Math (GRE2)
"if y=5+x and y=12-x, and if y^2=x^2+K, then K equals which of the following?"
y-x=5 y+x=12 k=y^2+x^2-> (y-x)(y+x)-> 5 x 12= 60 60
if y=5+x and y=12-x ,and if y^2=x^2+k, then k equals which of the following?
y= 5+x -> y-x=5 y=12-x -> y+x=12 k= y^2-x^2 -> (y-x)(y+x) -> 5 x 12-> 60
in a certain company, 50% of ed's salary is 20% of ruth's salary. if the difference between their salaries is $90,000, whats ruth's salary?
1/2E= 1/5R R-E=90,000 E=2/5R -> R- 2/5R=3/5R=90,000 1/5R=30,000 -> R=150,000
Wendy left the house with d dollars in cash. she made the following cash pruchases: gas, for $3 less than 1/3 of D; a book, for 1/6 of D; stationary, for 6 dollars more than 1/6 of D, and groceried, for 1/4 of D. after these four purchases, she has 4$ left. what is the value of d?
1/3D-3+1/6D+1/6D+6+1/4D+4=D 4/12D+4/12D+3/12D+7=D 11/12D+7=D -> 7=1/12D -> D= 7 x 12 84
when q is divided by w, the quotient is r and the remainder is e. which of the following expressions is equal to e?
2 a/b-c(d) -> c(b)(d)=a q/w=r(e)-> rw+e=q e=q-rw ANSWER: q-rw
a: the # of distincit prime factors of 20^6 b: the # of distinict prime factors of 32^10 which one is greater/ less/ equal/ unsure?
20^6-> (2^2 x 5)^6 -> 2^12 x 5^6 32^10-> (2^5)^10 COLUMN A bc has 2 and 5, while COLUMN B has only2
if x is the greatest common divisor of 90 and 18, and y is the least common multiple of 51 and 34, then what's x+y=?
90-> 3x3x5x2, 18-> 3x3x2 ..... therefore 3x3x2= 18 51-> 3x17, 34-> 2x17......... therefore 2x17x3= 102 102+18 ANSWER: 120
Mark is 8 years older than lisa, and peter's age is 3 years less than three times lisa's age. if the sum of their ages is 80, what is peter's age?
M=L+8 L+M+P=80 P= 3L-3 L+(L+8)+ (3L-3)=80 5L+5=80 5L=75 L=15 P= 3(15)-3-> 45-3 -> 42
right now, steve's age is half of tom's age. in eight years, twice tom's age will be 5 more than 3 times steve's age. how old is tom right now?
T=25 2(T+8)= 3(S+8) +5 2(2S+8)=3(S+8)+5 4S+16= 3S+24+5 S+16=29 S=13 T=13 x 2 = 26
alice and bruce each bought a fridge, and the sum of their purchases was $900. if twice of what alice paid was $75 more than what bruce paid, what did alice pay for her fridge?
a+b=900 -> b=900-a 2a= b+75 2a= 900-A+75 3a=900 + 75 -> A=300+25-> 325
A: the # of prime factors divisible by 13 B: the # of prime factors divisible by 2
both are equal bc both r prime #s
w,x,y are consequtive integers. wxy=0 w<x<y A: x B:0
could be: -2, 0, 2 OR 0, 2, 4 SO X COULD BE EITHER O OR 2. ANSWER: unsure
"x is less than 100. when x is divided by 5, the remainder is 4. when x is divided by 23, the remainder is 7. what's the value of x?"
first= list the possible values of x that it oculd be when divided by 23 and remainder of 7: 7, 30, 53, 76, and 99. second= divide each one by 5 and see if theres a remainder of 4 ANSWER= 99
which of the following are divisible by 6 and not 18? 1296 2744 3072 4356 5832 6000 7290 8112
for 6= must be divisible by 3 when added up for 18= must be divisible by 9 when added up ^^this is bc all are divisible by 2 bc all r even #s ANSWER: 3072, 6000, 8112
m is a positive 2 digit #. when the digits are reversed, the # is N. if k= m+n, which of the following is true?
m= xy m=10x+y n=yx n= 10y+x k=m+n= (10x+y)+(10y+x) =11x+11y 11(x+y) K IS DIVISIBLE BY 11
