GMAT Data Sufficiency Discussions

MBA GMAT
1701
If x, y, and z are integers greater than 1, and (3^27)(5^10)(z) = (xy), then what is the value of x?

(1) y is prime

(2) x is prime

nuttyvarun Says
yep.. good catch.. its x^y.. sorry for that miss..

So now the corrected version:
(3^27)(5^10) z = (5^ (x^y)

As we're solving for x, move all the numbers to the 'z' side.

(5^2)(z)/(3) = x^y

(25/3)z = x^y

Now:
we know that x, y and z are all integers greater than 1, So we can say that x^y is also an integer.
Since the right side is an integer, the left side must also be an integer.
Now its clear that ,for (25/3)z to be an integer, z MUST be a multiple of 3.

Coming to statements now:
1. y is prime:

z = (3/25)x^y

as z is integer , right side must be also integer. So x^y must be a multiple of 25.

we can not say anything as we are not sure about x.

INSUFFICIENT.

2.x is prime:
z = (3/25)x^y
Again, as z is an integer, the right side must also be an integer.
so x^y has to be a multiple of 25.

For x^y to be a multiple of 25, x MUST be a multiple of 5 (since x and y are integers). If x is a multiple of 5 AND prime, x MUST be equal to 5.
SUFFICIENT.
1702
1)In 2003 Acme Computer priced its computers five times higher than its printers. What is the ratio of its gross revenue for computers and printers respectively in the year 2003?

(1) In the first half of 2003 it sold computers and printers in the ratio of 3:2, respectively, and in the second half in the ratio of 2:1.

(2) It sold each computer for $1000.


option 1: NOT SUFF.. we dunno the price..

option2: NOT SUFF, we dunno the ratio

both together.. NOT SUFF.. becuase we dunno the absolute ratio for the entire year.. we just have half yearly figure (relative, NOT absolute..)..

answer must be option E

24) If Jim earns x dollars per hour, it will take him 4 hours to earn exactly enough money to purchase a particular jacket. If Tom earns y dollars per hour, it will take him exactly 5 hours to earn enough money to purchase the same jacket. How much does the jacket cost?

(1) Tom makes 20% less per hour than Jim does.

(2) x + y = $43.75


option1: NOT SUFF

option2: SUFF
by forming & solving the eqn from the ques stem we know that Tom makes 80% of wat Jim makes..

so by substituting the values from ques stem into X + Y = 43.75, we can solve it for X and Y and find out the cost of Jacket..

the answer must be option B.
1703

as I understand u think answer is option B.. correct me if I am wrong.. but as per the Manhattan thing, the OA is option A ;)

So now the corrected version:
(3^27)(5^10) z = (5^ (x^y)
As we're solving for x, move all the numbers to the 'z' side.
(5^2)(z)/(3) = x^y
(25/3)z = x^y
Now:
we know that x, y and z are all integers greater than 1, So we can say that x^y is also an integer.
Since the right side is an integer, the left side must also be an integer.
Now its clear that ,for (25/3)z to be an integer, z MUST be a multiple of 3.
Coming to statements now:
1. y is prime:
z = (3/25)x^y
as z is integer , right side must be also integer. So x^y must be a multiple of 25.
we can not say anything as we are not sure about x.
INSUFFICIENT.
2.x is prime:
z = (3/25)x^y
Again, as z is an integer, the right side must also be an integer.
so x^y has to be a multiple of 25.
For x^y to be a multiple of 25, x MUST be a multiple of 5 (since x and y are integers). If x is a multiple of 5 AND prime, x MUST be equal to 5.
SUFFICIENT.
1704
nuttyvarun Says
as I understand u think answer is option B.. correct me if I am wrong.. but as per the Manhattan thing, the OA is option A ;)

OA can be A

If your first statement is "if z is prime" and not "y is prime"..

check if you have posted correctly...
1705

wrong post

1706

1. E
2. B

Please let me know if I need to provide explanation.

1)In 2003 Acme Computer priced its computers five times higher than its printers. What is the ratio of its gross revenue for computers and printers respectively in the year 2003?

(1) In the first half of 2003 it sold computers and printers in the ratio of 3:2, respectively, and in the second half in the ratio of 2:1.

(2) It sold each computer for $1000.

24) If Jim earns x dollars per hour, it will take him 4 hours to earn exactly enough money to purchase a particular jacket. If Tom earns y dollars per hour, it will take him exactly 5 hours to earn enough money to purchase the same jacket. How much does the jacket cost?

(1) Tom makes 20% less per hour than Jim does.

(2) x + y = $43.75
1707

IMO C

Stmnt resolves to x Stmnt resolves to x > -7 -- Not suff

Combining both and the fact that x is an nteger,
x can -6

If x is an integer, what is the value of x?

(1) -5x > -3x + 10
(2) -11x 10
1708

IMO C

let Jim's sal - x
June's y

Stmnt says: x + y =50000 -- Many possibilities. Not suff
Stmnt 2 says 0.1x + 1.12 y = 5600 -- Many possibilities. Not suff

Combining two, we can obtain values of x and y.

Solve this

1.what is Jim's annual salary and June's annual salary ?

a)The combined total of the annual salaries of Jim and June is $50,000

b)If Jim were to receive a 10% increase in annual salary and June a 12% increase,their combined annual salaries would be $55,600.
1709
If x, y, and z are integers greater than 1, and (3^27)(5^10)(z) = (xy), then what is the value of x?

(1) y is prime

(2) x is prime



Here we finally have:

25*z/3=x^y

so from 1 we have y is prime.

this equation can be satisfied only when z=3 and x=5 and y=2

hence suff

take 2) we have

y is prime.
here we can have diff values satisfying the eq.

So insuff.

Hence A

Some how i'm not convinced abt my expln. :lookround:
1710

A can not be the ans. Put diff values of z into equation:
25*z/3=x^y

when Z = 12, x = 10, y = 2(prime num)
when Z = 15, x = 5, y = 3(prime again).

Hence insuff

Considering stmnt 2: x ia prime
25*z/3=x^y
5^2*z = 3*x^y

Any number can written as multiples of prime numbers raised to their powers.
On the LHS: 5 is prime
On the RHS: 3 is prime and x is prime

In order for them to be equal, x has to be 5. Hence sufficient.
B should be the ans.




Here we finally have:

25*z/3=x^y

so from 1 we have y is prime.

this equation can be satisfied only when z=3 and x=5 and y=2

hence suff

take 2) we have

y is prime.
here we can have diff values satisfying the eq.

So insuff.

Hence A

Some how i'm not convinced abt my expln. :lookround:
1711
1)In 2003 Acme Computer priced its computers five times higher than its printers. What is the ratio of its gross revenue for computers and printers respectively in the year 2003?

(1) In the first half of 2003 it sold computers and printers in the ratio of 3:2, respectively, and in the second half in the ratio of 2:1.

(2) It sold each computer for $1000.


24) If Jim earns x dollars per hour, it will take him 4 hours to earn exactly enough money to purchase a particular jacket. If Tom earns y dollars per hour, it will take him exactly 5 hours to earn enough money to purchase the same jacket. How much does the jacket cost?

(1) Tom makes 20% less per hour than Jim does.

(2) x + y = $43.75


@bizzarenym , @nuttyvarun & deepakraam
you all got the answers right..

OA ->

E
B
1712

M and R are 2 numbers, what is R?
1) Distance between r and 0 is 3 times the distance between m and 0
2) 12 is halfway between M and R

1713
M and R are 2 numbers, what is R?
1) Distance between r and 0 is 3 times the distance between m and 0
2) 12 is halfway between M and R


posting after a long time

Ans E..

St 1 : r = 3 m ...notsuff

St 2 : m +r = 24 ...not suff

Combined : r = 3m or r = -3m

Hence, 4m = 24 or -2m = 24

Hence, poss points are (6,1 OR (-12, 36) ...not suff ...
1714
posting after a long time

Ans E..

St 1 : r = 3 m ...notsuff

St 2 : m +r = 24 ...not suff

Combined : r = 3m or r = -3m

Hence, 4m = 24 or -2m = 24

Hence, poss points are (6,1 OR (-12, 36) ...not suff ...

"posting after a long time "...
and posting it right.....i don't know, why the heck i din't apply the mod in first place......

OA is E
1715

If p q and p r, is pqr p?
(1) pq
(2) pr

1716
M and R are 2 numbers, what is R?
1) Distance between r and 0 is 3 times the distance between m and 0
2) 12 is halfway between M and R


IMO C

consider 1) we dont know on which side of the number line are m and r so insuff.

Consider 2) there can be a number of combinations for this. so insuff

Combine both now we have

3m=m+(r-m)

2m= (r-m)

so we have distance between the r and m as 2m

so the distance is in the ration as 1:2 and we have 12 as the mid point.

Hence C

Plz post the OA .:biggrin::biggrin:
1717

one miss here..

when you talk about distance from 0, you mean absolute distance, which can be on either side of zero..

so the answer cannot be reached with both statement combined.. 😉 must be option E

IMO C

consider 1) we dont know on which side of the number line are m and r so insuff.

Consider 2) there can be a number of combinations for this. so insuff

Combine both now we have

3m=m+(r-m)

2m= (r-m)

so we have distance between the r and m as 2m

so the distance is in the ration as 1:2 and we have 12 as the mid point.

Hence C

Plz post the OA .:biggrin::biggrin:
1718

If x and y are non-zero integers and x + |y = 32, what is xy?

(1) -4x 12y = 0

(2) x| y = 16

1719
If p q and p r, is pqr p?
(1) pq
(2) pr

1=> p is -ve & q is +ve as p2=> p is -ve & r is +ve as p
using 1 & 2=>
pqr is -ve & p is -ve
but if qr>1 then pqr

p so not suff.

therefore ans is E

1720
If x and y are non-zero integers and x + |y = 32, what is xy?

(1) -4x 12y = 0

(2) x| |y = 16


by gven information in question x| + |y = 32
this is a rhombus with 4 vertices (-32,0) (0,-32) ( 32,0) & (0,32)
or it can be displayed with the delp of 4 eqns

x+y=32
x-y=32
y-x=32
x+y=-32

1=>
y=-1/3 x this is a straight line with negative slope hence it passes through
x-y=32 & y-x=32
on solving we get two points (24,- &(8,-24) so NOT SUFF

2=> this is the curve inthe form of >
1&2=> putting the points (24,- & (8,-24) in x|-y=16 both satisfies so NOT SUFF
So ans is E IMO