Here's one of the most commonly seen DS questions.. want to check what's the best way to approach such questions in GMAT.
Is it tru that (a)^1/3 (1). a (2). a > -1
Share your thought(s) and approach(es) to address such questions plz..
Here's one of the most commonly seen DS questions.. want to check what's the best way to approach such questions in GMAT.
Is it tru that (a)^1/3 (1). a (2). a > -1
Share your thought(s) and approach(es) to address such questions plz..
FROM 1ST A
if we assume value of a=-8,-64.... then we can give ans a^1/3>a
so first is sufficient
from 2nd a>-1
means value of A=0 or 1....
in 0 LHS=RHS
in 1,2.... RHS>LHS (for equation)
so 2 not sufficient
Here's one of the most commonly seen DS questions.. want to check what's the best way to approach such questions in GMAT.
Is it tru that (a)^1/3 (1). a (2). a > -1
Share your thought(s) and approach(es) to address such questions plz..
hey varun ...Ans is C ....
the best and shortest way to arrive at the solution :
Consider number line to be broken into 4 distinct parts
Part1 : xPart2 : -1
This is becoz every real no within a particular range behave in a similar fashion ..and the pattern alternates between 2 consecutive range.
So if the statements completely lie within a particular range, it is sufficient to answer the question ..
St 1 is a mix of part 1 and part 2 ...not sufficient
St 2 is a mix of part 2, 3 and 4..not sufficient ...
St 1 and 2 combined .. part 2 ...one definite pattern ...sufficient ....Ans C
Elaboration of how number line can be assumed to be composed of 4 parts only and relation in every range ...
part 1 : eg a= -8 implies -2>-8 implies a^1/3 >a
( same is the case for any real no lesser than -1)
Hence, if aa
Part 2 : eg a= -1/8 implies -1/2
Part 3 : eg a = 1/8 implies 1/2 > 1/8 implies a^1/3 >a
Hence, for 0 a
Part 4 : eg a= 8 implies 2Hence, if a>1 then root of a no is lesser than no i.e a^1/3
Hence, we observe that rule fluctuates between 2 consecutive ranges on a number line ...
we can establish a similar pattern for relation between higher powers and no ..it wud simply be opposite in nature as compared to roots
eg for questions like : Is a^3>a ?
So next time for such questions no need to even remember their pattern, if it belongs to one particular range possible it is sufficient to answer !!
Hope this helps...long post , feel free to clarify !!
FROM 1ST A
if we assume value of a=-8,-64.... then we can give ans a^1/3>a
so first is sufficient
from 2nd a>-1
means value of A=0 or 1....
in 0 LHS=RHS
in 1,2.... RHS>LHS (for equation)
so 2 not sufficient
St 1 is not sufficient buddy ....when a is negative , u have forgotten to evaluate for negative fraction values of a between 0 and -1 ....
bhavin422 SaysSt 1 is not sufficient buddy ....when a is negative , u have forgotten to evaluate for negative fraction values of a between 0 and -1 ....
yep friend u totally correct
i forgot to think for a=-1
tnx
the answer to this can be found only if we know in which range a lies out of the following ranges:
1. a a
2. -1a
4. a>1, a^1/3
So the answer will be c.
Is it D?
According to first statement and given data if m=n then p is also even and n+2=According to sec statement LCM of m and p is 30. Factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30. m>2 So possible values of m and p are 3 and 10 or 5 and 6 and in both the cases remainder is 1.
So both statements are individually sufficient.
According to first statement and given data if m=n then p is also even and n+2=According to sec statement LCM of m and p is 30. Factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30. m>2 So possible values of m and p are 3 and 10 or 5 and 6 and in both the cases remainder is 1.
So both statements are individually sufficient.
The question was
Q. The integers m and p are such that 2
1 ?
1. the greatest common factor of m and p is 2
2. the least common multiple of m and p is 30
When an even no. is divided by an even no. the remainder will always be even (provided one is not a multiple of other. in that case remainder will be zero). So statement 1 is sufficient to answer the question.
But the second statement gives the option as:
the two no.s can be (10,3), (10,15), (10,6), (15,6), (15,2). In the first case the remainder is 1 and in all the other cases, remainder is greater than 1. So 2 alone is not sufficient to answer the question.
So the answer should be a.
There are two trees in a flat small park, an oak tree and a pine tree. At 3pm, the shadow from the pine tree is 32
feet long and the shadow from the oak tree is 40 feet long. Approximately how tall is the oak tree?
(1) The pine tree is 24 feet tall.
(2) The oak tree is 20 feet from the Pine tree.
A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.
B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.
C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER
statement BY ITSELF is sufficient.
D. Either statement BY ITSELF is sufficient to answer the question.
E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, meaning that further
information would be needed to answer the question.
The answer says A. But shouldn't it be E considering the case that the two trees can be at two ends of the park with the sun in the zenith?
There are two trees in a flat small park, an oak tree and a pine tree. At 3pm, the shadow from the pine tree is 32
feet long and the shadow from the oak tree is 40 feet long. Approximately how tall is the oak tree?
(1) The pine tree is 24 feet tall.
(2) The oak tree is 20 feet from the Pine tree.
A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.
B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.
C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER
statement BY ITSELF is sufficient.
D. Either statement BY ITSELF is sufficient to answer the question.
E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, meaning that further
information would be needed to answer the question.
The answer says A. But shouldn't it be E considering the case that the two trees can be at two ends of the park with the sun in the zenith?
Use the fundamentals of similar triangles.. ABC and PQR
Height - Base - Hypotenuse be represented by (AB, PQ) - (BC, QR) - (AC, RP) respectively..
BC = 32, QR = 40
Now if we have AB, then we can find out PQ. Done!!
Answer is option A :)
Use the fundamentals of similar triangles.. ABC and PQR
Height - Base - Hypotenuse be represented by (AB, PQ) - (BC, QR) - (AC, RP) respectively..
BC = 32, QR = 40
Now if we have AB, then we can find out PQ. Done!!
Answer is option A :)
I agree with varun. Here is another way to solve the problem:
1. Ratio of height to shade height --> 24:32 --> 2:3. This ratio is true for the other tree as well and hence we can find the height.
I have got one question:
Every student of a certain class in a school volunteered to contribute equally for a picnic on a new year's eve. If the total contribution was $600, how many students were there in the class?
1) Each student contributed $10
2) 10 Students failed to contribute and the remaining students ended up paying $2 more than they would have contributed otherwise.
My answer is D but the OA is A.
1) Easily answers the question
2) on Substitution, I was able to arrive at single answer. 60 students.
I do not know where am going wrong.
I have got one question:
Every student of a certain class in a school volunteered to contribute equally for a picnic on a new year's eve. If the total contribution was $600, how many students were there in the class?
1) Each student contributed $10
2) 10 Students failed to contribute and the remaining students ended up paying $2 more than they would have contributed otherwise.
My answer is D but the OA is A.
1) Easily answers the question
2) on Substitution, I was able to arrive at single answer. 60 students.
I do not know where am going wrong.
We all know that option 1 answers the questions on its own... so let's just concentrate on option 2 and see if it can answer on it's own
Total contri = $600
Lets total students be x and contribution per student be y
so as per the statement given in question, we have;
(x)(y) = 600
let's substitute option 2 in here;
(x-10)(y+2)=600
xy + 2x - 10y -20 = 600
i.e 2x - 10y = 20
substitute x = 600/y
2(600/y) - 10y = 20
(1200/y) - 10y = 20
y^2 + 2y -120 = 0
i.e. y = 10, which means x = 600/10 = 60
quadratic equation... we would get a unique answer.. as per my understanding option 2 is enough to answer the question..
Answer should be option D
Here's one for all;
Is the integer K divisible by 4?
1) 8k is divisible by 16
2) 9k is divisible by 12
this one took me 6+ minutes to solve... 
Here's one for all;
Is the integer K divisible by 4?
1) 8k is divisible by 16
2) 9k is divisible by 12
this one took me 6+ minutes to solve...
My Answer is B. It took me about a minute to solve this. Here is some help.
1. Sub k = 2. 8k is divisible by 16 but not divisible by 4. If k = 4 then it is divisible by 4. Not sufficient
2. LCM for 9 and 12 is 36. In order for 9k to be divisible by 12, it should be a multiple of 36. So K has to be multiple of 4. Sufficient.
Here's one for all;
Is the integer K divisible by 4?
1) 8k is divisible by 16
2) 9k is divisible by 12
this one took me 6+ minutes to solve...
my ans is B !!! wats the OA ?
My Answer is B. It took me about a minute to solve this. Here is some help.
1. Sub k = 2. 8k is divisible by 16 but not divisible by 4. If k = 4 then it is divisible by 4. Not sufficient
2. LCM for 9 and 12 is 36. In order for 9k to be divisible by 12, it should be a multiple of 36. So K has to be multiple of 4. Sufficient.
that's a good approach.. this did not occur to me when I was solving the question.. thanks man!! ;)
btw.. that's the correct answer!!
If (243)^X(463)^y = n, where x and y are positive integers, what is the units digit of n?
(1) x + y = 7
(2) x = 4
What do you think the answer could be?
If (243)^X(463)^y = n, where x and y are positive integers, what is the units digit of n?
(1) x + y = 7
(2) x = 4
What do you think the answer could be?
here
x+y=7 means
x=0 to 7 & Y=7 to 0
if we take x=0 & y=7 then last ligit=1*7=7
x=1 & y=6 then last digit=3*9=7
x=2 & y=5 then last digit=9*3=7
in all case last digit =7
here , to find last digit of 3^0 to 3^7 u can use cyclist of 3 means 3,9,7,1,3,9,7,1........
so statement 1 is sufficient to ans
for st 2
x=4
(243)^X(463)^y so last digit of 243^4=1 but u dont have value of Y
so not sufficient
so sta. 1 sufficient to give ans
If x^2+5y=49, is y an integer?
1. 1
My answer was C (both together can solve) but the exam says E (not solvable even when both options are taken together). This was a Kaplan exam - I really can't ignore the answer but I don't think it is right.
Any take?
If x^2+5y=49, is y an integer?
1. 12. x^2 is an integer.
My answer was C (both together can solve) but the exam says E (not solvable even when both options are taken together). This was a Kaplan exam - I really can't ignore the answer but I don't think it is right.
Any take?
from st 1 u cant not say anything
from st 2 ,
if u take x=1 so 5y=48 so y float value
x=2 so 5y=45 so y integer value
from both
possible value 2 & 3
now when x=2 value of y in integer
but when u take x=1.73 means sqrt3 so x^2=3 then value of y float value
so ans is E