 70 metres, has a 2.8 metre-broad garden around it. What is the area of the garden in square metres?
Options:
A)540.72
B)740.64
C)640.64
D)620.45
E)725.26
Rationale: Req. area = Ï€[(37.8)2 â€“ (35)2]
= 22â„7 Ã— (72.8 Ã— 2.8)[since a2 - b2 = (a + b)(a - b)]
= 22 Ã— 72.8Ã— 0.4 = 640.64 sq m
Answer C
Answer: C
Question: R is the set of positive odd integers less than 10, and S is the set of the squares of the integers in R. How many elements does the intersection of R and S contain ?
Options:
A)None
B)Two
C)Four
D)Five
E)Seven
Rationale: squares < 10 {1,4,9}
S = {1,9}
R = {1,3,.....10}
Hence B.
Answer: B
Question: The average of first five multiples of 5 is :
Options:
A)3
B)9
C)12
D)15
E)17
Rationale: Solution
Average = 5(1+2+3+4+5)/5 =75/5 =15 Answer D
Answer: D
Question: Arabica coffee costs $0.4 per ounce while Robusta coffee costs $0.3 per ounce. If the blend of Arabica and Robusta costs $0.35 per ounce, what is the share of Arabica in this blend?
Options:
A)20%
B)24%
C)50%
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:
.4a + .3(1-a) = .35
.4a + .3 - .3a = .35
a= .5
therefore: .5/1 ounce = 50%. Therefore, the answer should be C
Answer: C
Question: Find the area of a cuboid of length 4cm , breadth 6 cm . and height 5cm.
Options:
A)120 cm cube
B)110 cm cube
C)220 cm cube
D)430 cm cube
E)480 cm cube
Rationale: Area of a cuboid = lxbxh =4cm x 6cm x 5cm = 120 cm cube
answer :A
Answer: A
Question: If all the sides of a right triangle increase in length by 10%, then by what percentage does the area of the triangle increase?
Options:
A)21%
B)42%
C)80%
D)96%
E)120%
Rationale: Let B be the base and H be the height of the original triangle.
The original area is (1/2)BH.
The area of the expanded triangle is (1/2)(1.1B)(1.1H) = (1.1)(1.1)(1/2)BH = 1.21(1/2)BH
The answer is A.
Answer: A
Question: A person takes 10 minutes more to cover a certain distance by decreasing his speed by 20%. What is the time taken to cover the distance at his original speed?
Options:
A)50 minutes
B)20 minutes
C)40 minutes
D)60 minutes
E)80 minutes
Rationale: Let the distance and original speed be d km and k kmph respectively.
d/0.8k - d/k = 10/60 => 5d/4k - d/k = 1/6
=> (5d - 4d)/4k = 1/6 => d = 4/6 k=2/3k
Time taken to cover the distance at original speed
= d/k = 2/3 hours = 40 minutes.
ANSWER:C
Answer: C
Question: A motor cyclist participant of a race says "We drove with the speed of 10 miles an hour one way, but while returning because of less traffic we drove on the same route with 17 miles per hour." What was their average speed in the whole journey?
Options:
A)10 miles/hour
B)12 miles/hour
C)11 miles/hour
D)12.6 miles/hour
E)14 miles/hour
Rationale: 2xy/x+y=12.6 miles/hour
ANSWER:D
Answer: D
Question: A certain city with a population of 144,000 is to be divided into 11 voting districts , and no district is to have a population that is more than 10 percent greater than the population of any other district What is the minimum possible population that the least populated district could have ?
Options:
A)a) 12,000
B)b) 10,800
C)c) 10,900
D)d) 11,000
E)e) 11,100
Rationale: Let x = number of people in smallest district
x*1.1 = number of people in largest district
x will be minimised when the number of people in largest district is maximised
10*x*1.1 = 11x = total number of people in other districts
So we have 11x + x = 144k
x = 12,000
Answer : A
Answer: A
Question: calendar=52097083 november=538=8651
march=2*308 blue=7154 december=?
Options:
A)9535&153
B)9585&153
C)9525&153
D)9525&*53
E)9525&*54
Rationale: from above in formation
d=9
e=5
c=2
e=5
m=3
b=1
e=5
r=8
95253158( Order doesnot matter i guess!)
another thing is &=8 for mathcing above ans
ANSWER:C
Answer: C
Question: How much water must be added to 10 gallons of 10% brine solution to decrease the concentration to 3%?
Options:
A)0—1.5 gal
B)1.5—3 gal
C)3—4.5 gal
D)4.5—6 gal
E)16+ gal
Rationale: Let amount of water that must be added in gallons to dilute concentration of brine solution = x
Amount of brine already present = 10/100 * 10 = 1 gallon
1/(10+x) *100 = 3
=>100 = 30 + 3x
=> x= 70/3 = 23
Answer E
Answer: E
Question: Three taps A, B and C can fill a tank in 12, 15 and 20 hours respectively. If A is open all the time and B and C are open for one hour each alternately, the tank will be full is?
Options:
A)6 hrs
B)6 2/3 hrs
C)7 hrs
D)7 1/2 hrs
E)8 hrs
Rationale: Explanation:
(A + B)'s 1 hour work = (1/12 + 1/15) = 3/20
(A + C)'s 1 hour work = (1/12 + 1/20) = 2/15
Part filled in 2 hrs = (3/20 + 2/15) = 17/60
Part filled in 6 hrs = 3 * 17/60 = 17/20
Remaining part = 1 - 17/20 = 3/20
Now, it is the turn of A and B and 3/20 part is filled by A and B in 1 hour.
Total time taken to fill the tank = (6 + 1) = 7 hrs.
ANSWER IS C
Answer: C
Question: A runs 5/2 time as fast as B, and gives B and a start of 40m. How long should the racecourse be so that A and B might reach in the same time?
Options:
A)150 m
B)100 m
C)75 m
D)80 m
E)90 m
Rationale: verification of options..... (2/5)*100 =40
So answer is 100m
ANSWER:B
Answer: B
Question: The game of blackjack is played with a deck consisting of 13 cards (one of each of the numbers 2-10, one jack, one queen, one king, and one of ace) in each of four suits: clubs, diamonds, hearts, and spades.
In a game of blackjack, if your first card is a spade, what are the R odds that it is an ace?
Options:
A)1/52
B)1/26
C)1/13
D)1/4
E)5/13
Rationale: The question should ask about the probability not the odds.
There are 13 spades, the probability R that the spade we already have is an ace is therefore 1/13.
Answer: C.
Answer: C
Question: In a 200 m race,A covers the distance in 45 seconds and B in 60 second.In this race A beats B by :
Options:
A)20 m
B)50 m
C)45 m
D)60 m
E)None of these
Rationale: Solution
Distance covered by B in 15 sec. = (200/60x15)m =50m.
∴ A beats B by 50 metres.
Answer B
Answer: B
Question: Ram professes to sell his goods at the cost price but he made use of 850 grms instead of a kg, what is the gain percent?
Options:
A)11 1/7%
B)11 7/7%
C)11 1/9%
D)17.64%
E)11 1/2%
Rationale: 850 --- 150
100 --- ? => 17.64%
Answer:D
Answer: D
Question: For 2consecutive yrs, my incomes are in the ratio of 4:7 and expenses in the ratio of 3:5. If my income in the 2nd yr is Rs. 42000 & my expenses in the first yr in Rs.21000, my total savings for the two-year is
Options:
A)Rs. 8000
B)Rs. 9000
C)Rs. 9900
D)Rs. 9990
E)Rs. 10000
Rationale: Sol. Income in first year = * x 42000 = Rs. 24000
Expenses in second year = \ x 21000 = Rs. 35000 Total savings = Total income - Total expenses = (42000 + 24000)- (21000 + 35000)
= 66000 - S6000 = Rs. 10000
E
Answer: E
Question: Find the area of a rhombus one side of which measures 20 cm and one diagonal is 24 cm?
Options:
A)320cm2
B)280cm2
C)384cm2
D)290cm2
E)350cm2
Rationale: Let other diagonal = 2x cm.
Since diagonals of a rhombus bisect each other at right angles, we have:
(20)2 = (12)2 + (x)2 =>x =√(20)2 – (12)2= √256= 16 cm.
So, other diagonal = 32 cm.
Area of rhombus = (1/2) x (Product of diagonals) =(1/2× 24 x 32) cm2 = 384 cm2
hence C
Answer: C
Question: A person starting with Rs.64 and making 6 bets, wins three times and loses 3times, the wins and loses occurring in random order. The chance for a win is equal to the chance for a loss. If each wager is for 1/2 the money remaining at the time of the bet, then the final result is?
Options:
A)Rs.23
B)Rs.37
C)Rs.45
D)Rs.67
E)Rs.77
Rationale: As the win leads to multiplying the amount by 1.5 and loss leads to multiplying the amount by 0.5, we will multiply initial amount by 1.5 thrice and by 0.5 thrice (in any order).
The overall resultant will remain same.
So final amount with the person will be (in all cases):
=64(1.5)(1.5)(1.5)(0.5)(0.5)(0.5)==64(1.5)(1.5)(1.5)(0.5)(0.5)(0.5)= Rs 2727
Hence the final result is:
64−27=3764−27=37:
A loss of Rs.37
B
Answer: B
Question: If the average (arithmetic mean) of a list of numbers is 12 and the standard deviation of that list of numbers is 1.3, then which of the following numbers is more than two standard deviations from the mean?
I. 14.7
II. 12.3
III. 9.5
Options:
A)I only
B)I and II only
C)II only
D)III only
E)I and III only
Rationale: Mean = 12
SD = 1.3
2 SD above mean = 12+2*1.3 = 14.6
2 SD below mean = 12-2*1.3 = 9.4
12.3 and 9.5 lies in the range of 2SD from mean
Answer: Option A
Answer: A
Question: Susan has nine hamsters. In order to feed each hamster 4 blocks of food each day, how much food must she buy for 7 days?
Options:
A)210
B)228
C)243
D)252
E)271
Rationale: 4 blocks of food per day multiplied by 9 hamsters = 36 blocks per day. 36 multiplied by 7 days = 252 blocks of food, hence answer : D.
Answer: D
Question: If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 2 years the amount to be paid is?
Options:
A)2287
B)2689
C)1667
D)8112
E)1691
Rationale: A = 7500(26/25)2 = 8112
Answer: D
Answer: D
Question: If the circus were to sell all of its 220 tickets for this month's performance at its usual price, the revenue from sales would be 10% greater than that collected last month. If the circus raised the ticket price by 7% and sold only 200 tickets as a result, what percent less would last month's revenue be compared to this month's revenue?
Options:
A)2
B)5
C)700/107
D)110/20
E)9/4
Rationale: Let price be 10/ticket
then 220 tickets for this month's performance at its usual price=2200
which is 10%greater than last month(let X)---->x(1+10/100)=2200----->x=2000
now new revenue this month=200*10.7=2140
as per question asked 2000=2140(1-A/100)----->A=700/107%
Ans C
Answer: C
Question: The circumferences of two circles are 264 meters and 704 meters. Find the difference between the areas of the larger and the smaller circles?
Options:
A)29960 sq m
B)33880 sq m
C)43120 sq m
D)27680 sq m
E)12786 sq m
Rationale: Let the radii of the smaller and the larger circles be s m and l m respectively.
2∏s = 264 and 2∏l = 704
s = 264/2∏ and l = 704/2∏
Difference between the areas = ∏l^2 - ∏s^2
= ∏{132^2/∏^2 - 352^2/∏^2}
= 132^2/∏ - 352^2/∏
= (132 - 352)(132 + 352)/∏
= (220)(484)/(22/7)
= 33880 sq m
Answer:B
Answer: B
Question: If |x – 9/2| = 5/2, and if y is the median of a set of t consecutive integers, where t is odd, which of the following must be true?
I. xyt is odd
II. xy(t^2 + t) is even
III. x^2y^2t^2 is even
Options:
A)II only is true
B)III only is true
C)I and III
D)II and III
E)I, II, and III
Rationale: given:
t is Odd
y is the median of odd numbers, hence y is Odd
x = solving the modulus you get 7 and 2. Hence x is Even or Odd
Therefore: t = O, y = O and x = O or E
Statement I = x*y*t = y*t*x = O x O x O/E = O x O/E = Odd or even. So False
Statement II = xy(t^2 + t) = O/E x O (O + O) = O/E x O(E) = O/E x E = Always Even. So true
Statement III. x^2y^2t^2 is even. E/O x O x O = Odd or even. Hence False.
Answer = A.
Answer: A
Question: The ratio of ages of two friends is 3:5 and sum of their ages is 80 years. What are their present ages in years?
Options:
A)10,60
B)20,60
C)40,30
D)30,50
E)20,50
Rationale: 3x + 5x== 80
x==10
(30,50)
ANSWER:D
Answer: D
Question: The table below shows how many coaches work with each of the major sports teams at Kristensen School. Although no single coach works with all three teams, 3 coaches work with both the Track and Tennis teams, 2 coaches work with both the Track and Baseball teams, and 1 coach works with both the Tennis and Baseball teams. How many different coaches work with these three teams?
Sports No of coaches
Track 8
Tennis 7
Baseball 4
Options:
A)6
B)9
C)11
D)13
E)17
Rationale: X = 8 + 7 + 4 - (3 + 2 + 1) = 13
Answer is D
Answer: D
Question: At what time, in minutes, between 3 o'clock and 4 o'clock, both the needles will coincide each other?
Options:
A)5 1/11 °
B)12 4/11 °
C)13 4/11°
D)16 4/11°
E)None
Rationale: Solution
At 3 o'clock, the minute hand is 15 min. spaces apart from the hour hand.
To be coincident, it must gain 15 min. spaces.55 min. are gained in 60 min.
15 min. are gained in
= (60/55 x 15)min
=16x4/11
The hands are coincident at 16x4/11 min past3.
Answer D
Answer: D
Question: If a motorist had driven 1 hour longer on a certain day and at an average rate of 5 miles per hour faster, he would have covered 80 more miles than he actually did. How many more miles would he have covered than he actually did if he had driven 2 hours longer and at an average rate of 10 miles per hour faster on that day?
Options:
A) 100
B) 120
C) 140
D) 150
E) 160
Rationale: Case 1:
let rate = R, Time = T, and Distance =D
so D=RT
Case 2:
(D+80)=(R+5)(T+1)
Case 3:
(D+X)=(R+10)(T+2)
X=160
Ans E
Answer: E
Question: The diagonal of a cube is cm. Find its surface area
Options:
A)216 sq.cm
B)316 sq.cm
C)416 sq.cm
D)516 sq.cm
E)None of these
Rationale: Explanation:
Let the edge of the cube be a.
so, the diagonal √3 a = 6√3
=> a=6
Surface area = 6a2 = 6 x 6 x 6 = 216 cm2
Answer: A
Answer: A
Question: The membership of a committee consists of 3 English teachers, 4 Mathematics teachers, and 2 Social Studies teachers. If 2 committee members are to be selected at random to write the committee’s report, what is the probability that the two members selected will both be maths teachers?
Options:
A)2/3
B)1/3
C)2/9
D)1/24
E)1/12
Rationale: Probability of first member an English teacher = 3/9
Probability of second member an English teacher = 2/8
Probability of both being english teacher = 3/9 x 2/8 =1/12 (E)
Answer: E
Question: Buses A and B start from a common bus stop X. Bus A begins to travel in a straight line away from bus B at a constant rate of 40 miles per hour. One hour later, bus B begins to travel in a straight line in the exact opposite direction at a constant rate of 80 miles per hour. If both buses travel indefinitely, what is the positive difference, in minutes, between the amount of time it takes bus B to cover the exact distance that bus A has covered and the amount of time it takes bus B to cover twice the distance that bus A has covered?
Options:
A)36
B)72
C)132
D)144
E)180
Rationale: 1st part: - In 1hr, Bus A covers 30 miles.
Relative speed of bus ABus B is (80-30) = 50mph.
So time required for Bus B to cover the exact distance as A is
50*t = 30
t=3/5 = 36min
2nd part
80*t=2d - B has to cover twice the distance
30*(t+1) = d - A traveled 1hr more and has to travel only only d
so
d/30 - 2d/80 = 1
D=120
T= 3hrs = 180 min
Question asks for +ve difference between part 1 and part 2 in minutes
= 180-36 = 72min
B
Answer: B
Question: A family pays $700 per year for an insurance plan that pays 70 percent of the first $1,000 in expenses and 100 percent of all medical expenses thereafter. In any given year, the total amount paid by the family will equal the amount paid by the plan when the family's medical expenses total how much?
Options:
A)$1,100
B)$1,300
C)$1,400
D)$1,800
E)$2,200
Rationale: Assuming the medical expenses are $1000 or more, the family pays $700 + $300 = $1000.
The total amount paid by insurance plan for the first $1000 of expenses is $700.
The insurance will pay another $300 when the medical expenses are $1300.
The answer is B.
Answer: B
Question: Betty took out a charge account at the General Store and agreed to pay 4% simple annual interest. If she charges $50 on her account in January, how much will she owe a year later, assuming she does not make any additional charges or payments?
Options:
A)$51.50
B)$52.00
C)$52.50
D)$53.00
E)$53.50
Rationale: 1.04*$50=$52.00
The answer is B.
Answer: B
Question: A train 110 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?
Options:
A)5
B)6
C)4
D)9
E)8
Rationale: Speed of train relative to man = (60 + 6) km/hr = 66 km/hr
[66 * 5/18] m/sec = [55/3] m/sec.
Time taken to pass the man = [110 * 3/55] sec = 6 sec
Answer: Option B
Answer: B
Question: A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 4 m, the volume of the box (in m3) is:
Options:
A)4480
B)5120
C)6420
D)8960
E)7960
Rationale: Clearly, l = (48 - 8)m = 40 m,
b = (36 -8)m = 28 m,
h = 8 m.
Volume of the box = (40 x 28 x 4) m3 = 4480 m3. Answer: Option A
Answer: A
Question: A 180 meter long train crosses a man standing on the platform in 6 sec. What is the speed of the train?
Options:
A)108 kmp
B)188 kmp
C)299 kmp
D)278 kmp
E)288 kmp
Rationale: S = 180/6 * 18/5
= 108 kmp
Answer: B
Answer: B
Question: If you are given $5, and the amount doubles every day, how much money will you have after 4 days?
Options:
A)$256
B)$512
C)$1024
D)$625
E)$720
Rationale: 5^4=625
The answer is D
Answer: D
Question: The difference b/w the compound interest payble half yearly and the simple interest on a certain sum lent out at 10% p.a for 1 year is Rs 25. What is the sum?
Options:
A)Rs. 15000
B)Rs. 12000
C)Rs. 10000
D)Rs. 20000
E)none of these
Rationale: in simple words S.I= PTR/100=(P*1*10)/100 P/10
HERE AMOUNT A= p+ S.I= P+ P/10=11P/10....
NOW FOR COMPOUND INTEREST WHEN CALCULATED HALF YEARLY AMOUNT=P[1+R/200]^2T=P[1+10/200]^2*1=441P/400
here its given in the question dat diff btwn simple interest and compound interest half yearly ... is 25
=> 441p/400-11p/10= 25 =>p/400=25 =>p= 400*25=10000 so sum = 10000
ANSWER:C
Answer: C
Question: How many different subsets of the set {0, 1, 2, 3, 4} do not contain 0?
Options:
A)A.16
B)B.27
C)C.31
D)D.32
E)E.64
Rationale: Number of subset
Since we have 4 digits other than 0, we can take any numbers from the set of 4 to make a subset. Also it is a matter of selection and not arrangement.So we will consider combinations.
4c1+4c2+4c3+4c4=15
And one set is the NULL set having no elements in it so
15+1=16.
ANSWER A.
Answer: A
Question: What number should replace the question mark?
105, 87, 70, ?, 35
Options:
A)52
B)37
C)70
D)55
E)83
Rationale: A
52
The sequence progresses -18, -17, -18, -17.
Answer: A
Question: An accurate clock shows 8 o'clock in the morning. Through how many degrees will the hour hand rotate when the clock shows 10 o'clock in the morning?
Options:
A)30
B)60
C)90
D)120
E)150
Rationale: The hour hand will move 2/12 of a circle.
(2/12)*360 = 60 degrees.
The answer is B.
Answer: B
Question: One root of the quadratic equation x2 - 12x + a = 0, is thrice the other. Find the value of a?
Options:
A)21
B)25
C)27
D)29
E)31
Rationale: Let the roots of the quadratic equation be x and 3x.
Sum of roots = -(-12) = 12
a + 3a = 4a = 12 => a = 3
Product of the roots = 3a2 = 3(3)2 = 27.
C)
Answer: C
Question: If 12/x is an integer and 3/x is an integer, which of the following must be true? I. 6/x is an integer II. 18/x is an integer III. 3/x is an integer
Options:
A)II only
B)II, III only
C)III only
D)I,III only
E)II only
Rationale: The question asks which of the following MUST be true, not COULD be true. The largest possible value of x is 3, GCD of 12 and 3, and if x=3 then ONLY III is true.
Answer: C
Answer: C
Question: You have a six-sided cube and six cans of paint, each a different color. You may not mix colors of paint. How many distinct ways can you paint the cube using a different color for each side? (If you can reorient a cube to look like another cube, then the two cubes are not distinct.)
Options:
A)24
B)30
C)48
D)60
E)120
Rationale: Paint one of the faces red and make it the top face.
5 options for the bottom face.
Now, four side faces can be painted in (4-1)! = 3! = 6 ways (circular arrangements of 4 colors).
Total = 5*6 = 30.
Answer: B.
Answer: B
Question: 6 dogs and 8 cats do a work in 12 days, while 5 dogs and 8 cats finish it in 16days, 4dogs and 8 cats will finish it in.
Options:
A)14 days
B)20 days
C)24 days
D)12 days
E)28 days
Rationale: Explanation:
(6dogs+8cats) 1 day work = 1/12
(5dogs+8cats) 1 day work = 1/16
substract 1 and 2
i.e 1/12 – 1/16= 1/48
i.e 1 dog 1 day work is 1/48
4dogs + 8cats 1day work is 1/16 – 1/48 = 1/24
thus 4 dogs and 8 cats will finish it in 24 days
Answer: Option C
Answer: C
Question: If w, x, and y are consecutive odd positive integers and w < x < y, which of the following could be equal to y - w - x ?
Options:
A)-4
B)-2
C)-1
D)0
E)-5
Rationale: Since W, X and Y are CONSECUTIVE ODD POSITIVE INTEGERS and W < X < Y, we can start with the easiest set of values that comes to mind:
W = 7
X = 9
Y = 11
Here, Y - W - X is....
11 - 7 - 9 = -5
-5 IS among the answer choices, so we're done.
E
Answer: E
Question: list of salaries of 8 employees are listed below. What is the median salary?
$40,000, $29,000, $35,500, $31,700, $43,000, $30,000, $27,000, $32,700
Options:
A)$28,000
B)$32,200
C)$30,200
D)$30,800
E)$31,500
Rationale: Ordering the data from least to greatest, we get:
$27,000, $29,000, $30,000, $31,700, $32,700, $35,500, $40,000, $43,000
Since there is an even number of items in the data set, we compute the median by taking the mean of the two middlemost numbers.
$31,700 + $32,700 = $64,400
The median salary is $32,200.
Answer : B
Answer: B
Question: The distance traveled by train in one year approximately 50,000,000 miles.The distance traveled by Train in 25 years?
Options:
A)10<9>
B)10<8>
C)10<11>
D)10<17>
E)10<7>
Rationale: The distance traveled by train in one year = 50,000,000 miles
The distance traveled by Train in 25 years = 50,000,000 miles*25 years =1,250,000,000
= 125*10<7> Answer = E
Answer: E
Question: Rahul's shop runs a sale on goldfish and platys. If one customer buys 13 goldfish and 12 platys for $5.60, and another buys 14 goldfish and 21 platys for $8.05, what is the ratio of the price of goldfish to platys?
Options:
A)0.8
B)0.75
C)c) 8/9
D)5/7
E)6/8
Rationale: The approach of plugging in the numbers is a fine approach. But, in this case, the answer was the first option and thus, by plugging in a number in the ration given, we arrived at the answer quickly!
However, what if the correct ratio was option D or C?
In any case, the algebraic solution isn't that complex if you realize a key concept:
The number 7 can be factored out of the second equation!
Here's the working:Rahul's shop runs a sale on goldfish and platys.
13x + 12y = 5.60 <<<<< Equation 1
14x + 21y = 8.05 <<<<< Equation 2
2x + 3y = 1.15 [Factor Out 7 from equation 2] <<<<< Equation 3
8x + 12y = 4.6 [Multiply Equation 3 with 4]
5x = 1.0 [Equation 1 - Equation 2]
x = 0.2
3y = 1.15 - 0.4 = 0.75 [Substitute for x in Equation 1]
y = 0.25
x/y = 0.2/0.25 = 20/25 = 4/5 = 0.8 [Answer A]
The whole thing must have taken me about 45 s :D
Answer: D