We need more information, for example if they are referring to a Pentium 4 dual core at 3.2 ghz the answer is most definitely yes. (A Pentium 4 Dual Core at 3.2 ghz is about the same as a 2.0 Ghz Core 2 Duo, and some of those things the 2.0 ghz Core 2 Duo will be not the same speed but twice as fast as the Pentium 4).

The pentium 4 has a very low IPC. Core 2 has a very good IPC though some processors that are newer has an even better IPC

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But to break it down, forget about ghz, forget about cores we need to go to the basics. Each cpu core has some number called IPC (instructions per clock or instructions per cycle.) The IPC determines how much work the cpu is capable of doing.

Lets say processor A has an IPC of 10 at the speed of 1 ghz.

===== ===== 10 units

If you increased the processor speed to 2 ghz (and assuming the cpu is stable and properly fed enough information to calculate), its IPC still remains 10 units but it can perform 20 units of calculations (10 units per ghz* 2 ghz=20)

===== ===== ===== ===== 20 units

Now Processor B has an IPC of 8 units at the speed of 1 ghz.

+++++ +++ 8 units

If the processors were compared at the same frequency than processor A will always be faster than processor B, but if processor B has a ghz frequency of 3 ghz it and an ipc of 8 units per ghz than it can calculate 24 units

+++++ +++++ +++++ +++++ ++++ 24 units

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Now this is where it will get kinda confusing and very murky. Increasing the ghz speed after a certain point for the most part is very hardy to do since the heat the processor creates and the voltage required grows much faster than the increase in efficency per the work done via the cpu. To combat this many cpus have more than 1 core, (a dual core is simply 2 cpus on the same die of silicon, it has 2 brains, a quad core is 4 cpus on the same die, etc.)

In theory if your software is properly designed (or if you are running multiple software at once), if a single core version of the chip could do 20 units of work,than the quad core version could do up to 80 units of work. (Assuming the same generation of chip, with the same frequency, and large enough cache.)

The problem occurs because to use a quad core effectively, the software has to be able to break down the inherent question into 4 parts, these parts must not require use of knowing the answer to the other 3 parts (able to work independently). If the software can't do this due to the inherent design of the problem (or if the software wasn't coded correctly due to human design.) Than the software may not be able to use the quad core to the maximum design.

If the software can only be broken down into 2 equal parts, then there is little benefit in using the quad core part over the dual core part. If the software can be broken down into 3 parts then the quad core will be 50% faster than the dual core because the quad core can always pretend it is a triple core, the 4th core will sit there doing nothing which is called idling.

If the software can be broken down into 4 parts but these parts are unequal (2 very hard parts that require 5 units of work and 2 easy parts that require 1 units of work) than the quad core will be faster than the dual core but not much faster (see below.)

Assumming a quad core with IPC of 10 units and ghz speed of 2, vs a dual core with IPC of 10 units and a ghz speed of 2.

AAAAA AAAAA AAAAA AAAAA Core 1
BBBBB BBBBB BBBBB BBBBB Core 2
C==== C==== C==== C==== Core 3
D==== D==== D==== D==== Core 4

So the quad core could solve the math problem 4 times in that situation

vs

AAAAA CAAAA ACAAA AAAC Core 1
BBBBB DBBBB BDBBB BBBD Core 2

So the dual core could solve the math problem 3 times in that situation. That means the dual core in this situation is 50% more efficient than the quad core since the problem couldn't be broken down in equal enough parts to take advantage of the quad core.

....

etc

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So to get you a simple yes / no answer we need to know a few things.

1) What software are you running
2) What generation if the package tells you is the required cpu and at what ghz
3) What cpu are you looking at to see if your cpu meets the minimum requirements.