Quant Question of the Day Chat

DS Question 2 - Dec 10

If [x] denotes the greatest integer less than or equal to x for any number x, is [a]+[b]=1?

(1) ab=2

(2) 0
Source: GMAT Club Test | Difficulty : Hard

Should be C.
Combining one and two
ab=2
A and B must be positive fractions s.t they multiply to 2. Therefore [a] is 1 and [b] is 1.

Will never be equal to 1

[quote="gmatophobia"]DS Question 2 - Dec 10

If [x] denotes the greatest integer less than or equal to x for any number x, is [a]+[b]=1?

(1) ab=2

(2) 0 [a] + [b] = 3
a=0.8, b=2.5 -> [a] + [b] = 2
a=1.6, b=1.25 -> [a] + [b] = 2
we can try for negative number but result (may) be same, so i am just stopping here and concluding that [a] + [b] is not equal to 1

keeping statement 1 SUFFICIENT for now....



statement 2: 0we have a defined region where we can plug some values, it’s nice
a=1, b=1.5, [a]+[b] = 2
a=0.2, b=1.66, [a]+[b] = 1

sometimes yes sometimes no , not a sufficient statement



so option A ??

I think you are right

[b] DS Question 3 - Dec 10

If m, p, and t are positive integers and m
(1) t - p = p - m
(2) t - m = 16

Source: Official Guide | Difficulty: Medium

A

for mpt to be even any of the m,p,t should be even

statement 1:
rearrange and we find p=(t+m)/2
m+t is even so they both are either odd are even
we still have no identification of p being odd or even
say, m+t=12; p=6 even
m+t=6; p=3 odd

Not a sufficient statement

statement 2:

t-m=16
range of the three numbers is 16. hardly any solid fact to reach to the conclusion if
mpt=even; NOt sufficient


combine: (1)+(2)
2p=t+m
16=t-m

adding 2 eqn above
2p+16=2t
so, t=p+8
From statement we talked about m,t both should be odd or both even
if m is odd, t is odd; p is also odd from above derivation
if m is even. t is even; p is also even from above derivation

so mpt can be odd or even in some cases

still not suff

option E is ans ?

Statement 1 tells us that p is at the midpoint of t and m. If the three numbers are odd, the product will be odd. However, if the three numbers are even, the product will be even. Statement 1 is not sufficient.


Nice Approach !

An alternative way to tackle Statement 1 can be to visualize the entire problem in on number line and use the concept of distance.

The premise provides us with the relative position of m, p and t on a number line

--- m --- p --- t ---

Statement 1 provides an additional information regarding the position of p.

S1 and S2 are individually insufficient, even with the statements combined we can have a combination of all even numbers or all odd numbers.

IMO sometimes visualization helps avoid equations

PS Question 3 - Dec 10

What is the minimum possible value of 2x² - 2xy + y² - 2x + 3?

A) 0
B) 1
C) 2
D) 3
E) 4

Source: GMATPrepNow | Difficulty : Medium

Think its E

This is how I approached:
1) t+m=2p
let p=3
t+m=6
we can get two answers using the same equation
t is 5, m is 1 then not even.
t is 4, m is 2, even. NS
2) t-m=16
t is larger than m, and both are positive so t can take on really any value. T can be 17 and m can be 1, or t can be 18 and m can be 2 etc
3) we can make many combinations
let t be 17 and m be 1, p is 9. not even
let t be 18 and m be 2, p is 10. even

imo that question is one that is best approached by sensible numbers and keeping good track of your work so you don’t have to do extra calculations.

We want to min, so we should max negative terms and min positive ones:
Test y is 1 and x is 1, and we get 2. That is the middle value, so we should probably test more:
test y is 0 and x is 1. we get value 3
test y is 1 and x is 2, we get value over 2.
Clearly, we cannot reduce y anymore and increasing x increases the value.
C.

Neat question. There is probably a more elegant solution, but that is how I did it

Not sure if this is the best one, but I would probably write the equation as ⇒ (x-y)^2 + (x -1)^2 + 2 , the minimum value of the first two term is 0 (as squares are non negative). Hence C

This is much nicer than my brute force method haha.

Any update on the first question you posted today gmatophobia?

This one ?

DS Question 1 - Dec 11

If wxyz does not equal 0, is w/x > y/z?

(1) wz > xy

(2) xz > 0

Source: Kaplan | Difficulty: Hard

PS Question 1 - Dec 11

a, b and c are three interior angles of a triangle ABC. If a, b and c are three integers, then what is the number of possible values of a – b + c, which are less than zero ?

A.88
B.90
C.178
D.179
E.180

Source: e-GMAT | Difficulty: Hard

Is this really a hard Q? I solved in 45 seconds
Given: wxyz are nonzero
1)wz>xy
We have two cases here:
if z and y share the same sign, then we have
w/x>y/z
If z and x are opposite signs, then we have the flipped inequality. INS.
2) This tells us that xz share the same sign, but we know nothing about wy. INS.

3) we know from 1) that if they share the same sign, the condition is satisfied. 2) tells us they share teh same sign.
C.

rearranging question stem, it translates to: is (wz-xy)/xz > 0 ?

individual statements are are not sufficient.
combining both -

xz is > 0 from statement_2 so x,z has same sign
if we cross multiply (wz-xy)/xz > 0 we don’t have to flip sign
so we get - is (wz-xy) > 0 ?

statement_1 takes care of this query,

Hence, both statements together make sense

option C ?