25 Hardest Questions From The GMAT Club Forum Solutions PDF
25 Hardest Questions From The GMAT Club Forum Solutions PDF
25 Hardest Questions From The GMAT Club Forum Solutions PDF
7. If x is positive, which of the following could be the correct ordering of 1/x,2x and x^2 ?
I. x^2<2x<1/x
II. x^2<1/x<2x
III. 2x<x^2<1/x
(A) None
(B) I only
(C) III only
(D) I and II only
(E) I II and III
First note that we are asked "which of the following COULD be the correct ordering" not MUST be.
Basically we should determine relationship between
When
-->
If
in three areas:
I.
--> can
? Can
can check it either algebraically or by picking numbers)
II.
--> can
for
and
-->
In this case
, the expression
, the expression
. (You
Answer: D.
Second condition:
The question is which of the following COULD be the correct ordering not MUST be.
Put
-->
-->
http://gmatclub.com/forum/if-x-is-positive-which-of-the-following-could-be-correct-71070.html
2
In a room filled with 7 people, 4 people have exactly 1 sibling in the room and 3 people have exactly 2 siblings in the room. If two
individuals are selected from the room at random, what is the probability that those two individuals are NOT siblings?
A. 5/21
B. 3/7
C. 4/7
D. 5/7
E. 16/21
As there are 4 people with exactly 1 sibling each: we have two pairs of siblings (1-2; 3-4).
As there are 3 people with exactly 2 siblings each: we have one triple of siblings (5-6-7).
Solution #1:
# of selections of 2 out of 7 -
Solution #2:
# of selections of 2 out of 7 -
# of selections of 2 siblings -
.
Solution #3:
.
Answer: E.
http://gmatclub.com/forum/in-a-room-filled-with-7-people-4-people-have-exactly-87550.html
3
As this is a COULD be true question then even one set of numbers proving that statement holds true is enough to say that this statement
should be part of correct answer choice.
Given:
1.
statement
.
--> the easiest one: if
and
(reverse order of
true.
):
some big number, let's say 1,000. Next, let's try the fractions for
and
http://gmatclub.com/forum/if-x-y-2-z-4-which-of-the-following-statements-could-be-100465.html
-->
out of the brackets
and
and
then
. The stem and this statement hold true for this set of numbers. So 3 also COULD be
Answer: E.
--> take
as well as given
. So 1 COULD be true.
2.
--> we have reverse order than in stem (
again the stem and this statement hold true. So 2 also COULD be true.
3.
-->
-->
-->
-->
-->
-->
-->
Answer: B.
http://gmatclub.com/forum/in-the-infinite-sequence-a-an-x-n-1-x-n-x-n-1-x-92110.html
5
For me the best way to solve this problem is not use Venn diagram or formulas but to draw simple bars (note: each dash is 5):
Min overlap is 10:
-------------------- 80 phones;
-------------------- 75 DVD's;
-------------------- 55 MP3.
Max overlap is 55:
-------------------- 80 phones;
-------------------- 75 DVD's;
-------------------- 55 MP3.
55-10=45.
Answer: C.
http://gmatclub.com/forum/in-a-village-of-100-households-75-have-at-least-one-dvd-98257.html
6
6 inches = 1/2 feet (there are 12 inches in a foot.), so 60*25*1/2=750 feet^3 of water must be removed, which equals to 750*7.5=5625 gallons.
Answer: E.
http://gmatclub.com/forum/the-water-level-in-a-rectangular-swimming-pool-measuring-110553.html
7
I. 0 < t < h. That is always correct, as the time needed for both fixtures leaking (working) together to fill the bucket,
than time needed for either of fixture leaking (working) alone to fill the bucket;
II. c < t < h. That cannot be correct:
, the time needed for both fixtures leaking (working) together to fill the bucket, must always be less
than time needed for either of fixture leaking (working) alone to fill the bucket. So
not true.
III. c/2 < t < h/2. To prove that this is always correct we can use pure logic or algebra.
Logic:
If both fixtures were leaking at identical rate then
and
but since
then
Given:
and
? break down:
? -->
? and
? -->
? -->
? -->
? -->
? -->
http://gmatclub.com/forum/in-a-certain-bathtub-both-the-cold-water-and-the-hot-water-127878.html
8
Please don't reword the questions. Original question is:
If
and
A. 87/20
B. 63/20
C. 47/20
D. 15/4
E. 14/5
Note that
Answer: B.
As for your question:
The point here is that square root function can not give negative result -->
example
-->
5^2 and (-5)^2 equal to 25.
About
-->
;
-->
, for
has TWO solutions, +5 and -5, because both
equal to?
So we got that:
, if
, if
What function does exactly the same thing? The absolute value function:
why
, if
and
, if
. That is
http://gmatclub.com/forum/if-x-3-4-and-y-2-5-what-is-the-value-of-110071.html
9
Given:
and
-->
, (as
there are 13 even numbers in the range from -12 to 12, inclusive each of which will give an integer value of
Answer: D.
http://gmatclub.com/forum/for-how-many-ordered-pairs-x-y-that-are-solutions-of-the-110687.html
10
Many approaches are possible. For example:
Consider numbers from 0 to 999 written as follows:
1. 000
2. 001
3. 002
4. 003
...
...
...
1000. 999
We have 1000 numbers. We used 3 digits per number, hence used total of 3*1000=3000 digits. Now, why should ANY digit have preferences
over another? We used each of 10 digits equal # of times, thus we used each digit (including 7) 3000/10=300 times.
Answer: D.
http://gmatclub.com/forum/how-many-times-will-the-digit-7-be-written-99914.html
11
First of all to simplify the given expression a little bit let's multiply it be 2:
-->
Now, find x and y intercepts of the region (x-intercept is a value(s) of x for y=0 and similarly y-intercept is a value(s) of y for x=0):
-->
-->
and
-->
-->
and
;
.
So we have 4 points: (10, 0), (-10, 0), (0, 10) and (-10, 0).
When you join them you'll get the region enclosed by
You can see that it's a square. Why a square? Because diagonals of the rectangle are equal (20 and 20), and also are perpendicular
bisectors of each other (as they are on X and Y axis), so it must be a square. As this square has a diagonal equal to 20, so
the
Or the
.
-->
Answer: D.
http://gmatclub.com/forum/if-equation-x-2-y-2-5-encloses-a-certain-region-126117.html
12
{Total}={Writers}+{Editors}-{Both}+{Neither}.
{Total}=100;
{Writers}=45;
{Editors}>38;
{Both}=x;
{Neither}=2x;
100=45+{Editors}-x+2x --> x=55-{Editors}. We want to maximize x, thus we should minimize {Editors}, minimum possible value of {Editors} is
39, thus x={Both}=55-39=16.
Answer: B.
http://gmatclub.com/forum/100-people-are-attending-a-newspaper-conference-45-of-them-127715.html
13
If x is an integer and |1-x|<2 then which of the following must be true?
|1-x| is just the distance between 1 and x on the number line. We are told that this distance is less than 2: --(-1)----1----3-- so, -1<x<3. Since
given that x is an integer then x can be 0, 1 or 2.
A. x is not a prime number. Not true if x=2.
B. x^2+x is not a prime number. Not true if x=1.
C. x is positive. Not true if x=0.
D. Number of distinct positive factors of x+2 is a prime number. True for all three values of x.
E. x is not a multiple of an odd prime number. Not true if x=0, since zeo is a multiple of every integer except zero itself.
Answer: D.
http://gmatclub.com/forum/if-x-is-an-integer-and-1-x-2-then-which-of-the-following-138328.html
14
Basically we are asked to find the range of
-->
or
for which
-->
is true.
Answer: C.
http://gmatclub.com/forum/which-of-the-following-represents-the-complete-range-of-x-108884.html
15
Coach Miller is filling out the starting lineup for his indoor soccer team. There are 10 boys on th team, and he must assign 6 starters to
the following positions: 1 goalkeeper, 2 on defense, 2 in midfield, and 1 forward. Only 2 of the boys can play goalkeeper, and they
cannot play any other positions. The other boys can each play any of the other positions. How many different groupings are possible?
A. 60
B. 210
C. 2580
D. 3360
E. 151200
2C1 select
8C2 select
6C2 select
4C1 select
Total # of selection=2C1*8C2*6C2*4C1=3360
Answer: D.
http://gmatclub.com/forum/coach-miller-is-filling-out-the-starting-lineup-for-his-57554.html
16
Using THREE non-zero digits a,b,c only, we can construct 3!=6 numbers: abc, acb, bac, bca, cab, cba. Their sum will be:
Answer: E (222).
http://gmatclub.com/forum/if-x-represents-the-sum-of-all-the-positive-three-digit-91007.html
17
18
We are given that
and
So we have that:
Option B says:
(side note: we can safely do this as absolute value is non-negative and in this case we know
-->
and
, so
or
, so
-->
or
--> ANY
. Note
-->
;
.
from above two ranges would be more than -1, so B is always true.
Answer: B.
http://gmatclub.com/forum/x-x-x-which-of-the-following-must-be-true-about-x-13943.html
19
Dolphin once in 2 min;
Beluga once in 5 min;
So, dolphin comes up 2.5 times frequently than beluga, which is 150% (5-2)/2*100.
"X's height is 110% greater than that of Y."
Means: x=(1+110%)*y=(1+1.1)*y=2.1*y
http://gmatclub.com/forum/on-average-the-bottle-nosed-dolphin-comes-up-for-air-once-85737.html
20
-->
. Thi inequality represents ALL points, the area, above the line
line you'll see that the mentioned area is "above" IV quadrant, does not contains any point of this quadrant.
is positive,
positive
E.
, negative
is positive and
Answer: E.
http://gmatclub.com/forum/in-the-rectangular-coordinate-system-shown-above-which-90285.html
21
First of all let's solve this inequality step by step and see what is the solution for it, or in other words let's see in which ranges this inequality
holds true.
-->
-->
-->
-->
-->
-->
-->
and
------{-1}xxxx{0}----{1}xxxxxx
Now, we are asked which of the following must be true about
range
, eg
and
, all "red",
Answer: B.
http://gmatclub.com/forum/if-x-x-x-which-of-the-following-must-be-true-about-x-68886.html
22
Pick some smart number for
From November to February
storage of 6 and so on.
, let
(I chose
).
rakes were produced and in March business paid for storage of 8-1=7 rakes, in next month for
--> as
, then
Answer: C.
http://gmatclub.com/forum/a-certain-business-produced-x-rakes-each-month-form-november101738.html
23
Step by step analyzes:
B speed:
mph;
A speed:
Track distance:
miles
Time needed for A and B to meet distance between them divided by the relative speed:
they are travelling in opposite directions relative speed would be the sum of their rates;
, as
hours;
hours;
hours;
Total time:
hours.
Answer: B.
http://gmatclub.com/forum/car-b-starts-at-point-x-and-moves-clockwise-around-128215.html
24
You should notice that inequality
and
of positive+negative will be less than |positive|+|negative|. For example |-2|+|3|>|-2+3|. In all other cases
So, basically the question is whether
and
and
. Not sufficient.
. Not sufficient.
Answer: E.
http://gmatclub.com/forum/is-a-b-a-b-105457.html
25
# of terms =
OR
42 terms after zero and 42 terms below zero will total 0. So, our new question will be consecutive integers with first term 43 have sum 372,
what is the last term:
Answer: D (50)