Sach tieng Anh thu vi cho mon Toán

1. 1. A password on Mr. Wallace'sbriefcase consistsof5 digits. What isthe probabilitythat the password
contains exactlythree digit6?
A. 860/90,000
B. 810/100,000
C. 858/100,000
D. 860/100,000
E. 1530/100,000
Total # of 5 digitcodesis10^5, notice thatit's not 9*10^4, since ina code we can have zeroas the firstdigit.
# of passwordswiththree digit6is : each outof twootherdigits(not6) has 9 choices,thus
we have 9*9 and iswaysto choose which3 digitswill be 6'sout of 5 digitswe have.
Answer: B.
2. If , then y is NOT divisible bywhichof the following?
A. 6^4
B. 62^2
C. 65^2
D. 15^4
E. 52^4
.
Now,if youanalyze eachoptionyou'll see thatonly isnot a factor of , since the power
of 13 init ishigherthanthe powerof 13 in .
Answer: E.
3. For the past k days the average (arithmeticmean) cupcakesper day that Liv baked was 55. Today Bibi
joinedand togetherwith Liv they baked100 cupcakes, whichraises the average to 60 cupcakes perday.
What is the value ofk?
A. 6
B. 8
C. 9
D. 10
E. 12
Total cupcakesfork dayswas 55k, whichmeansthattotal cupcakesfor k+1 dayswas 55k+100. The new
average is(55k+100)/(k+1)=60 -->55k+100=60k+60 -->k=8
Answer: B.

2. 4. What is the smallestpositive integer such that is the square of a positive integer?
A. 14
B. 36
C. 144
D. 196
E. 441
, so inorder to be a square of an integer mustcomplete the powersof 2and
7 to evennumber,sothe leastvalue of mustequal to2*7=14, whichmakesthe leasvalue of equal
to 14^2=196.
Answer: D.
5. There are 7 red and 5 blue marbles in a jar. In how many ways 8 marblescan be selectedfromthe jar so
that at least one red marble and at leastone blue marble to remain in the jar?
A. 460
B. 490
C. 493
D. 455
E. 445
Total waysto select8 marblesoutof 7+5=12 is ;
Ways to select8 marblessothat zeroredmarblesisleftinthe jar is ;
Ways to select8 marblessothat zeroblue marblesisleftinthe jaris ;
Hence ways to select8 marblessothat at leastone redmarble and at leastone blue marble toremainthe
jar is .
Answer: D.
6. A pool has two water pumps A and B and one drain C. Pump A alone can fill the whole pool in x hours, and
pump B alone can fill the whole pool in y hours. The drain can emptythe whole pool inz hours,where z>x.
Withpumps A and B both running and the drain C unstoppedtill the pool is filled,whichofthe following
representsthe amount of water in terms of the fraction of the pool whichpump A pumped intothe pool?
A.
B.
C.
D.
E.

3. WithpumpsA and B both runningandthe drainunstoppedthe pool will be filledina
rate pool/hour.So,the pool will be filledin hours(time is
reciprocal of rate).
In hoursA will pump amountof the water intothe pool.
Answer: B.
7. MetropolisCorporationhas 4 shareholders:Fritz, Luis,Alfredand Werner.Numberofshares that Fritz
owns is 2/3 rd ofnumber of the shares of the otherthree shareholders,numberofthe shares that Luis
owns is 3/7 th of number of the shares of the otherthree shareholdersandnumber of the shares that
Alfredowns is 4/11 th of numberof the sharesof the other three shareholders.Ifdividendsof$3,600,000
were distributedamong the 4 shareholders,howmuch of this amount did Wernerreceive?
A. $60,000
B. $90,000
C. $100,000
D. $120,000
E. $180,000
Fritzownsis rd of the sharesof the otherthree shareholders -->Fritzowns thof all shares;
Luisownsis th of the sharesof the otherthree shareholders -->Luisowns thof all shares;
Alfredownsis thof the sharesof the otherthree shareholders -->Alfredowns thof all
shares;
Togetherthose three own thof all shares,whichmeansthatWernerowns .
Hence from$3,600,000 Wernergets .
Answer: D.
8. A set A consists of7 consecutive odd integers.Ifthe sum of 5 largest integersof setA is -185 what is the
sum of the 5 smallestintegersof setA?
A. -165
B. -175
C. -195
D. -205
E. -215
Say 7 consecutive oddintegersare: , , , , , , .
Question:
Given: --
> --> --
>

4. Answer: D.
9. If x and y are negative numbers,what is the value of ?
A. 1+y
B. 1-y
C. -1-y
D. y-1
E. x-y
Note that . Next,since and then and .
So,
Answer: D.
10. If x^2<81 and y^2<25, what isthe largest prime number that can be equal to x-2y?
A. 7
B. 11
C. 13
D. 17
E. 19
Notice thatwe are not toldthat and are integers.
meansthat and meansthat . Now,since the largestvalue of is
almost9 andthe largestvalue of isalmost10 (forexample if ),thenthe largestvalue
of isalmost9+10=19, so the actual value islessthan19, whichmeansthat the largestprime that
can be equal to is 17. For example: and .
Answer: D.
11. In an infinite sequence 1,3, 9, 27, ... each term after the firstis three timesthe previousterm. What is the
difference betweenthe sumof13th and 15th terms and the sum of12th and 14th terms of the sequence?
A. 10*3^11
B. 20*3^11
C. 10*3^12
D. 40*3^11
E. 20*3^12
You don't needtoknowgeometricprogressionformulatosolve thisquestion.All youneedistofindthe
pattern:
;
;
;
;

5. ...
;
Answer: B.
12. x, y and z are positive integerssuchthat whenx is dividedbyy the remainderis 3 and when y is dividedby
z the remainderis 8. What is the smallestpossible value ofx+y+z?
A. 12
B. 20
C. 24
D. 29
E. 33
Given , where isa quotient,aninteger .Whichmeansthatthe leastvalue of is
when , inthat case . This basicallymeansthat islessthan . For example 3dividedby4
yieldsremainderof 3.
Thus we have that:
is dividedby the remainderis3 --> minimumvalue of is3;
is dividedby the remainderis8 --> minimumvalue of is8 andminimumvalue of isone more
than 8, so 9 (8 dividedby9yieldsthe remainderof 8);
So,the smallestpossiblevalue of is3+8+9=20.
Answer: B.
13. If , what isthe product of the tensand the units digitsof ?
A. 0
B. 6
C. 7
D. 12
E. 14
Apply : .
Next, .
Now,since has2 and 5 as itsmultiples,thenitwill have 0as the units digit,so will have twozerosinthe
end,whichmeansthat will have 00-38=62 as the last digits:6*2=12.
Answer: D.