divelab/Sys2Bench huggingface dataset:
Question: One year ago the ratio of Yamini’s and Gamini’s ages was 6 : 7 respectively. Four years hence this ratio would become 7 : 8. How old is Gamini?
Options:
A)35 years
B)30 years
C)31 years
D)Cannot be determined
E)None of these
Rationale: Y : G = 6 : 7; One year before
Y : G = 7 : 8; After 4 years
Now, 1 → 5
∴ 7 → 35
Therefore, the age of Gamini now is 35 + 1 = 36 years
Answer E
Answer: E
Question: A man buys 20 lts of liquid which contains 30% of the liquid and the rest is water. He then mixes it with 20 lts of another mixture with 20% of liquid. What is the % of water in the new mixture?
Options:
A)59
B)95
C)80
D)75
E)65
Rationale: 30% in 20 lts is 6. So water = 20-6 = 14lts.20% of 20 lts = 4. So water in 2nd mixture = 20-4 = 16 lts. Now total quantity = 20 + 20 = 40 lts. Total water in it will be 14 + 16 = 30 lts. % of water = (100*30)/40 = 75.
ANSWER:D
Answer: D
Question: The base of a right triangle is 8 and hypotenuse is 10. Its area is?
Options:
A)12
B)80
C)59
D)24
E)25
Rationale: Explanation:
h2=(10)2-(8)2-(6)2->h=6
1/2*8*6=24
ANSWER IS D
Answer: D
Question: At what price must an article costing Rs.75 be marked in order that after deducting 5% from the list price. It may be sold at a profit of 25% on the cost price?
Options:
A)62.5
B)62.0
C)62.6
D)62.1
E)98.68
Rationale: CP = 75
SP = 75*(125/100) = 93.75
MP*(95/100) = 93.75
MP = 98.68
Answer:E
Answer: E
Question: Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
Options:
A)20.8 sec
B)10.7 sec
C)10.3 sec
D)10.8 sec
E)10.2 sec
Rationale: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other
= 140 + 160 = 300 m.
Required time = 300 * 9/250
= 54/5
= 10.8 sec.
Answer:D
Answer: D
Question: A train speeds past a pole in 20 seconds and passes through a tunnel 500 m long in 40 seconds. Its length is :
Options:
A)200 m
B)400 m
C)500 m
D)700 m
E)None of the above
Rationale: Sol.Let the length of the train be x metres and its speed be y m/sec. Then, x / y = 20 ⇒ y = x / 20∴ (x + 500) / 40 = x / 20 ⇔ x = 500 m. Answer C
Answer: C
Question: In how many ways can 16 different gifts be divided among four children such that each child receives exactly three gifts?
Options:
A)16^4
B)(4!)^4
C)16!/(3!)^4
D)16!/4!
E)4^16
Rationale: Total 16 different Gifts, and 4 children.
Thus any one child gets 16C3 gifts,
then the other child gets 13C3 gifts(16 total - 3 already given),
then the third one gets 10C3 gifts,
and the last child gets 7C3 gifts.
Since order in which each child gets the gift is not imp, thus, ans :
16C3 * 13C3 * 10C3 * 7C3 = 16! / (3!)^4
Ans : C.
Answer: C
Question: The following sets each have a mean of 50 and the standard deviations are given in variable form.
Set I = {20, 20, 20, 80, 80, 80}, standard deviation = A
Set II = {20, 30, 40, 60, 70, 80}, standard deviation = B
Set III = {50, 50, 50, 50, 50, 50}, standard deviation = C
Rank these three standard deviations from least to greatest.
Options:
A)A, B, C
B)B, C, A
C)C, A, B
D)B, A, C
E)C, B, A
Rationale: The answer should be E as the mean is least deviated in Set III followed by Set II and then Set I.
Answer: E
Question: A can give B 100 meters start and C 170 meters start in a kilometer race. How much start can B give C in a kilometer race?
Options:
A)11.77 meters
B)55.77 meters
C)77.77 meters
D)113.77 meters
E)None of these
Rationale: Explanation:
A runs 1000 meters while B runs 900 meters and C runs 830 meters.
Therefore, B runs 900 meters while C runs 830 meters.
So, the number of meters that C runs when B runs 1000 meters = (1000 x 830)/900 = 922.22 meters
Thus, B can give C (1000 - 922.22) = 77.77 meters start
Answer: C
Answer: C
Question: A Card marked 1 and 2 on its two faces. Two colors, white and black are used to paint the two faces of the card. If the card is painted with the different colors, in how many ways can the card be painted?
Options:
A)3
B)6
C)2
D)12
E)27
Rationale: If the base of the card is white, then in order the card to be painted with the different colors, the top must be white.Another side can be painted in Black.
But we can have the base painted in either of the two colors, thus the total number of ways to paint the card is 2*1=2.
Answer: C.
Answer: C
Question: If the sample interest on a sum of money 20% per annum for 2 years is $400, find the compound interest on the same sum for the same period at the same rate?
Options:
A)$460
B)$510
C)$440
D)$500
E)$550
Rationale: Rate = 20%
Time = 2years
S.I. = $400
Principal = 100*400/20*2 = $1000
Amount = 1000(1+20/100)^2 = $1440
C.I. = 1440-1000 = $440
Answer is C
Answer: C
Question: A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 3 employees to 2 different offices?
Options:
A)5
B)6
C)7
D)8
E)9
Rationale: for each employee there are two possibilities: first office and second office.
Therefore,
N=2^3=8
ANS:D
Answer: D
Question: A train covers a distance of 12 km in 10 min. If it takes 7 sec to pass a telegraph post, then the length of the train is?
Options:
A)298
B)288
C)140
D)776
E)991
Rationale: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec.
Length of the train = 20 * 7
= 140 m.
Answer:C
Answer: C
Question: Let y = 2m + x^2 and m = 5x + 2. If m^2 =49, then which of the following can be a value of 2y + 3m?
Options:
A)48
B)56
C)61
D)51
E)71
Rationale: m^2 = 49 => m=7
7= 5x+2 => x=1
y= 2*7+1^2 = 15
2y+3m = 2*15+3*7 = 51
Answer : D
Answer: D
Question: There were two candidates in an election. Winner candidate received 62% of votes and won the election by 288 votes. Find the number of votes casted to the winning candidate?
Options:
A)748
B)744
C)725
D)727
E)272
Rationale: W = 62% L = 38%
62% - 38% = 24%
24% -------- 288
62% -------- ? => 744
Answer:B
Answer: B
Question: The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?
Options:
A)17
B)16
C)17
D)19
E)62
Rationale: Average of 20 numbers = 0
Sum of 20 numbers = (0 * 20) = 0
It is quite possible that 19 of these numbers may be positive and if their sum is a, then 20th number is (-a).
Answer: D
Answer: D
Question: A trained covered x km at 40 kmph and another 2x km at 20 kmph. Find the average speed of the train in covering the entire 5x km.
Options:
A)20kmph
B)25kmph
C)30kmph
D)35kmph
E)40kmph
Rationale: Total time taken = x/40 + 2x/20 hours
= 5x/40 = x/8 hours
Average speed = 5x/(x/8)
= 40 kmph
Answer:E
Answer: E
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?
Options:
A)288
B)127
C)2999
D)277
E)299
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
Question: An "integrated" team consists of 2 members from the engineering team and 2 members from the design team. If the engineering team has 6 members and the design team has 4 members, how many "integrated" team formations are possible?
Options:
A)36
B)54
C)76
D)90
E)112
Rationale: Possible Integrated teams=6!/2!∗4!*4!/2!∗2=15*6=90
So,Correct Answer D
Answer: D
Question: A man whose speed is 4.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey?
Options:
A)5
B)4
C)6
D)8
E)32
Rationale: M = 45
S = 1.5
DS = 6
US = 3
AS = (2 * 6 * 3) /9 = 4
Answer: B
Answer: B
Question: A cycle is bought for Rs.900 and sold for Rs.1140, find the gain percent?
Options:
A)11
B)27
C)99
D)77
E)18
Rationale: 900 ---- 240
100 ---- ? => 27%
Answer: B
Answer: B
Question: In one year, the population, of a village increased by 30% and in the next year, it decreased by 30%. If at the end of 2nd year, the population was 13650, what was it in the beginning?
Options:
A)7787
B)8000
C)15000
D)1277
E)2081
Rationale: x*130/100 * 70/100 = 13650
X*0.91=13650
X=13650/0.91
=> 15000
Answer:C
Answer: C
Question: The equation x = 2y^2 + 5y - 19, describes a parabola in the xy coordinate plane. If line l, with slope of 3, intersects the parabola in the upper-left quadrant at x = -5, the equation for l is
Options:
A)3x + y + 15 = 0
B)y - 3x - 11 = 0
C)-3x + y - 19 = 0
D)-2x - y - 7 = 0
E)-3x + y + 13.5 = 0
Rationale: The question is made to look difficult though it is pretty simple if you focus on just the line and use process of elimination. (Remember that GMAT does not focus on parabolas so basically, the question should be quite do-able even if someone doesn't know how to handle parabolas.)
We need equation of l. Its slope must be 3.
Slope in option A and D is not 3 so we are left with B, C and E
The line has a point (-5, y) on it where y is positive (since the point lies in upper left quadrant).
In options B and E, if you put x = -5, you get -ve value for y co-ordinate. So ignore them.
Answer must be (C)
Answer: C
Question: A man buys 50 pens at marked price of 46 pens from a whole seller. If he sells these pens giving a discount of 1% , what is the profit percent?
Options:
A)7.6 %
B)7.7 %
C)7.32 %
D)3.6 %
E)7.8 %
Rationale: Explanation:
Let Marked price be Re. 1 each
C.P. of 50 pens = Rs. 46
S.P. of 50 pens = 99% of Rs. 50 = Rs. 49.50
Profit % = (Profit /C.P.) x 100
Profit% = (3.50/46) x 100 = 7.6 %
ANSWER: A
Answer: A
Question: If a and b are each greater than x and y, which of the following must be true?
I.|a| + |b| > |x| + |y|
II. ab > xy
III. a + b > x + y
Options:
A)I only
B)II only
C)I and II
D)III only
E)I, II and III
Rationale: I. a + b > x + y. Since a and b are each greater than x and y, then the sum of a and b will also be greater than the sum of x and y.
II. ab > xy. Not necessarily true, consider a = b = 0 and x = y = -1 --> ab = 0 < 1 = xy.
III. |a| + |b| > |x| + |y|. Not necessarily true, consider a = b = 0 and x = y = -1 --> |a| + |b| = 0 < 2 = |x| + |y|.
Answer: D.
Answer: D
Question: If a tap could fill entire tank in 20 hrs due to leakage, then in how much time
tank can be emptied by leakage if tap can fill entire tank in 12 hrs without leakage
Options:
A)30hrs
B)24hrs
C)36hrs
D)48hrs
E)52hrs
Rationale: time take to fill[withleakage] =20hrs so workdone in 1hr=1/20
time tkae to fill[without leakage]=12hrs so workdone in 1hr=1/12
if u subtract both u'll get time taken by leakage to empty...
1/20-1/12=2/60 = 1/30 so 30hrs
ANSWER:A
Answer: A
Question: What is the tenth digit of (5!*5! - 5!*3!)/5?
Options:
A)1
B)2
C)0
D)6
E)7
Rationale: (5!*5! + 5!*3!)/5
=5!(5! + 3!)/5
=120 (120+6)/5
=3024
Units digit of the above product will be equal to 2
Answer B
Answer: B
Question: A man can row at 5 kmph in still water. If the velocity of the current is 1 kmph and it takes him 1 hour to row to a place and come back. how far is that place.
Options:
A)4 km
B)1.4 km
C)2.4 km
D)3.4 km
E)4.4 km
Rationale: Explanation:
Let the distance is x km
Rate downstream = 5 + 1 = 6 kmph
Rate upstream = 5 - 1 = 4 kmph
then
x/6 + x/4 = 1 [because distance/speed = time]
=> 2x + 3x = 12
=> x = 12/5 = 2.4 km
ANSWER IS C
Answer: C
Question: A man bought 10 crates of apples for $120 total. If he lost 2 of the crates, at what price would he have to sell each of the remaining crates in order to earn a total profit of 50 percent of the total cost?
Options:
A)$22.50
B)$25
C)$28
D)$30
E)$35
Rationale: As given, after lost, the remaining 8 crates total cost = $120
So, 1 crate cost = 120/8 =15
To get 50% profit, 1 crate cost should be =15+15*50/100 =$22.5
Answer : A
Answer: A
Question: If the quantity 3^4+ 3^6 + 3^8 is written as (a + b)(a – b), in which both a and b are integers, which of the following could be the value of b?
Options:
A)57
B)26
C)52
D)81
E)25
Rationale: (a+b)(a-b) = a^2 - b^2
3^4+ 3^6 + 3^8 = 3^4 (1+3^2+3^4)
if the above expression is solved even then every term of the expression will remain a multiple of 3^4 which is out of parenthesis
hence, b must be a multiple of 3^4 i.e. 81
Answer: option D
Answer: D
Question: Balls of equal size are arranged in rows to form an equilateral triangle. the top most row consists of one ball, the 2nd row of two balls and so on. If 19 balls are added, then all the balls can be arranged in the shape of square and each of the sides of the square contain 8 balls less than the each side of the triangle did. How many balls made up the triangle?
Options:
A)465
B)2209
C)2878
D)1210
E)1560
Rationale: As expected, this question boils down to 2 equation,
Consider total number of Balls in Triangle = T and number of balls in last row = x.
1+2+3+...+x = T
x(x+1)/2 = T ----(a)
As mentioned in the question, side of a square will be (x-8) and total number of Balls in square will be (T+19)
(x-8)^2 = T+19 -----(b)
Now the hardest part of the question will be to solve these 2 equations and this looks like time consuming BUT the easy way will be plug and play. Also, we've to find a value of T (from 5 optiosn given below) which can make a square of a a number. One we know this, it will be a cake walk.
We can see that option A fits this criteria in eq (b). Add - 465+19 = 484 = 22^2 = (x-8)^2 Hence, x = 30
Cross check by putting in eq (a) = x(x+1)/2 = T = > 30*31/2=465
Hence, answer is A.
Answer: A
Question: The average of a couple was 28Yrs when they were married 5Yrs ago.The avg age of
the couple and a child, who was born during the interval, is 23Yrs now. How old is the
child now ?
Options:
A)2 Yrs
B)4 Yrs
C)3 Yrs
D)1 Yrs
E)None of these
Rationale: (a+b-5-5)/2=28;
a+b=66;
a+b+c/3=23;
solving both c=3
ANSWER:C
Answer: C
Question: If 8 men can reap 80 hectares in 24 days , then how many hectares can 36 men reap in 30 days?
Options:
A)127
B)237
C)287
D)450
E)281
Rationale: Explanation:
Let the required no of hectares be x. Then
More men, More hectares (Direct proportion)
More days, More hectares (Direct proportion)
Men\: 8:36\\ Days\: 24:30 \end{matrix}\right\} :80:x
\inline \fn_jvn \therefore \inline \fn_jvn 8\times 24\times x=36\times 30\times 80 \inline \fn_jvn \Leftrightarrow \inline \fn_jvn x=\frac{36\times 30\times 80}{8\times 24} \inline \fn_jvn \Leftrightarrow x= 450
Answer: D
Answer: D
Question: What proximate value should come in place of the question mark (?) in the following question?
6.695 Ã— 1084 + 2568.34 â€“ 1708.34 = ?
Options:
A)6,000
B)12,000
C)10,000
D)8,096
E)9,000
Rationale: ? â‰ˆ 6.7 Ã— 1080 + 2560 â€“ 1700 â‰ˆ 7236 + 860 â‰ˆ 8096
Answer D
Answer: D
Question: The average of first 6 natural numbers is?
Options:
A)5.2
B)3.5
C)5.3
D)5.9
E)5.1
Rationale: Sum of 6 natural no. = 42/2 = 21
Average = 21/6 = 3.5
Answer:B
Answer: B
Question: Twenty four men can do a work in 48 days. How many men are required to complete the work in 12 days?
Options:
A)85
B)46
C)50
D)96
E)60
Rationale: D
96
We have M1 D1 = M2 D2
So, 24 * 48 = M2 * 12 => M2 = 96.
Answer: D
Question: A train 360 m long is running at a speed of 45 kmph.In what time will it pass a bridge 140 m long?
Options:
A)40 sec
B)42 sec
C)45 sec
D)48 sec
E)49 sec
Rationale: speed of the train 45* 5/18 = 25/2 m/sec
time = (360+140)/25/2
= 500*2/25
=40sec
ANSWER:A
Answer: A
Question: kumar saves 32% of his monthly salary. If he spends Rs. 27200, then find his savings?
Options:
A)15400
B)14300
C)13200
D)12800
E)9500
Rationale: Answer: Option D
Let the monthly salary of kumar be Rs. x.
68% of x = 27200
=> x = (27200 * 100)/68 = 40000
His savings = 32/100 * 40000 = 12800.
Answer: D
Question: When a whole no. n is divided by 4,we will get 3 as remainder. What will be the remainder if 2n is divided by 4?
Options:
A)1
B)4
C)2
D)6
E)7
Rationale: Let n ÷ 4 = p , remainder = 3
=> n = 4p + 3
2n = 2(4p + 3)
= 8p + 6
= 8p + 4 + 2
= 4(2p + 1) + 2
Hence, if 2n is divided by 4, we will get 2 as remainder.
C
Answer: C
Question: Sn = n^2 + 5n + 94 and K = S6 – S5 + S4 – S3 - S2 + S1. What is the value of K?
Options:
A)67
B)20
C)45
D)41
E)36
Rationale: I used brute force for this question:
S6: 36+30+94=160
S5: 25+25+94=144
S4: 16+20+94=130
S3: 9+15+94=118
S2: 4+10+94=108
S1: 1+5+94=100
S6-S5+S4-S3+S2-S1= 16+12-8=20
Answer B
Answer: B
Question: A total of x tourists were transported by bus to a certain museum. If there were y tourists on each bus, which of the following expresses the number of buses used?
Options:
A) xy
B) x/y
C) y/x
D) x - y
E) y^2
Rationale: IMHO (B) x/y as well !
Number of buses used = Total number of tourists / Number of tourists per bus => x/y
PS : In case of any doubt , plug in some numbers
Total number of tourists transported by bus = 500
Number of tourists per bus = 10
No of buses required = 500/10
Answer: B
Question: John bought a total of 16 Mangoes and Oranges. Each Mango costs 80 cents and each orange costs 60 cents. If the average price of the 16 mangoes and oranges that John originally purchased was 65 cents, then how many oranges needs to return to raise the average price of his purchase to 72 cents?
Options:
A)4
B)5
C)6
D)7
E)10
Rationale: Let number of mangoes be x, number of oranges be 16-x
0.80x +(16-x)0.60/16 = 0.65
solving for x, we get x = 4 --> Mangoes 4, Oranges 12
Now, number of oranges to be returned be y
0.80*4 + (12-y)*0.60/16-y = 0.72
solving for y, y = 10
Ans:E
Answer: E
Question: To mail a package, the rate is 10 cents for the first pound and 5 cents for each additional pound. Two packages weighing 4 pounds and 6 pounds, respectively can be mailed seperately or combined as one package. Which method is cheaper and how much money is saved?
Options:
A)Combined, with a saving of 15 cents
B)Combined, with a saving of 10 cents
C)Combined, with a saving of 5 cents
D)Separately, with a saving of 5 cents
E)Separately, with a saving of 15 cents
Rationale: 4 pounds cost = 10+3*5 = 25
6 pounds cost = 10+5*5 = 35
Total = 60
10 pounds cost = 10+ 9*5 =55
Answer : C
Answer: C
Question: The probability of Sam passing the exam is 1/5. The probability of Sam passing the exam and Michael passing the driving test is 1/6. What is the probability of Michael passing his driving test?
Options:
A)5/6.
B)1/2.
C)1/3.
D)2/3.
E)2/5
Rationale: 1/5 *1/m= 1/6 , 1/m = 5/6
Answer A
Answer: A
Question: If the compound interest on an amount of Rs. 29000 in two years is Rs. 9352.5, what is the rate of interest?
Options:
A)11
B)9
C)15
D)18
E)25
Rationale: let interest rate be x.
(2x+(x^2)/100)*(1/100)*29000 = 9352.5
x = 15
ANSWER:C
Answer: C
Question: Rs.8000 become Rs.8487.20 in a certain interval of time at the rate of 3% per annum of C.I. Find the time?
Options:
A)6 years
B)8 years
C)9 years
D)3 years
E)2 years
Rationale: 8487.20 = 8000(34/30)N
(34/30)^2 = (34/30)N => N = 2
At the end of three years what will be the comp.Answer: E
Answer: E
Question: My watch gains 5 min every hour. How many degrees the second hand moves in every min?
Options:
A)300
B)350
C)390
D)400
E)450
Rationale: Gain 5 min
every 1 hr
degrees moves ==>390
ANSWER C
Answer: C
Question: Three candidates contested an election and received 1136, 7636 and 14000 votes respectively. What percentage of the total votes did the winning candidate get?
Options:
A)46%
B)61%
C)74%
D)63%
E)68%
Rationale: B
14000/(1136 + 7636 + 14000) = 61%.
Answer: B
Question: At the end of year 1998, Shepard bought nine dozen goats. Henceforth, every year he added p% of the goats at the beginning of the year and sold q% of the goats at the end of the year where p > 0 and q > 0. If Shepard had nine dozen goats at the end of year 2002, after making the sales for that year, which of the following is true?
Options:
A)p = q
B)p < q
C)p > q
D)p = q/2
E)None of these
Rationale: Explanation :
The number of goats remain the same. If the percentage that is added every time is equal to the percentage that is sold, then there should be net decrease.
The same will be the case if the percentage added is less than the percentage sold.
The only way the number of goats remain the same if p>q.
Answer : C
Answer: C
Question: A can do a certain job in 25 days which B alone can do in 20 days. A started the work and was joined by B after 10 days. The number of days taken in completing the wotk were ?
Options:
A)14 2/3kmph
B)15 2/3kmph
C)16 2/3kmph
D)17 2/3kmph
E)18 2/3kmph
Rationale: Explanation:
Work done by A in l0 days = (1/25) *10 = 2/5
Remaining work = 1 - (2/5) = 3/5
(A+B)s 1 days work = (1/25) + (1/20) = 9/100
9/100 work is done by them in 1 day.
hence 3/5 work will be done by them in (3/5)*(100/9)
= 20/3days.
Total time taken = (10 + 20/3) = 16*(2/3) days
Option C
Answer: C
Question: Suppose there is an outlet which is pouring water at a constant rate and is able to fill a swimming pool in nine hours. There is another outlet that is able to fill the pool in five hours. If we open both the outlets and let them pour the water together How many hours will it take to fill the pool ?
Options:
A)3.11 hours
B)2.21 hours
C)3.21 hours
D)4.21 hours
E)5.21 hours
Rationale: total work=1/9+1/5=14/45 so reqired time=45/14
=3.21 hours
ANSWER:C
Answer: C
Question: Carol is three times Alice’s age but only twice as old as Betty. Alice is twenty-four years younger than Carol. How old is Betty?
Options:
A)26
B)19
C)22
D)18
E)24
Rationale: Beyond the obvious Algebra approach to this question, it can also be solved by TESTing THE ANSWERS.
We're told 3 facts about the relative ages of 3 people:
1) Carol's age is 3 times Alice's age
2) Carol's age is 2 times Betty's age
3) Carol is 24 years older than Alice
We're asked for BETTY'S age.
From the answer choices and the information provided, Carol can't be that old (The difference of 12 years = 3 times; that relationship can only occur when the numbers are relatively small). Since Carol is TWICE Betty's age, Betty is clearly younger than Carol, so we'll TEST a smaller answer first.
IF....
Betty = 18
Then Carol = 2(18) = 36
Then Alice = 36 - 24 = 12 AND 36/3 = 12
All of these values mesh perfectly with the facts and with one another, so Betty MUST be 18
D
Answer: D
Question: If the sides of a triangle are 9 cm, 16 cm and 19 cm, what is its area?
Options:
A)69
B)72
C)75
D)89
E)93
Rationale: The triangle with sides 9 cm, 16 cm and 19 cm is right angled, where the hypotenuse is 19 cm.
Area of the triangle = 1/2 * 9 * 16 = 72 cm2
Answer: Option B
Answer: B
Question: Three candidates contested an election and received 5000, 22000 and 34800 votes respectively. What percentage of the total votes did the winning candidate get ?
Options:
A)56.31
B)45%
C)75.20%
D)86%
E)95.15%
Rationale: Explanation :
Total number of votes polled = (5000+ 22000 + 34800)
= 61800.
Required percentage = (34800/ 61800) X100
= 56.31%.
Answer : A
Answer: A
Question: By selling an article at Rs.500, a profit of 25% is made. Find its cost price?
Options:
A)400
B)267
C)287
D)480
E)811
Rationale: SP = 500
CP = (SP)*[100/(100+P)]
= 500 * [100/(100+25)]
= 500 * [100/125] = Rs.400
Answer: A
Answer: A
Question: A group of college friends plan to rent a house together for x dollars per month, which is to be shared equally among them. If four, rather than six people rent the house together, how many more dollars, in terms of x, will each person have to pay for rent per month?
Options:
A)x/4
B)x/6
C)x/12
D)x/10
E)x/24
Rationale: If 6 people share the rent, each person would pay x/6.
If 4 people share the rent, each person will pay x/4.
The extra amount each person pays is x/4 - x/6 = 3x/12 - 2x/12 = x/12
The answer is C.
Answer: C
Question: For any integer p, *p is equal to the product of all the integers between 1 and p, inclusive. How many prime numbers are there between *9 + 3 and *9 + 9, inclusive?
Options:
A) None
B) One
C) Two
D) Three
E) Four
Rationale: Generally *p or p! will be divisible by ALL numbers from 1 to p. Therefore, *9 would be divisible by all numbers from 1 to 9.
=> *9+3 would give me a number which is a multiple of 3 and therefore divisible (since *9 is divisible by 3)
In fact adding anyprimenumber between 1 to 9 to *9 will definitely be divisible.
So the answer is none (A)!
Supposing if the question had asked for prime numbers between *9 + 3 and *9 + 11 then the answer would be 1. For *9 +3 and *9 + 13, it is 2 and so on...
A
Answer: A