gmat quant concepts & formulae
gmat quant concepts & formulae
... < x < 5 is
a compound inequality, as is a < b < c < d. When manipulating, the same
operations must be done to every term in the inequality. For example, given x < y +
2 < ... function, where x
is the input, f(x) is read as "f as a function of x" or "f of x" and refers to the output
(also known as the "y" value), and x + 5 is the rule for...
Manhattan advanced GMAT quant
... something you don't know. This could be an intermediate unknown
quantity that you didn't think of earlier.
Other times, you don't know something, and you don't care. For ... can
rephrase the information: n is a positive prime number.
What don't
I know?
Here's something I don't know: I don't know the value of x as a series of digits. Using a
calculat...
gmat quant topic 1 (general arithmetic) solutions
... dessert don't order
coffee. But be careful! The problem does not say that 20% of the total diners order dessert and
don't order coffee, so you CANNOT fill in 40 under "dessert, ... the first statement, so we'll start with statement (2).
(2) INSUFFICIENT: This statement gives us information only about the cell labeled "vegetarian
non-student"; further it only .....
gmat quant topic 2 statistics solutions
... integers is ascending, so a < b and e < f. Therefore a + e < b + f, and b +
f = (4/3)(c + d) according to this statement. However, we don't know whether a + e < (2/3)(c
+ d).
(1) ... inequality
symbol does not change.
Is 2 > 25/24 ?
2 is NOT greater than 13/8, so the answer is a definite "No." Recall that a definite "No"
is
sufficient. The correct...
gmat quant topic 3 (inequalities + absolute value) solutions
... D.
25.
X-2Y < -6 => -X + 2Y > 6
Combined X - Y > -2, we know Y > 4
X - Y > -2 => -2X + 2Y < 4
Combined X - 2Y < -6, we know -X < -2 => X > 2
Therefore, XY > 0
Answer ... line. Asking "Is |
x
| less than 1?" can then be reinterpreted as "Is
x
less than 1
unit away from zero on the number line?" or "Is -1 <
x
< 1?"...
gmat quant topic 4 - numbers solutions
... even. (Recall that "no" is a sufficient answer to a yes/no data sufficiency question;
only "maybe" is insufficient.)
(2) INSUFFICIENT: If
yz
is even, then it's possible ... even. (Recall that "no" is a sufficient answer to a yes/no data sufficiency question;
only "maybe" is insufficient.)
(2) INSUFFICIENT: If
yz
is even, then it's possib...
gmat quant topic 5 - geometry solutions
...
their difference (i.e. |
y
-
z
| <
x
<
y
+
z
).
In this question:
|
BC
-
AC
| <
AB
<
BC
+
AC
9 - 6 <
AB
< 9 + 6
3 <
AB
< 15
Only 13.5 is in this range. ... =
12c/2.
(3)
a
+
b
+
c
= 60 The problem states that triangle PQR's perimeter is 60
(4)
a
>
b
PQ > QR is given
(5) (
a
+
b
)
2
= (
a
2
+
b
2
) + 2
ab
Expansion of...
gmat quant topic 6 co-ordinate geometry solutions
... below).
Let's call R the midpoint of the line segment between P and Q. R's coordinates
will just be the respective average of P's and Q's coordinates. Therefore R's x-
coordinate ... s=+/-1=>s=1
8. The two intersections: (0,4) and (y, 0) So, 4 * y/ 2 = 12 => y= 6
Slope is positive => y is below the x-axis => y = -6
9. First, let’s rewrite both equations i...
gmat quant topic 7 - p and c sol
... gold medalists,
there has been a lot of "overcounting!" How much overcounting? Let's consider one of the 24 possible Gold-
GMAT / Quant / P&C / Page 3 of 4
Gold-Gold victory ... these 16 "daughters-sitting-adjacent" scenarios from the total number of "parent-driving"
scenarios, we get: 48 – 16 = 32 The correct answer is B.
54.
Ignoring Frankie&apo...
gmat quant topic 8 - probability solutions
... R/(B+W+R)>W/(B+W+R). B, W, R are positive, so, we just need to know is R>W.
For 1, R/(B+W)> W/(B+R)=>R/(B+W)-W/(B+R) >0
[ R(B+R)-W(B+W)]/(B+W)(B+R) >0
(R-W)(R+W+B)/(B+W)(B+R) >0 ... analytically for any card by building a probability "tree" and
summing the probability of all of its "branches."
For example, let's find the probability that the 2n...
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