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Data Sifficiency

Expert replies
by Tagne » Wed Mar 16, 2011 7:34 pm
1. If I x + 2I =4 , what is the value for x?
a. X^2 is not equal to 4
b. X^2 = 36

2. At a certain bakery, each roll cost r cents and each doughnut cost d cents. If John bought rolld and doughnut, how many cents did he pay for each roll?
a. John paid $5.00 for 8 rolls and 6 dougnuts
b. John would have paid $10.00 if he had bought 16 rolls and 12 doughnuts

3. if c and d are integers, is c even?
a. C(d+1) is even
b. (c+2)(d+4) is even

4. Are positive integers p and q both greater than n?
a. P - q is greater than n
b. Q > p

5. John bought several chairs. If each chair was either a 23 cents chair or a 21 cent chair, how many 23 cents chair did John buy?
a. John bought a total of 6 chairs
b. The total value of chairs bought was 130 cents

6. If q is a positive integer less than 17 and r is the remainder when 17 is divided by q, what is the value of r?
a. Q > 10
b. Q = 2^k , where k is a positive integer

7. In a certain senior class, 72 percent of the male students and 80 percent of the female students have applied to college. What fraction of students in the senior class are male?
a. There are 840 students in the senior class
b. 75 percent of students in the senior class have applied to college
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Source: — Problem Solving |

by 6983manish » Wed Mar 16, 2011 7:59 pm
Tagne wrote:1. If I x + 2I =4 , what is the value for x?
a. X^2 is not equal to 4
b. X^2 = 36

Given Ix + 2I = 4

I think the variable "I" signifies here an integer. ( Please correct me if I am wrong )

Option a -> x^2 <>4 , means x can be any number except +2 / -2 .
It is not sufficient to give an answer. ( As I is integer for x = -6 , 0 , -1 etc )

Now we left with answers choices BCE.

Option b -> x^2 = 36 , means x can be +6 or -6.

we can put the value of x in the main equation.

For -6 , we get I = -1 which is an integer.
For 6 , we get I = 1/2 which is not an integer.

So we can say , the value of x is -6.

We can mark the answer as "B".
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by srcc25anu » Wed Mar 16, 2011 8:01 pm
Q2. to find 'r'

stat 1: 8r+6d = 50 Not sufficinet to solve two variables with one eqn

stat 2: 16r+12d = 100 Not sufficinet to solve two variables with one eqn

Together: 8r + 6d = 50 and 16r + 12d = 100 are one and the same equation. so the 2 together are still Not sufficient

hence E
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by srcc25anu » Wed Mar 16, 2011 8:05 pm
Q5. to determine the number of 23 cent chairs or Y???

let X be number of 21 cent chair
let Y be number of 23 cent chair

stat 1: x + y = 6 (Not Sufficient)
Stat 2: 21x + 23y = 130 ((Not Sufficient)

Together: 1 and 2 statements are sufficient to solve for Y
hence C
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by Tagne » Wed Mar 16, 2011 8:07 pm
I x + 2I =4 means Absolute value of x + 2 =4. ie I x+2 I. Sorry about the confusion!
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by srcc25anu » Wed Mar 16, 2011 8:11 pm
Q6. to determine 'r'where r is remainder when 17 is divided by q [0 < q < 17]

stat 1: Q>10 so Q can take values 11,12, 13,14,15,16 Not sufficient

stat 2: Q=2^k (k = +ve integer)
2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 16

hence Not sufficient

Together, the two statements are sufficient if Q >10 and Q <17, only 2^4 = 16 satisfies the equation. if 17 / 16, r=1. although this calculation wasnt needed to determine sufficinecy.
Therefore answer = C
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by Tagne » Wed Mar 16, 2011 8:13 pm
The answer to question 5 is B. Did any one get B?
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by Tagne » Wed Mar 16, 2011 8:16 pm
I got the same answer as you in Q6, but the book says B. Did anyone get B?
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by srcc25anu » Wed Mar 16, 2011 8:17 pm
Q3.is C even?

stat1: c(d+1) = even
C - even; D - odd, D+1 - even c(d+1) = even
C - even; D - even, D+1 - odd c(d+1) = even
C - odd; D - odd, D+1 - even c(d+1) = even

hence Not sufficient

stat 2: (c+2) * (d+4) = even
c - even; c+2 - even; d - even, d+4 - even thus (c+2) * (d+4) = even
c - even; c+2 - even; d - odd, d+4 - odd thus (c+2) * (d+4) = even
c - odd; c+2 - odd; d - even, d+4 - even thus (c+2) * (d+4) = even

Hence Not sufficient

Together: still not sufficient hence E
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by 6983manish » Wed Mar 16, 2011 8:19 pm
Tagne wrote: 3. if c and d are integers, is c even?
a. C(d+1) is even
b. (c+2)(d+4) is even

Given c and d are integers.

Option a (cd + c ) is even.
Means it should be either even+even or odd+odd.
Hence , c can be odd or even => Not sufficient.

Option b (cd + 2d + 4c +8 ) is even.
Means its a case of "even+even+even+even" only

cd should be even , even*even / even*odd / odd*even.
c can be even or odd both => Not sufficient.

Combining both also not sufficient to give a concrete answer.

Answer E
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by srcc25anu » Wed Mar 16, 2011 8:22 pm
Q7. Male % in senior class = ???
given: 72% males applied to college
80% females applied to college

stat 1: total students in senior class = 840
doesnt tell us about number of males
hence not sufficient

stat 2: 75% of students in senior class have applied to college
still doesnt tell us the number of males versus females in the class hence not sufficient

Together they are sufficient hence C

.72x + .8 (840-x) = .75*840 hence we can solve for x that is total number of males in senior class
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by srcc25anu » Wed Mar 16, 2011 8:41 pm
Q1. |x+2| = 4, then x can equal +2 or -6
stat 1: x is not equal to +/-2 therefore X = -6 sufficient
stat 2: x=+/-6 hence sufficinet

thus answer D.
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by srcc25anu » Wed Mar 16, 2011 8:47 pm
Q4. is p and q both >n??? p and q are +ve

stat 1: p-q > n
n=p-q
p=5, q=1, then p-q = 3 or p-q > 2(q<n, p>n)
p=5, q=4, then p-q = 1 or p-q > 0 (p,q > n)
not sufficinet

stat 2: q>p
no relation to n hence not sufficinet

together both ae sufficient to answer
p=3, q=5 then p-q = -ve
p=1, q=2 then p-q = -ve
if q>p, q >0, p>0 then p-Q = n is always -ve
hence C
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by Geva@EconomistGMAT » Wed Mar 16, 2011 10:58 pm
srcc25anu wrote:Q5. to determine the number of 23 cent chairs or Y???

let X be number of 21 cent chair
let Y be number of 23 cent chair

stat 1: x + y = 6 (Not Sufficient)
Stat 2: 21x + 23y = 130 ((Not Sufficient)

Together: 1 and 2 statements are sufficient to solve for Y
hence C
(2) is actually sufficient on is own, specfically because x and y have to be integers - they represent number of chairs, and you can't buy half a chair for less than 12.5 cents, for example. The only configuration of 21 and 23 cents that reaches 130 in total is 4 X chairs of 21 cents and 2 Y chairs of 23 cents: 4*21+2*23 = 84+46 = 130.

The GMAT will do that sometimes: introduce the sum of two quantities of real things (people, chairs, cars), ostensibly unsolvable because there's only one equation with 2 unknowns, but actually doable if you remember to assume that the variables are integers.
Geva
Senior Instructor
Master GMAT
1-888-780-GMAT
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by Geva@EconomistGMAT » Wed Mar 16, 2011 11:00 pm
srcc25anu wrote:Q6. to determine 'r'where r is remainder when 17 is divided by q [0 < q < 17]

stat 1: Q>10 so Q can take values 11,12, 13,14,15,16 Not sufficient

stat 2: Q=2^k (k = +ve integer)
2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 16

hence Not sufficient

Together, the two statements are sufficient if Q >10 and Q <17, only 2^4 = 16 satisfies the equation. if 17 / 16, r=1. although this calculation wasnt needed to determine sufficinecy.
Therefore answer = C
(2) is sufficient alone: the remainder when 17 is divided by 2, 4, 8 and 16 is always 1, so r has a single value. The answer is B.
Geva
Senior Instructor
Master GMAT
1-888-780-GMAT
https://www.mastergmat.com
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